WO2025207151A2 - Photonic chip for interfacing trapped atoms with nanophotonic devices, and associated methods - Google Patents

Abstract

A photonic chip includes a substrate and several nanophotonic devices extending laterally away from an edge of the substrate. Each nanophotonic device is free-standing where it extends laterally past the edge of the substrate, with each neighboring pair of nanophotonic devices forming a gap therebetween. Atoms trapped in optical tweezers may be transported into the gap and close enough to a nanophotonic device that the atoms strongly couple to the nanophotonic device. Each nanophotonic device may include a waveguide, resonator, coupler, or a combination thereof. To excite modes of a nanophotonic device, a free-space optical beam may be coupled into a distal end of the nanophotonic device. A top face of each nanophotonic device may be reflective to create an optical lattice over the top face. An atom may then be trapped in the potential minimum of the optical lattice that is closest to the top face.

Description

PHOTONIC CHIP FOR INTERFACING TRAPPED ATOMS WITH

NANOPHOTONIC DEVICES, AND ASSOCIATED METHODS

RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63/546,620, filed October 31, 2023, and U.S. Provisional Patent Application No. 63/659,687, filed June 13, 2024. Each of these applications is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY

SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under grant numbers 2016136. 2138068, and 2238860 awarded by the National Science Foundation. The government has certain rights in the invention.

BACKGROUND

[0003] Arrays of neutral atoms trapped in optical tweezers are a leading platform for quantum information processing and quantum simulation due to their scalability, reconfigurable connectivity, and high-fidelity operations. Individual atoms are also promising candidates for quantum networking due to their capability to emit indistinguishable photons that are entangled with their internal atomic states.

SUMMARY

[0004] Integrating atom arrays with photonic interfaces can enable distributed architectures in which nodes hosting many processing qubits could be linked together via the distribution of remote entanglement. However, many atom-array techniques cease to work in close proximity to photonic interfaces, where atom detection via standard fluorescence imaging is challenging due to scattering of light off of nearby photonic devices, structures, and surfaces.

[0005] The present embodiments include a photonic chip that interfaces nanophotonic devices with atom arrays such that atoms of the atom arrays are strongly coupled to the nanophotonic devices. As described in more detail below, a millimeter-scale prototype of this photonic chip was used to experimentally combine atom arrays (with up to 64 optical tweezers) with more than 100 nanophotonic cavities hosted by the photonic chip. The atoms were rearranged into defect-free arrays, which were then loaded simultaneously onto the same nanophotonic device or multiple nanophotonic devices. The present embodiments also includes a method for coupling a free-space optical beam into and out of the nanophotonic devices.

[0006] The present embodiments also include a multichromatic excitation and detection technique that solves the problem of scattered light off of the photonic chip. This technique was implemented to perform high-fidelity (~99.2%), background-free imaging of atoms located only a few hundred nanometers above the dielectric surfaces of the nanophotonic cavities.

BRIEF DESCRIPTION OF THE FIGURES

[0007] FIG. 1 A is a perspective view of a photonic chip, in embodiments.

[0008] FIG. IB shows a platform for interfacing nanophotonic devices of the photonic chip of FIG. 1A with an atom array, in embodiments.

[0009] FIG. 1C is a plot showing reflection spectra of a nanophotonic cavity.

[0010] FIG. ID is a diagram of the energ -level structure of ¹³³Cs.

[0011] FIGS. 2A, 2B, 2C, and 2D illustrate background-free imaging of the atom array, in embodiments.

[0012] FIGS. 3A, 3B, 3C, and 3D illustrate imaging of atoms located on top of the nanophotonic devices, in embodiments.

[0013] FIGS. 4A, 4B, and 4C illustrate defect-free atom rearrangement and loading onto the nanophotonic devices, in embodiments.

[0014] FIGS. 5A and 5B are scanning electron microscope (SEM) images of the photonic chip of FIG. 1A.

[0015] FIGS. 6A, 6B, and 6C illustrate Stark shifts induced in ¹³³Cs atoms.

[0016] FIGS. 7A and 7B illustrate atom-lifetime measurements and atom-array imaging on the nanophotonic devices.

[0017] FIGS. 8A and 8B illustrate rearrangement and movement of trapped atoms in the atom array.

[0018] FIGS. 9A, 9B, and 9C illustrate free-space coupling of light into the nanophotonic devices, in embodiments.

[0019] FIG. 10 is a flowchart of a method for background-free imaging of one or more atoms, in embodiments. DETAILED DESCRIPTION

Introduction

[0020] Neutral atom arrays trapped in optical tweezers show promise as quantum information processors due to their characteristic scalability' [1, 2] and programmability with any-to-any connectivity [3, 4], High-fidelity’ entangling operations [5-7] and mid-circuit readout and feedback [8-11] have also been demonstrated in atom-array systems. Combining these systems with a photonic interface can further enhance their capabilities by enabling quantum communication [12], blind and distributed quantum computation [13-16], mid-circuit and faster readout techniques [17], distributed sensing [18, 19], as well as by extending the set of long-range interaction Hamiltonians that can be simulated [20-26],

[0021] Trapped atoms have been integrated with macroscopic Fabry-Perot cavities [27-30], fiber cavities [31], nanofiber-based waveguides [32-37], and nanophotonic waveguides and cavities [38-40], Among these, nanophotonic cavities and waveguides offer some of the highest atom-photon interaction strengths owing to their small mode volumes and high quality factors [41], Up to two atoms have been deterministically trapped on top of a nanophotonic cavity and entangled using cavity-carving techniques [41, 42],

[0022] Scaling systems that combine atoms with photonic interfaces, and that incorporate atom-array capabilities, is not straightforward. The presence of a dielectric structure can significantly impact the process of loading atoms into traps. While atoms have been cooled and loaded directly into traps in the vicinity of a single nanophotonic cavity' [40] or waveguide [32-37], the viability' of directly loading traps near a chip-scale structure has been undermined by unbalanced scattering and reflections from the dielectric surface. Techniques such as loading from an atomic fountain [43, 44] or a double magneto-optical trap (MOT) [38] have overcome this challenge near larger dielectric structures. Additionally, techniques such as stage-based transport of a tweezer array, an optical conveyor belt, and an optical funnel formed through a transparent dielectric structure have been employed to increase the trap filling fraction near chip-scale structures [45-49],

[0023] Fluorescence imaging of atoms in the vicinity and on top of nanophotonic devices presents another challenge due to scattering of the imaging beams from the device. Transmission and reflection measurements have been explored to estimate the number of atoms coupled to a device [32-38. 43. 44], enabling fast readout. However, these techniques only provide global system information rather than site-resolved atomic state information. To achieve the site-resolved, single-shot readout necessary for quantum information processing and networking, techniques such as confocal microscopy [41], exciting atoms through propagating waveguide modes [50]. and polarization filtering combined with spatial filtering [48] have been implemented. However, these techniques have been limited to either a few atoms, single devices, or specific device geometries. Demonstrating atom-array techniques, such as rearrangement and single-shot readout of large atom arrays near arbitrary nanophotonic devices, remains an outstanding challenge.

[0024] The present embodiments include an experimental platform for creating an atom array on a silicon chip hosting more than 100 silicon-nitride nanophotonic devices. The present embodiments also include a background-free imaging scheme to overcome scattering from the nearby chip. A semi-open chip geometry, where devices are suspended from the edge of the chip, provides sufficient laser cooling access to enable MOT formation near the chip structure. A free-space atom array can be loaded in the open space to the side of the chip. The chip has a minimal effect on the atom loading characteristics into the tweezers, with loading probabilities and temperatures similar to conventional atom-array experiments [ 1], Further, light can be coupled in or out of the nanophotonic devices via efficient free-space coupling, enabling fiber- free photon coupling to any devices inside the chamber [45. 52],

[0025] In some embodiments, a multichromatic imaging technique [53-56] suppresses the device scattering, enabling single-shot readout of the entire atom array close to, or even on top of, the nanophotonic devices. This technique may use an electron-multiplying charge- coupled device (EMCCD) camera similar to that used for the standard fluorescence imaging of free-space atom arrays. Combining the above capabilities, the atoms can be rearranged and “loaded” onto multiple nanophotonic devices at the same time or to a single nanophotonic device, where they can be imaged in a single shot using the present embodiments.

[0026] The techniques and methods presented herein represent a general recipe for integrating arrays of atoms with a wide range of nanophotonic structures, including alligator waveguides [38], corrugated cavities [57], or a more complex combination of one-dimensional (ID) cavities using a semi-open chip geometry, multichromatic fluorescence imaging, and a method for coupling light into and out of the nanophotonic devices. This platform combines the measurement and rearrangement capabilities of atom arrays with the ability to engineer the photonic environment via integrated cavities and waveguides, representing an enabling step towards multiplexed telecom quantum networking with resonant cavities [59, 60], fault- tolerant distributed quantum computing with Rydberg integration [61], and demonstrations of novel many-body phenomena in atom-waveguide systems, including self-organization of atoms and the generation of arbitrary photonic states [22, 24], Photonic Chip with Integrated Nanophotonic Devices

[0027] FIG. 1 A is a perspective view of a photonic chip 100, in accordance with some of the present embodiments. The photonic chip 100 includes a substrate 102 and a plurality of nanophotonic devices 110 that extend laterally away from an edge 108 of the substrate 102. Herein, the term “laterally” refers to the -x direction of a right-handed Cartesian coordinate system 120. The nanophotonic devices 110 extend laterally into a suspended region 122 that is adjacent to the substrate 102. Where each nanophotonic device 110 extends laterally past the edge 108, the nanophotonic device 110 is free-standing in the sense that no other material physically contacts the nanophotonic device 110 to mechanically support the nanophotonic device 110. Equivalently, each nanophotonic device 110 is “suspended” over the edge 108. Therefore, the nanophotonic devices 110 do not physically contact each other in the suspended region 122, nor does any other object or component (e.g., the substrate 102) physically contact the nanophotonic devices 110 in the suspended region 122.

[0028] Each nanophotonic device 110 has a proximal end 116 where the nanophotonic device 110 meets the edge 108 of the substrate 102 and a distal end 118 that is opposite the proximal end 116. Thus, each nanophotonic device 110 has a free-standing length /. as measured parallel to the x axis of the coordinate system 120, between the proximal end 116 and the distal end 118. Each nanophotonic device 110 has a width iv, as measured parallel to the y axis of the coordinate system 120, and a height , as measured parallel to the z axis of the coordinate system 120. In the example of FIG. 1A, the edge 108 is a straight edge that extends parallel to the y axis. Alternatively, the edge 108 may be curved edge. Alternatively, the edge 108 may be a piecewise combination of straight and curved edge segments.

