WO2013059404A1

WO2013059404A1 - Systems and methods for deterministic emitter switch microscopy

Info

Publication number: WO2013059404A1
Application number: PCT/US2012/060735
Authority: WO
Inventors: Dirk R. ENGLUND; Edward H. CHEN
Original assignee: The Trustees Of Columbia University In The City Of New York
Priority date: 2011-10-19
Filing date: 2012-10-18
Publication date: 2013-04-25
Also published as: EP2769417A4; EP2769417A1

Abstract

Techniques for deterministic switch microscopy include resolving at least one nitrogen vacancy center in a diamond structure. A magnetic field can be applied across the diamond structure and the nitrogen vacancy centers can be optically excited. The nitrogen vacancy centers can be switched from a dark state to a bright state or a bright state by a dark state by applying at least one microwave pulse. A fluorescent response of each nitrogen vacancy center can be detected and a nitrogen vacancy center can be resolved based on the fluorescent response of each nitrogen vacancy center as it corresponds to the orientation of the nitrogen vacancy center relative to the applied magnetic field.

Description

SYSTEMS AND METHODS FOR DETERMINISTIC EMITTER SWITCH

MICROSCOPY

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. Provisional Application Serial No. 61/549,046, filed October 19, 2011, U.S. Provisional Application Serial No.

61/562,551, filed on November 22, 2011, U.S. Provisional Application Serial No. 61/591 ,570, filed on January 27, 2012, and U.S. Provisional Application Serial No. 61/624,647, filed on April 16, 2012, which are each incorporated herein by reference in their entirety and from which priority is claimed.

BACKGROUND

The disclosed subject matter relates to techniques for superresolution microscopy, including techniques for deterministic emitter switch microscopy.

In certain conventional far-field optical microscopes, imaging resolution is limited to the diffraction limit, /2(n*sin(9)), where λ is the illuminating light wavelength, n is the refractive index, and Θ is the collection angle of the imaging optics. Generally speaking, the diffraction limit can be approximately half of the illuminating light's wavelength, or, e.g., approximately 200 nm in the visible spectrum.

In certain instances, it can be desirable to image at resolution below the diffraction limit. For example, as semiconductor device fabrication continues its trend toward increasingly smaller architecture, imaging techniques to resolve and inspect elements smaller than the diffraction limit can be useful for inspection or other purposes. Additionally, imaging for the biological sciences, such as imaging cell structures or certain proteins, can require imaging below the diffraction limit.

Certain techniques for imaging below the diffraction limit can generally be partitioned into two groups: (i) techniques to modify the fluorescence of a cluster of particles around an arbitrarily small area (for example in connection with stimulated emission depletion (STED), reversible saturable optical fluorescence transitions (RESOLFT), or saturated structured illumination microscopy (SSIM)), and (ii) techniques that rely on the stochastic switching of fluorescence molecules to reconstruct the positions of the molecules (for example in connection with stochastic

NY02:757642.1 optical reconstruction microscopy (STORM), photoactivated localization microscopy (PALM), or fluorescence photoactivation localization microscopy (FPALM).

However, these techniques can require high excitation power, use of narrow spectrum light sources, particular fluorescent samples, expensive optical detection equipment, and intensive data processing techniques. For example, STED can require an excitation power higher than ~ GW/cm^". Moreover, techniques such as STED/RESOLFT can be limited to a small read out area for reasonable acquisition times (e.g., on the order of seconds) due to use of serial scanning imaging techniques rather than wide-field imaging. Techniques that rely on stochastic switching, for example, can require centroid fitting or other statistical processing of readouts over a period of time, which can inherently delay acquisition times due to the stochastic nature of the emitters. Moreover, certain fluorescent biomarkers used in connections with techniques for imaging below the diffraction limit can have brightness approximately an order of magnitude less than 10⁵ counts/sec, can bleach, blink or degrade during excitation, and/or are toxic to cells.

SUMMARY

The disclosed subject matter provides techniques for deterministic emitter switch, microscopy.

In one aspect of the disclosed subject matter, a method for resolving at least one nitrogen vacancy (NV) center includes providing at least one diamond structure with one or more nitrogen vacancy centers within a local location, each being in either a dark state or a bright state. A magnetic field can be applied across the diamond structure. The nitrogen vacancy centers can be optically excited to produce a fluorescent response. A nitrogen vacancy center can be switched from a dark state to a bright state of from the bright state to the dark state by applying at least one microwave pulse to the nitrogen vacancy center, and the fluorescent response of each center can be detected. At least one nitrogen vacancy center can be resolved based on the fluorescent response, the fluorescent response corresponding to the orientation of the nitrogen vacancy center relative to the applied magnetic field.

In one embodiment, optically exciting the nitrogen vacancy center can include directing a continuous wave of pump light at approximately 532 nm to the nitrogen vacancy center. Alternatively, a pulse of pump light at approximately 532

NY02:757642.1 nm can polarize the electron spin of the nitrogen vacancy center prior to applying at least one microwave pulse, and at least a second pulse of pump light at 532 nm can be applied subsequent to application of the at least one microwave pulse to measure the coherence time of the electron spin state. Different pulse combinations can result in measurements of the spin properties; such measurements can include dynamic decoupling techniques.

In one embodiment, a diamond structure can be provided including a plurality of nitrogen vacancy centers, at least some of which having a different orientation relative to the applied magnetic field. A spin sublevel of each nitrogen vacancy center can experience a Zeeman splitting corresponding to the orientation of the nitrogen vacancy center with respect to the magnetic field. A microwave pulse can be applied, e.g., by tuning a first microwave pulse to a field splitting frequency of a first nitrogen vacancy center, which can modulate the fluorescent response of the first nitrogen vacancy center. Additionally, a second microwave pulse that is tuned to a field splitting frequency of at least a second nitrogen vacancy center can also be applied, thus modeling the fluorescent response of the second nitrogen vacancy center.

In one embodiment, a method can include applying a first microwave pulse at a first frequency. The first frequency can be tuned to a field splitting frequency of a first nitrogen vacancy center. A first intensity plot of a first fluorescent response corresponding to the first frequency can be generated. A second microwave pulse can be applied at a second frequency. The second frequency can be tuned to a field splitting frequency of a second nitrogen vacancy center. A second intensity plot of a second fluorescent response corresponding to the second frequency can be generated. A third microwave pulse can be applied at a third frequency. The third frequency can be tuned to a frequency that is not the field splitting frequency of either the first or second nitrogen vacancy center. An intensity plot of a third fluorescent response corresponding to the third frequency can be generated. The position of the nitrogen vacancy center can be resolved by subtracting the first and third intensity plots from the second intensity plot. In certain embodiments, the frequency of microwave emission can be continuously varied.

In one embodiment, the method can further include applying a plurality of microwave pulses and detecting a plurality of fluorescent responses,

NY02:757642.1 corresponding to the plurality of microwave pulses, to obtain a full electron spin resonance spectrum for a plurality of locations of a sample. Resolving the nitrogen vacancy center can include fitting the electronic spin resonance spectrum with a sum of Lorentzian dips and generating an intensity map for the nitrogen vacancy center using contrasts from the fitted electron spin resonance spectrum.

In one embodiment, the method can include providing at least one fluorophore having an emission spectrum at least partially overlapping with an emission spectrum of the one or more nitrogen vacancy centers. The fluorescent response of one of the nitrogen vacancy centers can optically excite the fluorophore if the nitrogen vacancy center is within a threshold distance of fluorophore. The fluorescent response of the fluorophore corresponding to the optical excitation of the one of the nitrogen vacancy centers can be detected. The distance of a nitrogen vacancy center from the fluorophore can be determined based on at least the fluorescent response of the nitrogen vacancy center and the fluorescent response of the fluorophore. Furthermore, the orientation of a magnetic dipole of a molecule coupled to the fluorophore can be determined based on at least the fluorescent response of the one of the nitrogen vacancy centers and the fluorescent response of the fluorophore.

In an embodiment, the diamond structure can be exposed to an environment. Two or more microwave pulses, each microwave pulse having a different frequency, can be applied, and a fluorescent response corresponding to each microwave pulse can be detected. Based on the fluorescent response of each nitrogen vacancy center, a characteristic of the environment can be determined. The characteristic can be a local magnetic field, local electric field, or pH of the environment.