[0029] Since the nanophotonic devices 110 are free-standing, neighboring pairs of the nanophotonic devices 110 form gaps 126 in the suspended region 122 that are devoid of solid material. For clarity in FIG. 1 A, only two of the gaps 126 are labeled. Each gap 126 has a gap size g. as measured parallel to the y axis. The gap size g is large enough for the waist of an optical -tweezers beam to fit within one of the gaps 126 with minimal clipping (e.g., see FIG. IB) of the optical-tweezers beam. Thus, the optical-tweezers beam may be used to trap an atom within the gap 126 with minimal scattering of light from the optical -tweezers beam off of the nearby pair of nanophotonic devices 110.

[0030] The gap size g of each gap 126 is typically in the range of 1-20 pm (e.g., 9.9 pm for the experimental demonstration described below). For a gap size g less than 1 pm, it may be challenging to focus an optical -tweezers beam tightly enough to fit within the gap 126. Thus, in some embodiments, the gap size is 1 pm or more. However, the gap size g may be less than

1 pm without departing from the scope hereof. Furthermore, while the example of FIG. 1A shows all the gaps 126 having the same value for the gap size g, some or all of the gaps 126 may alternatively have different values for the gap size g.

[0031] The free-standing length I of each nanophotonic device 110 is typically in the range of 10-100 pm (e.g., 63 pm for the experimental demonstration described below). In some embodiments, the free-standing length I is 5 pm or more. However, the free-standing length I may be less than 5 pm without departing from the scope hereof. Furthermore, while the example of FIG. 1A shows all the nanophotonic devices 110 having the same value for the free-standing length I. some or all of the nanophotonic devices 110 may alternatively have different values for the free-standing length I.

[0032] The width w of each nanophotonic device 110 is typically in the range of 0. 1- 5 pm (e.g., 1.1 pm for the experimental demonstration described below). In some embodiments, the width w is 3 pm or less. However, the width w may be more than 3 pm without departing from the scope hereof. Furthermore, wdiile the example of FIG. 1 A shows all the nanophotonic devices 110 having the same value for the width w, some or all of the nanophotonic devices 110 may alternatively have different values for the width w.

[0033] The height h of each nanophotonic device 110 is typically in the range of 0.1-

2 pm (e g., 0.33 pm for the experimental demonstration described below), which allows the nanophotonic device 110 to operate, at least in part, as an optical waveguide. In some embodiments, the height h is 2 pm or less. However, the height h may be greater than 2 pm without departing from the scope hereof. While FIG. I A shows all the nanophotonic devices 110 having the same value for the height h, some or all of the nanophotonic devices 110 may alternatively have different values for the height h. In some embodiments, the height h of one or more nanophotonic devices 110 is less than the width w. In other embodiments, the height h of one or more nanophotonic devices 110 is greater than the width w.

[0034] The substrate 102 has a substrate thickness t_s, as measured parallel to the z axis, that is ty pically in the range of 100-1000 pm (e.g., 600 pm for the experimental demonstration described below). However, the substrate thickness t_s may alternatively be less than 100 pm or greater than 1000 pm without departing from the scope hereof. The substrate 102 is composed of a substrate material, examples which include, but are not limited to, silicon (e.g., monocrystalline, amorphous, etc.), silicon dioxide (e.g., crystalline quartz, fused silica, etc.), aluminum oxide (e.g., crystalline sapphire, alumina, etc.), silicon carbide, silicon nitride, and glass (e.g., borosilicate, BK7, soda lime, etc.).

[0035] The photonic chip 100 may also include atop layer 104 formed on atop surface of the substrate 102 (i.e., the top surface faces the +z direction of the coordinate system 120). The top layer 104 has a top-layer thickness t_t, as measured parallel to the z axis, that is typically in the range of 100-1000 nm (e.g., 330 nm for the experimental demonstration described below). However, the top-layer thickness t_t may alternatively be less than 100 nm or greater than 1000 nm without departing from the scope hereof. The top layer 104 is composed of a top-layer material that is different from the substrate material. The top-layer material may be a dielectric material. Examples of the top-layer material include, but are not limited to, silicon dioxide, silicon carbide, silicon nitride, lithium niobate, gallium arsenide, and diamond.

[0036] In some embodiments, the nanophotonic devices 110 are part of the top layer 104. In this case, the height h of each nanophotonic device 110 may be the same as the top- layer thickness t_t. In these embodiments, the nanophotonic devices 110 may be formed by etching away portions of the top layer 104 and the underlying regions of the substrate 102. As show n in FIG. 1 A, the nanophotonic devices 110 may be undercut in the suspended region 122 such that no portion of the substrate 102 remains attached to the nanophotonic devices 110. In this case, a bottom surface of each nanophotonic device 110 (i.e., the surface of the nanophotonic device 110 that faces the -z direction) is co-planar with a bottom surface of the top layer 104 and the top surface of the substrate 102. Advantageously, undercutting the nanophotonic devices 110 reduces the height h. and therefore removes material that can scatter light out of the optical-tweezers beams passing through the gaps 126.

[0037] While the example of FIG. 1A shows the photonic chip 100 with eight nanophotonic devices 1 10 forming seven gaps 126, the photonic chip 100 may have a different number of nanophotonic devices 110 (and therefore a different number of gaps 126) without departing from the scope hereof. For example, the photonic chip 100 may have hundreds of nanophotonic devices 110, or more. Furthermore, while the example of FIG. 1A shows the eight nanophotonic devices 110 being uniformly spaced along the edge 108 such that the gap size g is the same for all of the gaps 126, the nanophotonic devices 110 may alternatively be non-uniformly spaced along the edge 108.

[0038] Each nanophotonic device 110 is a single photonic element or a combination of such photonic elements. Examples of these photonic elements include, but are not limited to. resonators, waveguides, filters, photonic cry stals (e.g., a distributed Bragg reflector), photonic metamaterials, mirrors, gratings, and optical couplers. For example, FIG. 1A shows each nanophotonic device 110 as a combination of a nanophotonic resonator 112 (also referred to as a nanophotonic cavity) and a tapered nanophotonic waveguide 114 that abuts one end of the nanophotonic resonator 112. The resonator 112 and waveguide 114 are “nanophotonic” in that the width w and height h are less than, or comparable to, the wavelength of light they contain. For many applications, the width w and height h are both strictly less than 1 pm. However, for applications where the nanophotonic devices 110 contain infrared light, it is possible for one or both of the width w and height h to equal or exceed 1 pm.

[0039] Each nanophotonic resonator 112 includes a linear sequence of elliptical holes, as shown in FIG. 1A. Each of these holes may be devoid of material (i.e., vacuum) or filled with a dielectric material that is different from the dielectric material forming the rest of the nanophotonic device 110. When the holes are filled, the nanophotonic resonator 112 is composed of at least two different materials. This example shows that it is not necessary' for each nanophotonic device 110 to be fabricated from only a single material.

[0040] At least one photonic element of each nanophotonic device 110 is an atomcoupling element that couples light contained therein to trapped atoms that are nearby. For this coupling to be sufficiently strong, the trapped atoms are ty pically located within a few microns of a surface of the atom-coupling element. For example, a free-space optical beam may be coupled into the distal end 118 of a nanophotonic device 110 to excite a propagating mode of the tapered nanophotonic waveguide 114. The tapered nanophotonic waveguide 114 guides this coupled light to the nanophotonic resonator 112, where it excites a resonant mode of the nanophotonic resonator 112. The tapering of the nanophotonic w aveguide 114 is configured to mode-match the guided light to the resonant mode of the nanophotonic resonator 112. As described in more detail below, trapped atoms may be located less than 1 pm away from a top surface of the nanophotonic resonator 112 to ensure sufficiently strong coupling to the resonator mode. In this example, the nanophotonic resonator 112 is the atom-coupling element while the tapered nanophotonic waveguide 114 is an ancillary' photonic element that does not directly couple to nearby trapped atoms. In other embodiments, trapped atoms may be located near a side wall of the nanophotonic resonator 112 (i.e., the side wall of the nanophotonic resonator 112 faces the +y or -y directions) to couple to the resonator mode.

[0041] In some embodiments, one or both of a top surface and a bottom surface of each nanophotonic device 110 is optically reflective. As described in more detail below, the reflection of a laser beam off one of these surfaces creates an optical lattice within which an atom can be trapped near the nanophotonic device 110. The surface may be partially reflective simply due to the step-change in refractive index introduced by the material forming the surface of the nanophotonic device 1 10 (i.e., the dielectric material of the top layer 104). Alternatively, a dielectric mirror coating may be deposited onto at least part of the surface. In this later case, the dielectric mirror coating serves as another photonic element making up the nanophotonic device 110. albeit one that does not operate with light contained within the nanophotonic device 110. This example demonstrates that one or more of the photonic elements of each nanophotonic device 1 10 may be used with light external to the nanophotonic device 110.

[0042] Due to the tapering, the width w is non-uniform (i.e., changes along x) in the region of the nanophotonic waveguide 114. By contrast, the width w is uniform (i.e.. does not change along x) in the region of the nanophotonic resonator 112. Thus, each nanophotonic device 110 in FIG. 1A is a combination of elements with uniform and non-uniform widths. Alternatively, the width w of one or more of the nanophotonic devices 110 may be uniform along the entire free-standing length I. One example of this case is where the tapered nanophotonic waveguide 114 is replaced by a non-tapered nanophotonic waveguide whose width w is the same as that of the nanophotonic resonator 112. In another alternative, the width w of one or more of the nanophotonic devices 110 is non-uniform along the entire free-standing length I. One example of this case is where the nanophotonic resonator 112 is tapered.

[0043] In the example of FIG. 1 A, the substrate 102 is rectangular in the x-y. However, the substrate 102 may alternatively have any shape, provided that it forms an edge from which the nanophotonic devices 110 extend laterally into the suspended region 122. Furthermore, the nanophotonic devices 110 in FIG. 1A span almost the entirety of the edge 108. Alternatively, the nanophotonic devices 110 may span only a portion of the edge 108. In other alternatives, one or more additional edges of the substrate 102 support additional nanophotonic devices that extend laterally away from the substrate 102. Thus, the photonic chip 100 may be only a portion of a larger chip that includes additional functionality for controlling and processing trapped atoms. For example, the photonic chip 100 may be part of a larger photonic integrated circuit (PIC) that includes additional on-chip optical components, electrical components, or both.