A system for resolving at least one nitrogen vacancy center within a focal location using an applied magnetic field is also provided. In an embodiment, the system can include a light source, operatively configured to excite the at least one nitrogen vacancy center in the presence of the applied magnetic field, to induce the nitrogen vacancy center to produce a fluorescent response. A photodetector can be arranged to detect the fluorescent response, if any. A tunable microwave emitter can be arranged to apply at least one microwave pulse to the nitrogen vacancy center. A control unit, coupled to the photodetector and the tunable microwave emitter, can be

NY02:757642, i con figured to adjust the frequency of the tunable microwave emitter, and configured to resolve the at least one nitrogen vacancy center based on the fluorescent response, the fluorescent response corresponding to its orientation relative to the magnetic field.

In one embodiment, the photodetector can include an array of pixels, and can be arranged to detect an intensity map of the fluorescent response across the array of pixels. The system can also include far-field optics to direct the fluorescent response to the photodetector. The focal location can include a diffraction-limited area, and the array of pixels can correspond to at least the diffraction-limited area.

In one embodiment, the light source can include a laser adapted to continuously irradiate at least one nitrogen vacancy center with approximately 532 nm light. Alternatively, the light source can be coupled to the control unit, and can include a laser adapted to apply a pulse of pump light at approximately 532 nm to the at least one nitrogen vacancy center prior to application of the at least one microwave pulse, and can be adapted to apply a pulse of pump light at approximately 532 nm to the nitrogen vacancy center subsequent to application of the at least one microwave pulse.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. la is a diagram showing a nitrogen-vacancy (NV) center in diamond.

Fig. lb illustrates an exemplary sample including a plurality of NV centers in accordance with an embodiment of the disclosed subject matter

Fig. lc illustrates a technique of resolving an NV center in accordance with an embodiment of the disclosed subject matter.

Fig. 2 illustrates a bulk diamond sample in an applied magnetic field with NV centers having field splitting frequencies corresponding to their alignment relative to the magnetic field in accordance with an embodiment of the disclosed subject matter.

Fig. 3 is a flow diagram illustrating a method for resolving a switchable emitter in accordance with an embodiment of the disclosed subject matter.

Fig. 4 is a schematic diagram of a system for resolving a switchable emitter in accordance with another embodiment of the disclosed subject matter.

NY02;757642. I Fig. 5 is an illustrative demonstration of resolving two NV centers within a diffraction-limited focal spot in accordance with an embodiment of the disclosed subject matter.

Fig. 6 is an illustrative demonstration of resolving NV centers within wide field of view in accordance with an embodiment of the disclosed subject matter.

Throughout the drawings, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the disclosed subject matter will now be described in detail with reference to the Figs., it is done so in connection with the illustrative embodiments.

DETAILED DESCRIPTION

Disclosed herein are techniques providing for the deterministic emitter switch microscopy. In one aspect of the disclosed subject matter, a technique for resolving a switchable emitter can include resolving an emitter within a diffraction- limited spot using optically detectable magnetic resonance (ODMR). For purposes of illustration and not limitation, an exemplary deterministic emitter can include the nitrogen- vacancy (NV) center in diamond. As disclosed herein below, a single NV center can be deterministically switched to locate emitters below 30 nm resolutions. Moreover, diamond nanoprobes with the NV can also be photostable. For example, single NV centers can emit without a change in brightness for months or longer. Additionally diamond is chemically inert, cell-compatible, and has surfaces that can be suitable for functio alization with ligands that target biological samples. NV centers can emit in excess of 10⁶ photons per second.

Diamond NV color centers can be formed when a nitrogen atom is substituted for a carbon atom in the carbon lattice, replacing two carbons and creating a physical vacancy with dangling bonds. Diamond NV centers can occur naturally or can be implanted in a diamond structure via ion radiation or the like. The NV- center has an additional electron associated with it, creating a desirable electronic S = 1 structure that has a long-lived spin triplet in its ground state that can be probed using optical and microwave excitation. The NV electron spin can act as a sensitive probe of the local environment, and their optical accessibi lity can allow their use in optically detected magnetic resonance schemes.