Experimental Results

[0044] FIG. IB shows a platform 190 for interfacing the photonic chip 100 of FIG. 1 A with an array of optical tweezers 180, in accordance with some of the present embodiments. The optical tweezers 180 were formed by a pair of crossed acousto-optic deflectors 170 and 172. Inside a vacuum chamber 160, the optical tweezers 180 were loaded with cesium (Cs) atoms less than 100 gm away from the photonic chip 100. Laterally, the substrate 102 of the photonic chip 100 measured 2 x 8 mm.

[0045] The photonic chip 100 used with the platform 190 hosted over 100 nanophotonic devices 110. For clarity⁷ in FIG. IB not all of the nanophotonic devices 110 are shown. Each nanophotonic device 110 included a nanophotonic cavity⁷ (e.g., see the nanophotonic resonator 112 of FIG. 1A) coupled to a tapered optical waveguide (e.g., see the nanophotonic waveguide 114 of FIG. 1A). However, the techniques and results presented herein are independent of the nanophotonic-device type and broadly⁷ apply to any kind of dielectric structure.

[0046] The nanophotonic devices 110 were fabricated from a 330-nm-thick layer of silicon nitride deposited on top of a silicon substrate, which is completely undercut from the device region (i.e., the suspended region 122 of FIG. 1A). This undercut configuration allows the optical -tweezer beams to pass by the photonic chip 100, even in close proximity' to the nanophotonic devices 110 (see “Supplementary Information"’ for more details). As shown in the inset 182 of FIG. IB, each nanophotonic device 110 had a free-standing length I of approximately 60 gm.

[0047] The nanophotonic devices 110 were characterized via a coupling lens 140 located outside the vacuum chamber 160. The coupling lens 140 w as used to focus a collimated optical beam 144 into focused optical beam 142 having a diffraction-limited spot that was mode-matched to the end mode of the tapered waveguide appended to each nanophotonic cavity [45, 52], The coupling efficiency 'as measured to be 20% and simulations show⁷ that up to 91% is possible (see “Supplementary Information” for more details).

[0048] Atoms were cooled with a MOT. Cold atoms were then loaded into the optical tweezers 180 during polarization gradient cooling (PGC) in a loading region tens of microns from the nanophotonic devices 110 (see FIG. 2B). The optical beams used to form the MOT and image the atoms w ere partially reflected by the photonic chip 100 and the nanophotonic devices 110, rendering the standard fluorescence imaging technique of driving the 852 nm cycling (D2) transition impractical as the scattering from the surface of the solid structure is many orders of magnitude more intense than the atomic fluorescence. The scale of this problem is demonstrated in FIG. 2A, w'here even away from the devices, in the loading region, this scattering leads to signals on the order of hundreds to thousands of photons per pixel, compared to atomic signals which are typically on the order of ~1.6 photons per pixel (25 photons detected within a 4x4 pixel region of interest). Near the region of the nanophotonic devices 110, several pixels detected more than 350,000 photons. At higher EM gain settings necessary for imaging single atoms, scattered light of this magnitude would damage the camera sensor.

[0049] A background-free imaging technique was used to circumvent this scattering. With this technique, a two-photon transition is driven to excite each atom to an excited state (here the 7S1/2 state), which has two decay pathways (see FIG. ID). Scattered light at the excitation wavelengths is spectrally fdtered. What is imaged is fluorescence emitted by the atoms when decaying along the other decay path at 895 nm. With this technique, the unwanted background (due to the scattering from the nanophotonic devices) is filtered and high detection fidelities can be achieved (see FIG. 2C). FIG. 2B shows an averaged fluorescence images of the atom array, both away from the nanophotonic devices 110 in the loading region (FIG. 2B, inset) and with the atoms interleaved between the nanophotonic devices 110 (FIG. 2B, main). The histogram in the inset of FIG. 2B. FIG. 2C is a typical histogram of the signal received from a single site (taken from the inset of FIG. 2B); this histogram shows the ability to discriminate with high fidelity between the presence and absence of an atom. An imaging fidelity of 99.2% was inferred by fitting the bimodal histogram and examining the overlap of the signal and the background, similar to typical fidelities obtained via D2 line fluorescence imaging [8], Here, a 40-ms exposure time was used, also comparable to the timescale of standard fluorescence imaging [51], making this technique applicable to a wide range of experimental setups that suffer from background light.

[0050] In FIG. 2D. the magnitude of the fluorescence signal detected from the atoms is plotted versus detunings of the two drive lasers. The 852-nm-laser detuning on the x-axis is measured with respect to the bare 68^2 F=4 -> 6P₃/₂ F'=5 transition frequency and the 1470- nm-laser detuning on the y-axis is measured with respect to the bare 6P_3/2 F'=5 7S_1/2 F"=4 transition frequency. The detected signal falls off as the 852-nm detuning approaches the 6Siy₂ F=4 -> 6P₃/₂ F'=5 transition frequency on the right side of the plot and when it approaches the 6S1/2 F=4 -» 0P₃/₂ F'=4 transition frequency (-251 MHz on the x-axis) on the left side of the plot. This fall-off in signal is attributed to atom loss from the tweezer due to resonant heating. The optimal point is far from a ground-state resonance, where cycling on the lower transition is suppressed and the two-photon excitation to the doubly excited state is the dominant process. The overall feature is blue-shifted from the bare two-photon resonance by tens of MHz due to the AC Stark shift induced by the tweezer.

[0051] Another important capability for nanophotonic integration is the ability to move atoms onto the photonic chip 100 in close enough proximity to couple the atoms to the light field of the nanophotonic devices 110. This capability can be achieved by adiabatically translating the optical tweezers, after they are loaded with individual atoms, away from the loading region until they are located directly over the top surfaces of the nanophotonic devices 110, where the tweezer beams partially retroreflect to form standing-wave traps whose potential minima (i.e., intensity⁷ maxima) are located above the nanophotonic devices 110, as shown in FIG. 3B. FIG. 3A shows an averaged image of the atoms loaded on top of the nanophotonic devices 110, overlaid with an image of the nanophotonic devices 110 (see “Experimental Techniques” for image processing details). The goal is to load the atoms into the closest intensity' maximum —300 nm from the surface of the silicon nitride, where the atoms can strongly couple to the cavity⁷ mode. The distance between the closest intensity maximum and the surface is set by⁷ a combination of the tweezer wavelength and the thickness of the device. This standing wave trap has an intensity approximately twice the intensity of the tweezer in free space. To determine whether the atom is loaded into the standing-wave trap, the AC Stark shift experienced by the atom is probed on the 68-^2 F=3 -> 6P_1/f2 F'=4 (Di) transition at 895 nm. This AC Stark shift, which is proportional to the intensity of the standingwave trap, is then compared to the Stark shift the atom experiences in the free-space tweezer. This specific transition is probed because the optical-tweezer wavelength of 2=935 nm is magic for the 6S_1/2 -» 6P_3/2 transition, meaning that the AC Stark shifts induced on the 6S_1/2 and 6P₃/₂ levels are equal in both sign and magnitude, rendering it insensitive to the intensity variation between the trapping potentials.

[0052] This Stark-shift measurement begin by loading the tweezers with atoms in the loading region, moving the tweezers between the nanophotonic devices 110 (i.e., into the gaps 126 of FIG. 1A), and then moving the tweezers onto the nanophotonic devices 110 from the side. A variable-frequency 895-nm laser pulse is then applied to blow out the atoms from the tweezer when the pulse is resonant with the Stark-shifted atomic transition. Finally, the atoms are imaged to detect the survival rate. FIG. 3C is a plot of typical blow-out survival curves that shows the increased Stark shift when the atoms are loaded onto the nanophotonic devices 110. FIG. 3D is a plot of the fitted centers of the blow-out survival curves as a function of y position (in pm) across the device region. The plot of FIG. 3D shows that the observed increase in the Stark shift only occurs when atoms are directly on top of the nanophotonic devices 110 and when they are trapped in the higher-intensity⁷ standing-wave potential shown in FIG. 3B. From the observed Stark shifts and blow-out curves of the individual atoms, modeling indicates varying loading probabilities across the nanophotonic devices 110, with a maximum loading probability of 29% into the first intensity maximum (see “Supplementary' Information” for details). The tweezer power, aberrations, and the angle between the devices and the tweezer focal plane contribute to the variations in the observed Stark shifts and loading probabilities across the devices; these parameters could be further optimized in future experiments.

[0053] To fully integrate atom arrays with nanophotonics, the atoms may be rearranged into defect-free arrays, after which these defect-free arrays may be loaded onto the nanophotonic devices 110. To perform this rearranging, an image of the initial random loading (25 ms) is taken. This image is rapidly processed (~7 ps) to obtain an occupation matrix which is then used to drop the unoccupied tweezers (i.e., turn off the laser beam for each occupied tweezer) and compress the remaining atoms into a defect-free array. The resulting-defect arrays are then translated to the nanophotonic devices 110 (see “Experimental Techniques” for details). FIG. 4A shows the experimental sequence for this procedure.

[0054] The final step of this procedure may be performed either by loading one atom per nanophotonic device or by loading multiple atoms to a single nanophotonic device. Both capabilities are demonstrated in FIGS. 4A-4C by showing initial images of the randomly loaded atoms in free-space tweezers next to a second image of the same atoms postrearrangement and loaded onto the nanophotonic devices 110 in each configuration, one atom per nanophotonic device (FIG. 4B) and three atoms on a single nanophotonic device (FIG. 4C). FIGS. 4B and 4C also show averaged post-rearrangement images for 15,000 stochastic loading and rearranging events in each configuration, where seven to eight atoms can be seen in each of the post-rearrangement averaged images from the nine initial loading sites.

Discussion

[0055] The platform 190 of FIG. IB advantageously combines atom arrays with an integrated chip hosting many nanophotonic devices, allowing large arrays of atoms to be loaded near the chip. Using the background-free imaging technique of the present embodiments, these atoms can be imaged with fidelities greater than 99.2%. This capability enables loading and imaging of atoms on top of the nanophotonic cavities, from which information about the Stark shift was extracted to demonstrate atom loading into the first few intensity maxima on top of the nanophotonic devices 110. With further optimizations of atomic temperature, tweezer parameters during loading, and device parameters, atoms can be deterministically loaded into the intensity maximum of interest [40], The rate of deterministic placement of atoms in FIGS. 4A-4C is currently limited by atom survival through the first image, probability of successful loading to the nanophotonic device, and survival during imaging on top of the nanophotonic devices. A small angle between the device plane and the tweezer plane also causes variation in the loading distribution to the various intensity’ maxima across the devices, as this distribution is highly sensitive to the relative z position of the device and the tweezer focus. Improved device alignment and techniques, such as stroboscopic imaging or Raman- sideband cooling of the atoms, may be used to further improve these metrics.

[0056] The devices presented in this work are nanophotonic cavities embedded in waveguides. Currently, the cavities are not resonant with the atomic transition, preventing direct atom-cavity interactions. In future work, tighter fabrication tolerances and thermal tuning can be incorporated to bring devices on resonance and to stabilize them to the atomic transition [62], The atom trapping distance of ~300 nm measured in this work is expected to give an atom-cavity interaction strength of 2a X 600 MHz [59], similar to other ID photonic cavities [41], These interaction strengths are two orders of magnitude larger than what is typically observed in mirror cavities [63] and an order of magnitude larger than fiber cavities [31], Along with increased interaction strengths, photonic cavities also have the highest photon loss rates from the cavities, making them suitable for fast photon extraction. In future work, these cavities can be utilized to entangle a subsection of the atoms with photons enabling multiplexed entanglement generation [59, 60], Furthermore, with the inherent rearrangement capability in the system, atoms can be moved sufficiently far away from the device for Rydberg-mediated gates [64], Incorporating these capabilities would enable quantum simulation and computation while preserving the ability' to distribute remote entanglement, providing a path towards multiplexed quantum repeaters and fault-tolerant distributed quantum computation [61],

[0057] Furthermore, the semi-open geometry of the photonic chip 100 of FIG. 1A is flexible and can be tailored towards many potential applications and a wide variety of nanophotonic structures. Alternative techniques for coupling light to the nanophotonics, such as grating couplers or tapered optical fibers via the chip surface, could be explored for possible applications where the ejected mode cannot overlap the free-space array. Overhanging nanobeams can be extended to loading tracks fabricated on the chip surface to provide atomic access to more complicated nanophotonic devices and circuits that cannot overhang the edge 108 [65], Waveguides for quantum simulation and cavities for atom-photon entanglement can be incorporated into the same photonic chip for distributed quantum simulation. Currently, the majority of the chip surface is not utilized, enabling further opportunities, such as the integration of beam splitters, modulators, and detectors directly on the photonic chip. Experimental Techniques

[0058] Platform Details

[0059] The experiment starts with ~ 170 ms of MOT loading to maintain a 1 : 1.5 MOT on/MOT off ratio in the experiment cycles (see '‘Supplementary Information’’). The atoms are sourced from a heated dispenser in the same chamber located ~5 cm from the MOT position. This is followed by 10 ms of polarization gradient cooling (PGC), during which atoms are stochastically loaded into the tweezers. A 55% loading efficiency into the tweezer array was observed, as well as atomic temperatures of approximately 50 pK. The six -beam MOT is formed by two retro-refl ected MOT beams in the plane of the photonic chip, a MOT beam sent through the tweezer objective, and a counter-propagating MOT beam sent though another objective located on the opposite side of the chamber. A home-built ECDL laser at 935 nm. and amplified using a tapered amplifier (MOGLabs MO A), is used to form the optical -tweezer array. The RF frequencies that drive the AODs (AA Opto-Electronic) are generated using an AWG for 8x8 array of tweezers and an FPGA for 1 x9 and 9x 1 arrays (Quantum Machines, OPX). A custom. high-NA objective (Special Optics 0.6 NA) is used to focus the tweezers into the vacuum chamber. Atomic fluorescence at the imaging wavelength is collected using the same objective and imaged onto an EMCCD camera (NuVii FINu 512 Gamma). For rearrangement, fast detection and feedback directly to the OPX was performed using an intermediate module that processes the camera images into occupation matrices and communicates that information to the OPX in real time (Observe camera readout module, Quantum Machines).

[0060] Device Fabrication

[0061] The nanophotonic chip is made from a 330-nm-thick layer of stoichiometric LPCVD-grown silicon nitride (Si₃N₄) on top of a 600 pm thick silicon substrate (Silicon Valley Microelectronics). The nanophotonic devices are 1.1 pm wide and 63 pm long and are repeated every 11 pm. The cavity design, electron-beam lithography (EBL), and reactive-ion etching (RIE) steps are carried out at the Center for Nanoscale Materials at Argonne National Laboratory, and the remaining processes and design are carried out in the Pritzker Nanofabrication Facility at the University of Chicago. The details of the fabrication are provided in the section below titled “Supplementary’ Information.”

[0062] Image Processing

[0063] For the single-shot images labelled Image 1 and Image 2 in FIGS. 4B and 4C, the two single-shot atom images are first plotted. Then, a semitransparent image of the devices is plotted over the two single-shot atom images to show the nanophotonic-device locations without obscuring the raw atom image data underneath. For FIG. 3A, FIG. 4B Image 2 Average, and FIG. 4C Image 2 Average, the background-subtracted atom image is scaled and added to the device image. A small offset is added before scaling to avoid any negative signals. This sum then forms the final plot shown.

Supplementary Information

[0064] Device Fabrication

[0065] The nanophotonic devices on the silicon nitride layer are patterned using conventional electron-beam lithography (EBL) with aZEP 520 A resist etch mask, followed by CHF₃/O₂ inductively coupled reactive-ion etching (RIE). Once the devices are patterned, the chip region of 2 X 8 mm around the devices is defined using photolithography with a AZ4620 resist etch mask. This is followed by deep reactive-ion etching (DRIE) and dicing to isolate the chip region. After protecting the silicon-nitride device side using a double layer PMMA mask, a final KOH etching step is performed to undercut the silicon from the device region by etching from the sides. The undercut devices are shown in FIGS. 5A and 5B.

[0066] Loading Atoms onto Devices

[0067] The atoms are loaded in the ‘‘loading region” (as marked in FIG. 2B) and then translated along the X-direction until they are in between the devices. At this position, the Stark shift from the tweezer is similar to that of a free-space tw eezer, as depicted in FIG. 6A. From here, atoms are loaded onto the devices by performing a Y -direction move, with a speed of 6 pm/ms. As the tw eezer approaches the device, the partial reflection of the tw eezer from the surface interferes with the incident beam causing a lattice to form, where each intensity maximum can trap atoms. The corresponding modified Stark shift on the atoms is shown in FIG. 6B. The proportion of atoms that load into various intensity maxima is optimized by adjusting the focal plane of the tw eezer with respect to the device position. Previous work has shown up to 94% loading efficiency into the closest intensity maximum of the standing wave potential, and Monte Carlo simulations show that up to 100% loading efficiency can be achieved [40, 45], For the device thickness of 330 nm used in this work, the maximum loading efficiency to the first intensity maximum from Monte Carlo simulations is ~40%. This loading efficiency is a function of the device thickness, atomic temperature, tweezer trap depth, angle of the devices with respect to the tweezer plane, and the adiabaticity of the tweezer movement while loading onto the devices. These further cause variations of loading probability into different pancakes across the array as seen in FIG. 3B. Further optimizations of these parameters can improve the loading efficiency. By performing Monte Carlo simulations of the Stark shifts experienced by the atoms in the various intensity maxima on top of the devices, the proportion of atoms loaded into each of the intensity maxima can be estimated. The dashed lines in FIG. 6B show the estimated Stark shifts experienced by atoms loaded into the three intensity maxima closest to the device surface (zl-z3). For the given atom, the blowout curves probing the Stark shift on the nanophotonic devices are fitted assuming random sampling from these three curves to obtain the best-fit estimate of the loading distribution of 29% into the intensity maximum closest to the device, 66% into the second intensity maximum, and 5% into the third intensity maximum. The achievable detunings for the Stark-shift measurements are currently limited by AOM bandwidth.

[0068] Tweezer Objective Z Positioning and MOT Coil Stabilization

[0069] The process of loading atoms onto the nanophotonic devices from free space is sensitive to the focal plane of the tweezers relative to the plane of the nanophotonic devices. To control the z position of the objective, the objective is mounted on a translation stage. A piezoelectric screw actuates this translation stage to move the objective forwards and backward, thereby varying the focal plane of the tweezers.

[0070] To optimize the position of the objective, the tweezers are blocked with a sliding optics mount holding a 900 nm LED, which is turned on to illuminate the photonic chip through the tweezer objective and image the photonic chip with the EMCCD. A focal score is then assigned to the image. The focal score is calculated by first applying a bilateral filter to the image to reduce the noise. Then the Laplacian of the filtered image is calculated to give a numeric value that is proportional to the contrast in the image. This numeric value is maximized when the image is in focus.

[0071] In general, the best loading results do not occur at the exact image focus. Thus, the focus is scanned to establish the maximum score and target a focus score relative to the measured maximum in order to counteract long timescale drift in the LED output power. A subsection of the image is chosen to target different planes due to the small relative angle between the chip and the objective.

[0072] During the course of the experiment, the variation in the focal score is monitored to ensure the stability of the Z-position reference. The focal position originally shifted by a few microns over the course of a couple of hours. The source of this variation was found to be the temperature gradient generated by the MOT coils during the experiment run time. To mitigate this problem, the temperature around the coils and the objective region was stabilized by maintaining a constant MOT on-off ratio during experiment cycles. When the experiment is not running, the MOT coil currents are maintained to have the same effective heat output as running the experiment at the controlled duty cycle. With this careful temperature control in the vicinity of the objective and its translation stage, stability of the / position for up to 24 hours can be achieved with less than 300-nm variation.

[0073] Atomic Lifetime and Imaging On Devices

[0074] To characterize the atomic lifetime in the tweezers, atoms are loaded in the tweezers and held for a variable amount of time before imaging. FIG. 7A is a plot of the corresponding probability to detect the atom versus the tweezer hold time. From the fits, an atomic lifetime of 13.6 s is estimated in the loading region and 0.78 s when trapped in the standing-wave traps on top of the nanophotonic devices. Reduction in the atomic lifetime in the standing-wave traps on nanophotonic devices is consistent with the earlier observations of atoms trapped on top of nanophotonic devices [41], and is expected from thermally excited phononic modes of the devices [66], This lifetime is, however, sufficiently large compared to observed coherence times on top of the devices of —2 ms [42], atom rearrangement times of -100 ps. and the required atom-cavity interaction time for entangled photon generation of ~100 ns [59], Before the installation of the chip inside the chamber, atomic lifetimes in excess of 60 s in free-space optical tweezers were observed, indicating a finite reduction in the lifetime with the chip placement and the associated increase in the atomic flux required to create the MOT in the presence of the chip. While imaging fidelities in excess of 99% are routinely obtained for atoms in the loading region, the imaging fidelity on the devices is reduced. An imaging histogram for an atom trapped on the device is shown in FIG. 7B, demonstrating an imaging fidelity⁷ of 86% and approaching the state-of-the-art value of -95% obtained in [50], While the background is comparable to that of atoms in the loading region, the atomic signal is shifted to lower photon numbers. This is due to an increased atomic loss during the imaging due to the modified trapping potential. This can be further optimized in future experiments by optimizing the tweezer power, imaging laser powers, and detunings. Additional techniques, such as employing Raman sideband cooling to achieve lower atomic temperatures or imaging with lower drive power for longer timescales [50], can improve this measurement.