NY02:757642.1 Referring to FIG. la, a diagram of an exemplary NV center is illustrated. NV centers can absorb photons with a wavelength around 532 nm and emit a fluorescent response, which can be between 637 and 800 nm. A spin- dependent intersystem crossing (^]A) 160 between excited state (³E) 120 triplet to a metastable, dark sing let level (^JA) 110 can change the integrated fluorescent response for the spin states 10) and j ± l) . The deshelving from the smglet 110 occurs primarily to the J O) spin state, which can provide a means to polarize the NVC.

As depicted in Fig. l , transitions from the NV ground state 110 to the excited state 120 are spin-conserving, keeping m_s constant. Such an excitation can be performed using laser light at approximately 532 nm 140; however, other wavelengths can be used, such as blue (480 nm) and yellow (580 nm). While the electronic excitation pathway preserves spin, the relaxation pathways contain non-conserving transitions involving an intersystem crossing (or singlet levels).

Due to the C_3v symmetry of the nitrogen defect, the splitting between one "bright" (m_s = 0) 111 and two "dark" (m_s = ±1) (112 and 113) ground states is given by the crystal field splitting 114. Notwithstanding the effects of an applied magnetic field or certain other factors, the zero field splitting frequency can be approximately equal to 2.87 GHz. The degeneracy of the two dark states can be lifted by an applied magnetic field due to the interaction of the field with the electron magnetic moment, often referred to as the Zeeman effect. The energy difference between the two dark states can be given by μ · B , where B is the magnetic field and μ is the electron magnetic moment.

A driving field at frequency ω (which can typically be in the microwave range) can induce electron spin resonance (ESR) transitions between the | 0 and J± l) split states. That is, microwave fields resonant at levels | θ and |± l can perturb the spin populations, and thus the fluorescent response of the NV center. Sweeping over the microwave frequency around the crystal field splitting of the NV center, an electron spin resonance spectrum 190 can be resolved. When excited on either the m_s = +1 112 or m_s = -1 113 resonance, the fluorescence intensity can drop by approximately 30%. That is, applying a microwave pulse at the field splitting frequency corresponding to either the m_s = +1 112 or m_s = -1 113 state can

deterministically "switch" an emitter from a bright m_s = 0 111 state to a dark m_s = +1

NY02:757642.1 112 or m_s = -1 113 state. Because the energy difference between the m_s = +1 112 or m_s = -1 113 states, and thus the field splitting frequency for each state, can depend via the Zeeman effect on the orientation of the axis of the NV center relative to the applied magnetic field, an NV center with a particular orientation can be uniquely resonantly excited into a dark state, thus providing individual addressability of individual NV centers where a plurality of NV centers have non-overlapping resonances.

Exemplary embodiments of a method and system for resolving a nitrogen vacancy center w ll now be described in detail, with reference Fig, 3 and Fig. 4, for purposes of illustration and not limitation.

In an exemplary embodiment, at least one diamond structure with one or more nitrogen vacancy centers can be provided (310), e.g., in a sample 420. For example, the diamond structure can be one or more bulk diamond structures. As noted above, bulk diamond structures can include naturally occurring nitrogen vacancy centers there. Additionally or alternatively, nitrogen vacancy centers can be created in bulk diamond using, e.g., ion implantation techniques. In bulk diamond, the NV centers can have one of four orientations within a single bulk diamond structure, owing to the lattice structure 157 of diamond, depicted for purposes of illustration and not limitation in Fig. lb. For example, as depicted in Fig. 2, a bulk diamond slab 210 can include NV centers (251a, 251b, 251c, and 251d) with different axial alignment, such that in the presence of a magnetic field 155, each orientation can exhibit a different field splitting frequency (252a, 252b, 252c, and 252d).

Alternatively, the at least one diamond structure can include one or more diamond nanocrystals. As with bulk diamond, nitrogen vacancy centers can occur naturally, or can be created using, e.g., ion implantation techniques. Fig. lb illustrates an exemplary sample 150 with a plurality of NV- probes (151a, 151b, and 151c), for example as included in a plurality of diamond nanocrystals. In certain embodiments, each diamond nanocrystal can include a single NV center. Alternatively, each diamond nanocrystal can include a plurality of NV centers.