[0075] Rearrangement

[0076] Loading atoms into the optical tweezer array is a stochastic process with a 55% loading probability. For deterministic placement of these atoms in a specific order onto a device or multiple devices, the stochastic loading pattern must be identified and moved to the target locations. This is achieved in a two-step process. In the first step, the tweezers that were originally loaded with atoms are identified. These identified tweezers are rearranged into a defect-free configuration. In the second step, the defect-free array is moved to the target location. To achieve a defect-free configuration of atoms, an image of the stochastically loaded array is taken to determine which tweezers have atoms. Tweezers that do not contain atoms are dropped. Following this, the remaining AOD frequencies that form the optical tweezers are chirped to compress the fully filled array into a defect-free configuration. This compression move occurs in 1 ms following a symmetric, piecewise, quadratic-frequency-chirp profile. Points in FIG. 8A show the probability of stochastically loading each tweezer index. Other points in FIG. 8A show the probability of detecting an atom at each tweezer site following the initial detection and rearrangement. A finite atomic loss during the first image and the losses due to the rearrangement result in non- unity atom probability after rearrangement. Around 10- 15% of the atoms are lost after the first round of imaging, resulting in a corresponding reduction of atomic probability in the second image. A curve in FIG. 8A shows the probability to detect atoms at each site after rearrangement, correcting for the site-specific atomic loss during imaging. The remaining 23% atomic loss stems from the losses during rearrangement. The power imbalance between the tweezers during the process of rearrangement and specific frequency chirp profile can cause atoms to heat out of these traps during the first step. The imaging loss can be reduced by stroboscopic imaging and the rearrangement losses can be reduced by further characterization and optimization of the tweezer power, phase, chirp profiles, and trajectories enabling near unity rearrangement efficiencies.

[0077] After the first step of creating a defect-free array, atoms are then moved close to the target device by translation along x. This is followed by an adiabatic translation along y onto the devices. FIG. 8B shows the combined step-l-and-step-2 trajectory of atoms. The left image in FIG. 8B shows the initial detection of the stochastically loaded atoms and their calculated trajectories. The right image in FIG. 8B shows the same atoms loaded on top of the device following the marked trajectories.

[0078] Free-Space Coupling

[0079] Efficient free-space coupling can be achieved by designing the mode supported by the waveguide taper end to match that of a diffraction-limited spot created by a lens having a relatively low numerical aperture (NA), as shown in FIG. 9A. Experimentally, an aspheric lens with a 40-mm focal length was used outside the chamber to couple light into and out of the waveguides with a y-polarized input beam (i.e., the collimated optical beam 144 of FIG. IB). As shown in FIG. 9B, this coupling excites the second TE mode supported by the end of the taper. The linear, adiabatic taper then converts this mode into the mode supported by the cavity. With this particular aspheric lens, a coupling efficiency of 20% was measured.

[0080] Using a finite-difference time-domain (FDTD) calculation, Gaussian beams generated by coupling lenses of various NA were injected into waveguides of varying widths to estimate the power distribution across the waveguide modes. From these calculations, a coupling efficiency up to 91% can be achieved using the free-space coupling technique described herein. As shown in FIG. 9C, the waveguide taper end width and the NA of the coupling lens are two important factors that determine the coupling efficiency.

[0081] Experimentally, coupling efficiencies up to 60% have been achieved for coupling performed outside the vacuum chamber. However, limited optical access restricted the types of lenses and objectives that could be used for coupling the light beams. The external lens was mounted on a piezo-controlled stage that allow for coupling to any of the nanophotonic devices 110 outside the vacuum chamber. A fiber array or array of AODs [67] could also be used to read out or probe several of the nanophotonic devices 110 at the same time.

[0082] In embodiments, a method for free-space coupling includes coupling light into a nanophotonic device that is one of the plurality of nanophotonic devices of a photonic chip. The nanophotonic device includes a nanophotonic waveguide having (i) a proximal end joined to the substrate of the photonic chip and (ii) a distal end opposite the proximal end. The nanophotonic waveguide guides the coupled light from the distal end toward the proximal end. In one example of these embodiments, FIG. I B shows the focused optical beam 142 being coupled into the distal end 118 of a nanophotonic waveguide 114 that forms part of a nanophotonic device 110 (also see FIG. 1A). The nanophotonic device 110 is one of several nanophotonic devices 110 extending laterally away from the edge 108 of the photonic chip 100.

[0083] In some embodiments, the method for free-space coupling further includes focusing a free-space optical beam to generate a focused optical beam. In this case, said coupling light includes coupling the focused optical beam into the nanophotonic device. In one example of these embodiments, FIG. IB shows the coupling lens 140 focusing the collimated optical beam 144 to produce the focused optical beam 142.

[0084] In some embodiments of the method for free-space coupling, the photonic chip is located inside a vacuum chamber while the lens is located outside the vacuum chamber. In one example of these embodiments. FIG. IB shows the photonic chip 100 located inside the vacuum chamber 160 while the coupling lens 140 is located outside the vacuum chamber 160. In other embodiments, both the photonic chip and the lens are located inside the vacuum chamber.

[0085] In some embodiments of the method for free-space coupling, the lens has a numerical aperture of 0.5 or less. For example, the coupling lens 140 of FIG. 1A may have a NA of 0.17, as described above.

[0086] In some embodiments, the method for free-space coupling further includes translating the lens parallel to the edge of the substrate to couple the focused optical beam into a second nanophotonic device that is another one of the plurality of nanophotonic devices. The second nanophotonic device includes a second nanophotonic waveguide having (i) a second proximal end joined to the substrate of the photonic chip and (ii) a second distal end opposite the second proximal end. The second nanophotonic waveguide guides the focused optical beam, as coupled into the second nanophotonic waveguide, from the second distal end toward the second proximal end. In one example of these embodiments, the coupling lens 140 of FIG. IB may be translated parallel to the y axis to couple the focused optical beam 142 from a first nanophotonic device 110 to a second nanophotonic device 110.

[0087] In some embodiments of the method for free-space coupling, the nanophotonic waveguide includes a tapered waveguide. The tapered waveguide may be linearly tapered. For example, FIG. 1 A shows each of the nanophotonic devices 110 having a tapered nanophotonic waveguide 114. In other embodiments, the nanophotonic waveguide is not tapered.

[0088] In some embodiments of the method for free-space coupling, the coupling excites at least a second transverse electric (TE) mode of the nanophotonic waveguide. FIG. 9B shows one example of a second TE mode supported by the waveguide taper end (i.e., the tapered nanophotonic waveguide 114 of FIG. 1A). In general, the coupling may excite additional or alternative modes of the nanophotonic waveguide (e.g., a first TE mode, a combination of the first and second TE modes, etc.).

[0089] In some embodiments of the method for free-space coupling, the nanophotonic device further includes a nanophotonic resonator abutting the nanophotonic waveguide. The nanophotonic waveguide guides the coupled light from the distal end toward the proximal end such that the coupled light excites a mode of the nanophotonic waveguide. In one example of these embodiments, FIG. 1A shows how each nanophotonic device 110 includes a nanophotonic resonator 112 that abuts a tapered nanophotonic waveguide 114. Background-Free Imaging

[0090] FIG. 10 is a flowchart of a method 1000 for background-free imaging of one or more atoms. The method 1000 is particularly advantageous for imaging atoms that are trapped near a dielectric structure. When driving a cycling transition in the atoms with a laser beam, the atoms will emit atomic fluorescence at a wavelength that is nearly the same as that of the laser beam. The dielectric structure will significantly scatter light from the laser beam. This scattered light frequently exceeds the fluorescence emitted by the atoms themselves, which in turn makes it difficult to “see” the atoms amongst so much scattered light. The method 1000 solves this problem by detecting atomic fluorescence at a wavelength that is significantly different from that of the excitation, which allows scattered light from the dielectric structure to be spectrally filtered without spectrally filtering the atomic fluorescence.

[0091] One example of the method 1000 is described above in the section titled “Experimental Results.” Here, the method 1000 was performed with an array of cold ¹³³Cs atoms that were optically trapped within the gaps 126 of the photonic chip 100 (e.g., see FIG. IB). More generally, the method 1000 be implemented with atoms of any alkali-metal species (e.g., Rb, K, Na. etc.), alkaline-earth-metal species (e.g., Sr, Ca, etc.), lanthanide species (e.g., Yb, Ho, Dy, etc.), or other atomic species that can be cooled and trapped. The atoms may be neutral or ionic. While the method 1000 is described herein as a method for imaging atoms, the method 1000 may also be used to image molecules. Furthermore, while the experimental demonstration described above was performed with trapped atoms, the method 1000 may also be performed with untrapped atoms (or molecules).

[0092] In some embodiments, the method 1000 begins with the step 1004, in which an atom is illuminated with first and second excitation laser beams having first and second excitation wavelengths, respectively. The first and second excitation laser beams drive a two- photon transition in the atom to transfer the atom from a ground state to an excited state. The atom then spontaneously decays via one of two decay paths. In the first decay path, the atom decays from the excited state to a first intermediate state by emitting a first photon at a first transition wavelength. The atom them subsequently decays from the first intermediate state to the ground state by emitting a second photon at a second transition w avelength. In the second decay path, the atom decays from the excited state to a second intermediate state by emitting a third photon at a third transition wavelength that is different from the first and second excitation wavelengths. The atom then subsequently decays from the second intermediate state to the ground state by emitting a fourth photon at a fourth transition wavelength that is different from the first and second excitation wavelengths. [0093] In one example of the step 1004, a ^kl3Cs atom is driven from the 68-^2 ground state to the 7S_1/2 excited state via a virtual state that is detuned from the 6P_3/2 intermediate state (see FIG. ID). In this case, the first and second excitation wavelengths are near 1470 and 852 nm, respectively. For the first decay path, the ¹³³Cs atom emits a photon at the first transition wavelength of 1470 nm when decaying from the 7S_1/2 excited state to the 6P_3/2 intermediate state. The ¹³³Cs atom then subsequently emits a photon at the second transition wavelength of 852 nm when decaying from the 6P₃/₂ intermediate state to the OS^ ground state. For the second decay path, the ¹³³Cs atom emits a photon at the third transition wavelength of 1359 nm when decaying from the 78^ excited state to the 6P_1/f2 intermediate state. The ¹³³Cs atom then subsequently emits a photon at the fourth transition wavelength of 895 nm when decaying from the 6P_1/2 intermediate state to the 6S_1/2 ground state.