A magnetic field 470 (also depicted in Fig. lb as magnetic field 155) can be applied to at least the NV centers of the diamond structures (i.e., the sample 420 can be exposed (320) to a magnetic field. The magnetic field 470 can be, for example, an applied external magnetic field, and in some embodiments can be

NY02:757642.1 substantially uniform. The magnetic field 470 can be created with conventional techniques. For example, the magnetic field 470 can be created by placing a large magnet in proximity to the sample 420 such that the magnetic field created by the magnet is substantially uniform over the sample 420. Additionally or alternatively, the magnetic field 470 can be created by arranging current-carrying coils around the sample 420 to create a magnetic field. In certain embodiments, shielding can be used to eliminate extraneous magnetic field interference, for example from the earth's magnetic field or surrounding electronic equipment. For fields below the strengths of approximately 500 Gauss of magnetic field 470 along the NV axis, a simple linear model can reliably approximate steady state solutions of the spin resonance. At strengths above 500 Gauss, unrelated effects of nuclear spin polarization can occur. Accordingly, in an exemplary embodiment, the magnetic field 470 can be

approximately 100 Gauss.

For purposes of illustration and not limitation, the number of resolvable NV centers can roughly correlate to the magnetic moment projected onto the incident magnetic field divided by the average linewidth of an electron spin resonance line. This correlation is analogous to that used in connection with magnetic resonance imaging (MRI). For example, and not limitation, if a magnetic field 470 of 100G is applied with a magnetic moment of 2.5MHz/G and an ESR linewidth of 5 MHz, approximately 50 NV centers can be resolved.

As noted above, by exposing the NV centers to a magnetic field 470, the degeneracy of the "dark" m_s = ±1 states is lifted via the Zeeman effect. The energy difference between the two dark states can be given by, e.g., μΒ cos(<9) , where Θ is the angle of the applied magnetic field, B, 470, with respect to the axis of each NV center and μ is the electron magnetic moment. Thus, the field splitting frequency for the m_s = ±1 states can differ from the zero field splitting frequency (i.e., approximately 2.87 GHz notwithstanding certain other factors) and can differ from each other by an amount corresponding to the energy difference between them.

The nitrogen vacancy centers of the sample 420 can be optically excited (330) with, for example, a light source 410. In one embodiment, for example, the light source 410 can optically excite the nitrogen vacancy centers with a continuous wave of pump light at approximately 523 nm 411. In certain

embodiments, as described in more detail below, the light source 410 can be

NY02:757642.1 configured (e.g., through coupling to a control unit 490} to generate pump light in a pulsed fashion to first optically excite the nitrogen vacancy centers, and then generate a readout pump light after, e.g., a sequence of microwave pulses such as a Rabi sequence or other echo sequence.

In certain embodiments, wide-field, speckle-free illumination with 530 nm polarized light upon a sample containing NV centers can be employed 416. For example, a broad field green illumination laser can be used. Certain optics 450, such as an objective lens and/or one or more apertures, can also be included to have a broad field light 412 on the focal plane. The broad field green illumination laser 416 can be operated at, for example, an incident power of approximately 2.8 kW/cm². Alternatively, a focused field laser 415 can be used. The focused field laser 415 can be operated at a power of approximately 1.25 kW/cm². In certain embodiments (e.g., in connection with the use of certain reconstruction algorithms similar to those used in STORM and PALM), light source 410 can include two lasers for charge state control. For example, a pump laser above 579 nm wavelength and a reset laser approximately equal to 450 nm can be used.

In certain embodiments, light from the light source 410 can be reflected or otherwise manipulated with one or more dichroic and/or flip mirrors and/or filters (441, 446, 440, 445), which can be reflective over certain wavelength ranges and transparent over others. For example, a mirror 441 can be used to reflect focused field light 411 from the focused field laser 415. In like manner, mirror 446 can be used to reflect broad field light 412 from broad field laser 416. A dichroic mirror 440 can reflect the incident light (e.g., 411 or 412) to the sample 420, e.g., in connection with conventional microscopy optics 455. That is, dichroic mirror 440 can be reflective over a wavelength range of the incident light. Additionally, Dichroic mirror 440 can, for example, be transparent over a wavelength range corresponding to a fluorescent response 413 of the NV centers, which ca be, for example, between approximately 637 nm and approximately 800 nm.