[0094] In step 1006 of the method 1000, signal light is detected with a photodetector. The signal light includes one or both of the third photon and the fourth photon. In one example of the step 1006. a 895-nm photon emitted by a ¹³³Cs atom is detected when the ¹³³Cs atom decays from the 6P_1/2 intermediate state to the 6S_1/2 ground state. Alternatively or additionally, a 1359-nm photon emitted by the ¹³³Cs atom is detected when the ¹³³Cs atom decays from the 7S_1/2 excited state to the 6P_1/2 intermediate state.

[0095] The photodetector may be a single-element detector, such as a pin photodetector, avalanche photodetector, photomultiplier tube, or silicon photomultiplier. Alternatively, the photodetector may be one or more pixels of a camera, such as an electronmultiplying charge-coupled device (EMCCD) camera. FIG. IB shows one example of an EMCCD camera detecting atomic fluorescence at 895 nm from ¹³³Cs atoms that have been driven, via two-photon excitation, to the 78^ excited state.

[0096] In step 1008 of the method 1000, background light is spectrally filtered such that the photodetector does not detect the background light. The background light includes scattered light from one or both of the first and second excitation laser beams. The scattered light may arise from scattering of the excitation laser beams off of the photonic chip 100 of FIG. 1A (e.g., off of the nanophotonic devices 110, the substrate 102, or both). In some embodiments, the background light is spectrally filtered with an optical filter (e.g., an interference filter) located in front of the photodetector. In one example of these embodiments, an optical filter 152 placed in front of the EMCCD camera 150 (e.g., see FIG. IB) filters background light at 852 nm while allowing atomic fluorescence at 895 nm to reach the EMCCD camera 150. [0097] In some embodiments, the method 1000 further includes the step 1002, in which the atom is trapped. The atom may be optically trapped, such as in an optical-tweezers beam or an optical lattice (e.g., an optical lattice at the magic wavelength of the atomic species trapped therein). The atom may be trapped during the steps 1004, 1006, and 1008. In this case, the atom is imaged while it is trapped. Alternatively, the trapped atom may be released from its trap prior to the steps 1004, 1006, 1008. In this case, the atom is imaged while it is in freefall.

[0098] In some embodiments, the method 1000 continuously performs the step 1004 to re-excite the atom, via the two-photon transition, after the atom decays to the ground state. In these embodiments, re-excitation of the atom generates more atomic fluorescence, which increases the signal -to-noise of the detection. The steps 1006 and 1008 may also be performed continuously to detect this increased fluorescence and spectrally filter background light during detection. These embodiments are indicated in FIG. 10 with an arrow that connects the step 1008 back to the step 1006. Although not shown in FIG. 10, repump light may also be applied to the atom (e.g., during the step 1004) to ensure that the atom does not remain in a dark state. The use of repumping in this manner is similar to repumping used in MOTs.

[0099] In some embodiments, the atom has an upper one-photon transition between the first intermediate state of the atom and the excited state of the atom. This upper one-photon transition has an upper transition frequency. The atom also has a lower one-photon transition between the ground state of the atom and the first intermediate state of the atom. This lower one-photon transition has a transition linewidth y and a lower transition frequency. The first excitation laser beam is detuned from the upper transition frequency by no more than 1 OOOy. Similarly, the second excitation laser beam is detuned from the lower transition frequency by no more than lOOOy.

[0100] FIG. 1C shows one example of these embodiments in which the second excitation laser beam is nearly resonant with the one-photon D₂ transition in ¹³³Cs between the 6S-L/2 ground state and the 6P_3/,₂ intermediate state. This lower one-photon transition has a transition linewidth y « 5.23 MHz and a lower transition frequency of approximately 351.725 THz. The second excitation laser beam is typically detuned from the lower transition frequency by no more than a few hundred megahertz. This example also shows how the first excitation laser, which is nearly resonant with the upper one-photon transition between the 6P₃/₂ intermediate state and the 78^ excited state, is typically detuned from this upper one- photon transition by no more than a few hundred megahertz. Each of these detunings may be a red detuning or a blue detuning. [0101] In another example of the method 1000, the two-photon transition in ¹³³Cs between the 6S_1/2 ground state and the 7S_1/2 excited state is driven via the 6P_1/2 intermediate state instead of the 6P₃/₂intermediate state. In this case, the 6P_x/₂ intermediate state is the first intermediate state and the 6P₃/₂ intermediate state is the second intermediate state. The second excitation laser beam is nearly resonant with the transition at 895 nm. For the steps 1006 and 1008, atomic fluorescence at 852 nm is detected (i.e., not spectrally filtered) while scattered light at 895 nm is spectrally filtered, and therefore blocked from the photodetector.

[0102] While the method 1000 may be performed with atoms that are trapped near a dielectric structure (e.g., the photonic chip 100 of FIG. 1A), the method 1000 may also be performed with atoms that are located away from any dielectric structure. Thus, the method 1000 may be used to image atoms even when there is minimal, if any, background light.

Figure Captions

[0103] FIGS. 1B-1D - the nanophotonic chip platform for interfacing with an atom array. FIG. IB: Schematic of the platform depicting the optical-tweezer array manipulating single cesium atoms near a chip hosting an array of nanophotonic devices. The zoomed-out view shows the chip inside a stainless-steel ultra-high-vacuum chamber along with optical components used to control and image the system. The inset shows a scanning electron microscope (SEM) image of the nanophotonic devices at the edge of the chip. FIG. 1C: Reflection spectra of a nanophotonic cavity inside the chamber measured using the free-space coupling technique. The cavity is designed for future quantum networking experiments. However, the techniques presented herein are general and applicable to cavities, waveguides, or other photonic structures. FIG. ID: Energy-level structure of ¹³³Cs that illustrates the background-free imaging technique of the present embodiments. Atoms are doubly excited from the 6S_1/2 ground state, following the straight black arrows, through the 6P_3/2 intermediate state, and spectrally filter the fluorescence reaching the camerato only image the 895 nm decay path from the 6P₁/₂ level. Here, A₈₅₂ is the detuning from the bare 6S_X/₂ F=4 6P₃/₂ F'=5 transition and A₁₄₇₀ is the detuning from the bare 6P₃/₂ F'=5 -> 7S_1/2 F"=4 transition.

[0104] FIGS. 2A-2D - Background-free imaging of the atom array. FIG. 2 A: Top: Fluorescence image using the standard 852 nm (£>₂) cycling transition near the photonic chip. Despite lowering the electron-multiplying gain process on the EMCCD camera to 10 (from a typical value of 1000), the image is still saturated at the single-atom scale, even tens of microns away from the nanophotonic devices. Bottom: A single-shot image of atoms (inside the boxes) taken using the background-free technique of the present embodiments. Here, both images were taken with a 40-ms exposure time. FIG. 2B: An averaged fluorescence image of the atom array interleaved between the nanophotonic device array. No post-processing has been applied here beyond averaging the individual images. A small residual background makes the nanophotonic devices appear as dark shadows. This background is attributed to fluorescence at the imaging wavelength from the silicon base layer of the photonic chip. The inset shows an averaged fluorescence image of an 8x8 atom array in the loading region. FIG. 2C: A typical histogram of the detected 895-nm photons within a 4x4 pixel region of interest over a 40-ms exposure time in the loading region. The bimodal distribution allows distinguishing between the presence and absence of an atom with a high fidelity ^99.2%. FIG. 2D: Average magnitude of the detected fluorescence signal from the atoms as a function of the two drive laser detunings. The signal falls off as the 852-nm laser approaches hyperfine resonances on each side of the plot, leading to atom loss from the tweezers.

[0105] FIGS. 3A-3D - Imaging atoms on top of devices. FIG. 3A: The averaged fluorescence from 15,000 individual images of atoms loaded onto the nanophotonic devices overlaid with an image of the devices (see ’‘Experimental Techniques” for image processing details). FIG. 3B: Cross section of the nanophotonic device and the expected Stark shift on the D_r transition for the different intensity maxima formed on top of the device by the partially reflected tweezer. FIG. 3C: Averaged Stark shift measurements on the 895-nm 6S_1/2 F=3 -» P1/2 F'=4 transition in between the devices and on top of the devices. Centers estimated from Lorentzian fits to similar plots at each position are used to generate FIG. 3D. Error bars represent standard error of the mean. FIG. 3D: The centers of the Stark shift curves for individual atoms as a function of their positions. The lines are estimated device positions from FIG. 3A. The Stark shifts are larger in magnitude when the atoms are on top of the devices, as expected from the modified trapping potential on top of the devices, as shown in FIG. 3B (for the trapping potential away from the devices, see Supplementary Information). The error bars represent the standard error of the Lorentzian fit.

[0106] FIGS. 4A-4C - Defect-free atom rearrangement and loading onto nanophotonic devices. FIG. 4A: Experimental sequence used for defect-free rearrangement of the atoms from free-space onto the devices. After cooling the atoms and loading them into the tweezers, Image 1 was taken to detect the stochastic loading pattern and use this information to rearrange the array into a defect-free configuration which is then translated over and onto the devices before Image 2 is taken (see “Experimental Techniques” for details). FIG. 4B: Image 1 shows a single- shot image of the randomly loaded atoms in a nine-tweezer array in the loading region. After detecting these atoms in the first image, they are rearranged into a defect-free array with the same spacing as the devices. This compressed array is then loaded onto the devices and the final configuration is shown in Image 2. An averaged image of the final configuration after this procedure is show n to the right (see ‘‘Experimental Techniques'’ for image processing details). For all images in this figure, a 25-ms exposure time was used to increase the atomic survival rate through the first image. FIG. 4C: Here, an array of stochastically loaded atoms in Image 1 is rearranged and loaded onto a single device, as shown in Image 2. In the bottom plot, the averaged image of the final configuration is shown. The bright single atom on the left of the averaged image is an atom that is rearranged to a position outside the device region.

[0107] FIGS. 5A and 5B - SEM image of the photonic chip with nanophotonic devices. FIG. 5A: The devices are marked w ith the box and are overhanging the edge of the 600-pm- thick chip by 80 pm. The nanophotonic devices were undercut through the entire chip thickness by etching the chip from the side. FIG. 5B: A zoomed-in SEM view from the direction of the arrow in FIG. 5A.

[0108] FIGS. 6A-6C - Stark shift. FIG. 6A: Stark shift of the 895-nm D₁ transition induced by a 2.4-mW, 935-nm optical tweezer with a waist of 1.1 pm. FIG. 6B: Modified trapping potential and the corresponding Stark shift with the introduction of a silicon nitride (SisN4) device at the location marked. The tweezer is partially reflected by the device, resulting in the formation of a lattice-like potential with the closest intensity maximum (zl) causing the largest Stark shift. FIG. 6C: Expected Stark shift survival curves for the first three intensity maxima (zl, z2, z3). The experimental curve is fitted to a random sampling from the three survival curves, with a probability of 0.29 to be in the first intensity maximum, 0.66 to be in the second intensity maximum, and 0.05 to be in the third intensity maximum.

[0109] FIGS. 7 A and 7B - Atom lifetime and imaging on devices. FIG. 7A: Atom survival probability in the tweezer as a function of holding time (in seconds) in the loading region and when trapped on top of the devices. Atoms are relatively long-lived even on top of the nanophotonic devices with lifetimes of individual atoms varying from 0.7-1 s. FIG. 7B: A typical single-atom imaging histogram (probability density vs. photons detected) while atoms are trapped on top of the nanophotonic devices. Here, the fidelity of detection is estimated to be 86% with a threshold of five photons. Optimization of the tweezer power and imaging parameters can further improve the imaging fidelity. [0110] FIGS. 8A and 8B - Rearrangement to the devices. FIG. 8A: Rearrangement success (probability to detect atom) in the compression part of the rearrangement to the nanophotonic devices. Stochastically loaded atoms are detected and compressed into a defect- free array. Atom loss of 10-15% during the first image results in a finite reduction of the atom probability after rearrangement. A line shows the rearrangement curve after correcting for the imaging losses. FIG. 8B: The atomic trajectory used for rearrangement in FIGS. 4A-4C. Atoms were first compressed into a defect-free array, then moved in between nanophotonic devices, and finally moved on top of the nanophotonic devices.

[0111] FIGS. 9A-9C - Free-space coupling: FIG. 9A: Normalized 2D intensity profile of the diffraction-limited mode generated by a 0.17 NA lens. A line cut along the Y axis at Z=0 is shown above. The dashed horizontal line shows the 1/e² amplitude. FIG. 9B: Second TE mode supported by the waveguide taper end. Corresponding line cut along the Y axis at Z=0 is shown above. The dashed horizontal line shows the 1/e² amplitude. FIG. 9C: Estimated coupling efficiency from Lumerical FDTD simulation for a waveguide with a constant thickness of 330 nm.

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Combinations of Features

[0112] Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following examples illustrate possible, non-limiting combinations of features and embodiments described above. It should be clear that other changes and modifications may be made to the present embodiments without departing from the spirit and scope of this invention:

[0113] (Al) A photonic chip includes a substrate and a plurality of nanophotonic devices extending laterally away from an edge of the substrate. Each nanophotonic device, of the plurality of nanophotonic devices, is free-standing where said each nanophotonic device extends laterally past the edge of the substrate. [0114] (A2) In the photonic chip denoted (Al), each neighboring pair of nanophotonic devices, of the plurality of photonic devices, forms a gap therebetween. The gap is devoid of material where said each neighboring pair of nanophotonic devices extends laterally past the edge of the substrate.

[0115] (A3) In the photonic chip denoted (A2), the gap has a gap size of 1 pm or more.

[0116] (A4) In any of the photonic chips denoted (Al) to (A3), each nano pho tonic device has a proximal end where said each nanophotonic device meets the edge of the substrate and a distal end opposite the proximal end.

[0117] (A5) In any of the photonic chips denoted (Al) to (A4), each nanophotonic device has a top face where said each nanophotonic device protrudes laterally past the edge of the substrate. No material contacts the top face.

[0118] (A6) In any of the photonic chips denoted (Al) to (A5), each nanophotonic device has a bottom face where said each nanophotonic device protrudes laterally past the edge of the substrate. No material contacts the bottom face.

[0119] (A7) In any of the photonic chips denoted (Al) to (A6), the plurality of nanophotonic devices form at least part of a top layer located on top of the substrate.

[0120] (A8) In the photonic chip denoted (A7), the substrate is composed of a substrate material and the top layer is composed of a top-layer material that is different from the substrate material.

[0121] (A9) In the photonic chip denoted (A8). the substrate material includes crystalline silicon, amorphous silicon, alumina, crystalline sapphire, silicon carbide, glass, fused silica, or a combination thereof. The top-layer material includes silicon nitride, lithium niobate, gallium arsenide, silicon oxide, diamond, silicon carbide, or a combination thereof.

[0122] (A10) In any of the photonic chips denoted (Al) to (A9), at least one of the plurality of nanophotonic devices includes one or both of a nanophotonic waveguide and a nanophotonic resonator.

[0123] (Al l) In the photonic chip denoted (A10), said at least one of the plurality of nanophotonic devices includes a nanophotonic waveguide coupled to a nanophotonic resonator.

[0124] (Al 2) In the photonic chip denoted (Al l), the nanophotonic waveguide includes a tapered nanophotonic waveguide.

[0125] (A13) In any of the photonic chips denoted (Al) to (A12), the plurality of nanophotonic devices are uniformly spaced along the edge. [0126] (A14) In any of the photonic chips denoted (Al) to (A13), each nanophotonic device has a top surface that is optically reflective.

[0127] (A15) In any of the photonic chips denoted (Al) to (A14), each nanophotonic device having a free-standing length of 5 gm or more.

[0128] (A16) In any of the photonic chips denoted (Al) to (A15), each nanophotonic device has a width of 3 pm or less.

[0129] (Al 7) In any of the photonic chips denoted (Al) to (Al 6), each nanophotonic device has a height of 2 pm or less.

[0130] (Bl) A method includes optically trapping a cold atom within a gap formed between a pair of neighboring nanophotonic devices of a plurality' of nanophotonic devices of a photonic chip. The photonic chip is any of the photonic chips denoted (Al) to (A17).

[0131] (B2) In the method denoted (Bl), said optically trapping includes optically trapping the cold atom with an optical-tweezers laser beam propagating through the gap.

[0132] (B3) In the method denoted (B2), the method further includes laterally- translating the optical-tweezers laser beam perpendicularly to the edge of the substrate of the photonic chip to adiabatically move the cold atom from outside the gap to inside the gap.

[0133] (B4) In the method denoted (B3), the method further includes laser cooling a hot atom outside the gap to create the cold atom. The method further includes turning on the optical-tweezers laser beam to initially trap the cold atom outside the gap.

[0134] (B5) In any of the methods denoted (B2) to (B4). the method further includes translating the optical -tweezers laser beam parallel to the edge of the substrate of the photonic chip to retroreflect the optical-tweezers laser beam off a top face of one of the plurality- of nanophotonic devices. The optical-tweezers laser beam creates an optical lattice upon retroreflecting off of the top face. The cold atom is trapped in a lattice site of the optical lattice.

[0135] (B6) In the method denoted (B5), the optical lattice has a plurality of lattice sites. The lattice site is the one of the plurality- of lattice sites that is closest to the top face.

[0136] (B7) In either of the methods denoted (B5) and (B6), the method further includes coupling the cold atom to the one of the plurality of nanophotonic devices while the cold atom is trapped in the lattice site.

[0137] (Cl) A method includes coupling light into ananophotonic device that is one of a plurality⁷ of nanophotonic devices of a photonic chip. The photonic chip is any one of the photonic chips denoted (Al) to (Al 7). The nanophotonic device includes a nanophotonic waveguide having (i) a proximal end joined to the substrate of the photonic chip and (ii) a distal end opposite the proximal end. The nanophotonic waveguide guides the coupled light from the distal end toward the proximal end.

[0138] (C2) In the method denoted (Cl), the method further includes focusing a free- space optical beam with a lens to generate a focused optical beam. Said coupling light includes coupling the focused optical beam into the nanophotonic device.

[0139] (C3) In the method denoted (C2), the photonic chip is located inside a vacuum system and the lens is located outside the vacuum system.

[0140] (C4) In either of the methods denoted (C2) and (C3), the lens has a numerical aperture of 0.5 or less.

[0141] (C5) In any of the methods denoted (C2) to (C4), the method further includes translating the lens parallel to the edge of the substrate to couple the focused optical beam into a second nanophotonic device that is another one of the plurality of nanophotonic devices. The second nanophotonic device includes a second nanophotonic waveguide having (i) a second proximal end joined to the substrate of the photonic chip and (ii) a second distal end opposite the second proximal end. The second nanophotonic waveguide guides the focused optical beam, as coupled into the second nanophotonic waveguide, from the second distal end toward the second proximal end.

[0142] (C6) In any of the methods denoted (Cl) to (C5), the nanophotonic waveguide includes a tapered waveguide.

[0143] (C7) In the method denoted (C6), the tapered waveguide is a linearly tapered waveguide.

[0144] (C8) In any of the methods denoted (Cl) to (C7), said coupling excites at least a second transverse electric (TE) mode of the nanophotonic waveguide.

[0145] (C9) In any of the methods denoted (Cl) to (C8), the nanophotonic device further includes a nanophotonic resonator abutting the nanophotonic waveguide. The nanophotonic waveguide guides the coupled light from the distal end toward the proximal end such that the coupled light excites a mode of the nanophotonic waveguide.

[0146] (CIO) In the method denoted (C9), the mode includes a second transverse electric (TE) mode.

[0147] (DI) A method includes simultaneously illuminating an atom with first and second excitation laser beams, detecting signal light with a photodetector, and spectrally filtering background light such that the photodetector does not detect the background light. The first and second excitation laser beams have first and second excitation wavelengths, respectively. The first and second excitation laser beams drive a two-photon transition in the atom to transfer the atom from a ground state to an excited state. The atom either (i) decays from the excited state to a first intermediate state by emitting a first photon at a first transition wavelength and then subsequently decays from the first intermediate state to the ground state by emitting a second photon at a second transition wavelength or (ii) decays from the excited state to a second intermediate state by emitting a third photon at a third transition wavelength that is different from the first excitation wavelength and the second excitation wavelength and then subsequently decays from the second intermediate state to the ground state by emitting a fourth photon at a fourth transition wavelength that is different from the first excitation w avelength and the second excitation w avelength. The signal includes one or both of the third photon and the fourth photon. The background light includes scattered light from one or both of the first and second excitation laser beams.

[0148] (D2) In the method denoted (DI), the first excitation wavelength differs from the first transition wavelength by no more than ten nanometers and the second excitation wavelength differs from the second transition wavelength by no more than ten nanometers.

[0149] (D3) In either of the methods denoted (DI) and (D2), the atom has an upper one-photon transition between the first intermediate state of the atom and the excited state of the atom, the upper one-photon transition having an upper transition frequency. The atom has a lower one-photon transition betw een the ground state of the atom and the first intermediate state of the atom, the lower one-photon transition having a transition linew idth y and a lower transition frequency. The first excitation laser beam is detuned from the upper transition frequency by no more than lOOOy. The second excitation laser beam is detuned from the lower transition frequency by no more than 1 OOOy.

[0150] (D4) In any of the methods denoted (DI) to (D3). the method further includes optically trapping the atom during said illuminating, said detecting, and said spectrally filtering.

[0151] (D5) In the method denoted (D4), said optically trapping includes optically trapping the atom in an optical-tweezers laser beam.

[0152] (D6) In either of the methods denoted (D4) and (D5), said optically trapping includes optically trapping the atom in an optical lattice.

[0153] (D7) In any of the methods denoted (DI) to (D6), the atom is an alkali-metal atom.

[0154] (D8) In any of the methods denoted (DI) to (D7), said spectrally filtering includes spectrally filtering the background light with an optical filter located in front of the photodetector. [0155] (D9) In any of the methods denoted (DI) to (D8), said detecting the signal light with the photodetector includes imaging the signal light with a camera.

[0156] (DIO) In the method denoted (D9), the camera includes an electron multiplying charge-coupled device (EMCCD) camera.

[0157] (Dl l) In any of the methods denoted (DI) to (DIO), said illuminating includes continuously illuminating the atom to re-excite the atom, via the two-photon transition, after the atom decays to the ground state.

[0158] Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.

Claims

CLAIMS What is claimed is:

1. A photonic chip, comprising: a substrate; and a pl urality of nanophotonic devices extending laterally away from an edge of the substrate; wherein each nanophotonic device, of the plurality of nanophotonic devices, is freestanding where said each nanophotonic device extends laterally past the edge of the substrate.

2. The photonic chip of claim 1, wherein each neighboring pair of nanophotonic devices, of the plurality of photonic devices, forms a gap therebetween, the gap being devoid of material where said each neighboring pair of nanophotonic devices extends laterally past the edge of the substrate.

3. The photonic chip of claim 2, the gap having a gap size of one micron or more.

4. The photonic chip of claim 1, each nanophotonic device having: a proximal end where said each nanophotonic device meets the edge of the substrate; and a distal end opposite the proximal end.

5. The photonic chip of claim 1, wherein: each nanophotonic device has a top face where said each nanophotonic device protrudes laterally past the edge of the substrate; and no material contacts the top face.

6. The photonic chip of claim 1 , wherein: each nanophotonic device has a bottom face where said each nanophotonic device protrudes laterally past the edge of the substrate; and no material contacts the bottom face.

7. The photonic chip of claim 1, the plurality of nanophotonic devices forming at least part of a top layer located on top of the substrate.

8. The photonic chip of claim 7, wherein: the substrate is composed of a substrate material; and the top layer is composed of a top-layer material that is different from the substrate material.

9. The photonic chip of claim 8, wherein: the substrate material comprises crystalline silicon, amorphous silicon, alumina, crystalline sapphire, silicon carbide, glass, fused silica; and the top-layer material comprises silicon nitride, lithium niobate. gallium arsenide, silicon oxide, diamond, silicon carbide.

10. The photonic chip of claim 1, at least one of the plurality' of nanophotonic devices comprising one or both of a nanophotonic waveguide and a nanophotonic resonator.

11. The photonic chip of claim 10, said at least one of the plurality of nanophotonic devices comprising a nanophotonic waveguide coupled to a nanophotonic resonator.

12. The photonic chip of claim 1 1, the nanophotonic waveguide comprising a tapered nanophotonic waveguide.

13. The photonic chip of claim 1, the plurality of nano photonic devices being uniformly spaced along the edge.

14. The photonic chip of claim 1, each nanophotonic device having a top surface that is optically reflective.

15. The photonic chip of claim 1, each nanophotonic device having a free-standing length of five microns or more.

16. The photonic chip of claim 1, each nanophotonic device having a width of three microns or less.

17. The photonic chip of claim 1, each nanophotonic device having a height of two microns or less.

18. A method, comprising optically trapping a cold atom within a gap formed between a pair of neighboring nanophotonic devices of the plurality of nanophotonic devices of the photonic chip of claim 1.

19. The method of claim 18, wherein said optically trapping comprises optically trapping the cold atom with an optical-tweezers laser beam propagating through the gap.

20. The method of claim 19, further comprising laterally translating the optical -tweezers laser beam perpendicularly to the edge of the substrate of the photonic chip to adiabatically move the cold atom from outside the gap to inside the gap.

21. The method of claim 20, further comprising: laser cooling a hot atom outside the gap to create the cold atom; and turning on the optical-tweezers laser beam to initially trap the cold atom outside the gap.

22. The method of claim 19, wherein: the method further comprises translating the optical-tweezers laser beam parallel to the edge of the substrate of the photonic chip to retroreflect the optical- tweezers laser beam off top face of one of the plurality of nanophotonic devices; the optical-tweezers laser beam creates an optical lattice upon retroreflecting off of the top face; and the cold atom is trapped in a lattice site of the optical lattice.

23. The method of claim 22, wherein: the optical lattice has a plurality of lattice sites; and the lattice site is the one of the plurality of lattice sites that is closest to the top face.

24. The method of claim 22, further comprising coupling the cold atom to the one of the plurality of nanophotonic devices while the cold atom is trapped in the lattice site.

25. A method, comprising: coupling light into a nanophotonic device that is one of the plurality of nanophotonic devices of the photonic chip of claim 1 ; wherein: the nanophotonic device includes a nanophotonic waveguide having (i) a proximal end joined to the substrate of the photonic chip and (ii) a distal end opposite the proximal end; and the nanophotonic waveguide guides the coupled light from the distal end toward the proximal end.

26. The method of claim 25, wherein: the method further comprises focusing a free-space optical beam with a lens to generate a focused optical beam; and said coupling light comprises coupling the focused optical beam into the nanophotonic device.

27. The method of claim 26, wherein: the photonic chip is located inside a vacuum system; and the lens is located outside the vacuum system.

28. The method of claim 26, the lens having a numerical aperture of 0.5 or less.

29. The method of claim 26, wherein: the method further comprises translating the lens parallel to the edge of the substrate to couple the focused optical beam into a second nanophotonic device that is another one of the plurality' of nanophotonic devices; the second nanophotonic device includes a second nanophotonic waveguide having (i) a second proximal end joined to the substrate of the photonic chip and (ii) a second distal end opposite the second proximal end; and the second nanophotonic waveguide guides the focused optical beam, as coupled into the second nanophotonic waveguide, from the second distal end toward the second proximal end.

30. The method of claim 25, the nanophotonic waveguide comprising a tapered waveguide.

31. The method of claim 30, the tapered waveguide comprising a linearly tapered waveguide.

32. The method of claim 25, wherein said coupling excites at least a second transverse electric (TE) mode of the nanophotonic waveguide.

33. The method of claim 25, wherein: the nanophotonic device further includes a nanophotonic resonator abutting the nanophotonic waveguide; and the nanophotonic waveguide guides the coupled light from the distal end toward the proximal end such that the coupled light excites a mode of the nanophotonic waveguide.

34. The method of claim 33, the mode comprising a second transverse electric (TE) mode.

35. A method, comprising simultaneously: illuminating an atom with first and second excitation laser beams having first and second excitation wavelengths, respectively, the first and second excitation laser beams driving a two-photon transition in the atom to transfer the atom from a ground state to an excited state, wherein the atom either: decays from the excited state to a first intermediate state by emitting a first photon at a first transition wavelength and then subsequently decays from the first intermediate state to the ground state by emitting a second photon at a second transition wavelength; or decays from the excited state to a second intermediate state by emitting a third photon at a third transition wavelength that is different from the first excitation wavelength and the second excitation wavelength and then subsequently decays from the second intermediate state to the ground state by emitting a fourth photon at a fourth transition w avelength that is different from the first excitation wavelength and the second excitation wavelength; delecting signal light with a photodetector, the signal comprising one or both of the third photon and the fourth photon; and spectrally filtering background light such that the photodetector does not detect the background light, the background light comprising scattered light from one or both of the first and second excitation laser beams.

36. The method of claim 35, wherein: the first excitation wavelength differs from the first transition wavelength by no more than ten nanometers; and the second excitation wavelength differs from the second transition wavelength by no more than ten nanometers.

37. The method of claim 35, wherein: the atom has an upper one-photon transition between the first intermediate state of the atom and the excited state of the atom, the upper one-photon transition having an upper transition frequency; the atom has a lower one-photon transition between the ground state of the atom and the first intermediate state of the atom, the lower one-photon transition having a transition linewidth y and a lower transition frequency; the first excitation laser beam is detuned from the upper transition frequency by no more than lOOOy; and the second excitation laser beam is detuned from the lower transition frequency by no more than lOOOy.

38. The method of claim 35. further comprising optically trapping the atom during said illuminating, said detecting, and said spectrally filtering.

39. The method of claim 38, wherein said optically trapping comprises optically trapping the atom in an optical -tweezers laser beam.

40. The method of claim 38, wherein said optically trapping comprises optically trapping the atom in an optical lattice.

41. The method of claim 35, the atom comprising an alkali-metal atom.

42. The method of claim 35, wherein said spectrally filtering comprises spectrally filtering the background light with an optical filter located in front of the photodetector.

43. The method of claim 35, wherein said detecting the signal light with the photodetector comprises imaging the signal light with a camera.

44. The method of claim 43, the camera comprising an electron multiplying charge- coupled device (EMCCD) camera.

45. The method of claim 35, wherein said illuminating comprises continuously illuminating the atom to re-excite the atom, via the two-photon transition, after the atom decays to the ground state.