As noted above, optically exciting the NV centers can drive the NV centers into an excited E state, which can then relax back down to the A ground state (i.e., the NV centers can absorb photons with a wavelength around 532 nm and emit a fluorescent response, which can be between 637 and 800 nm). The transition between the ground state to the excited state can be spin conserving. However, the

NY02:757642.1 relaxation pathway through spin-dependent intersystem crossing ( A) between excited state (³E) triplet to a metastable, dark singlet level (³A) can change the integrated fluorescent response for the spin states | θ) and |± l . Because deshelving from the singlet occurs primarily to the 10) spin state, continuous optical pumping can provide a means to polarize the NVC to the ( o) spin state. Moreover, relaxation through the spin-dependent intersystem crossing does not emit a photon in the visible spectrum. Thus, the fluorescent response of the system can correspond to populations of j 0) and

I ± l spin states, where an increase in the m_s = ±1 populations correspond to a lower intensity fluorescent response.

Accordingly, the nitrogen vacancy centers can be "switched" from a dark state to a bright state or from a bright state to a dark state by applying at least one microwave pulse (340). Applying a microwave pulse equal to the field splitting frequency of a nitrogen vacancy center can drive the spin state from the m_s = 0 state to the m_s = ±1 state. For example, assuming degeneracy of the m_s = ±1 states (i.e., without application of a magnetic field or certain other factors), the field splitting frequency can be equal to approximately 2.87 GHz, Thus, applying approximately a 2.87 GHz microwave pulse to the nitrogen vacancy centers can increase the population of spin states toward the m_s = ±1. As noted above, in the presence of magnetic field 470, the degeneracy of the m_s = ±1 states is broken such that the m_s = - 1 state corresponds to a certain field splitting frequency and the m_s= +1 state corresponds to another field splitting frequency (the frequency depending on the orientation of the NV axis with respect to the magnetic field 470. That is, the electron spin resonance (ESR) spectrum includes two dips (i.e., dark "spots") corresponding to the m_s = +1 and the m_s = -1 spin states, as illustrated in Fig. 1 as spectrum 190.

Because the field splitting frequency corresponds to the orientation of the NV axis with respect to the magnetic field 470, individual NV centers can be uniquely addressed. For example, for a plurality of diamond nanocrystals, there can be a large number of unique orientations of NV centers with respect to the magnetic field 470, and thus individual NV centers can have a high probability of having a unique orientation, and thus a unique field splitting frequency.

The microwave pulse can be applied, for example, using a microwave emitter 460 such as a strip line or other suitable homogenously emitting antenna. The

NY02:757642.1 microwave emitter 460 can be coupled to a control unit 490 (connection not shown) or other suitable control instrumentation. The microwave emission can be tuned, e.g., using the control unit 490 to a predetermined frequency, such as corresponding to a field splitting frequency of the NV center.

In one embodiment, a microwave pulse can be tuned to a field splitting frequency of one of the nitrogen vacancy centers in the sample 420 (e.g., either to the m_s = +1 or the m_s = -1 state). This microwave pulse can increase the population of the m_s ~ ±1 states, and thus modulate the intensity of the fluorescent response 413.

Additionally, other microwave pulses can be tuned to a field splitting frequency of other NV centers in the sample 420. In certain embodiments, a plurality of microwave pulses can be applied to obtain a substantially full ESR spectrum of one or more NV centers.

The fluorescent response 213 of the nitrogen vacancy centers can be detected (350), and the fluorescent response 213 can be processed (360) to resolve at least one NV center. As disclosed herein, certain embodiments can enable the resolution of NV centers within a diffraction-limited spot (e.g., down to

approximately 30 nm). Detection of the fluorescent response can be accomplished, e.g., with an array of pixels 430, such as a CCD or emCCD array. In certain embodiments, the array of pixels 430 can include a 13x13 array over an area of 1 micron. Suitable magnification onto a CCD array (which can be, e.g., 512x512 or 1024x1024 pixels) can depend on the background noise and the expected number of photons for a given integration time. For a bright emitter such as the NV and using high-end CCDs, a magnification of approximately 16 μηι/85 and approximately 200x can be used. That is, for example, each pixel on the CCD can correspond to about 80 nm of the sample. Higher magnification can enhance measurements for higher-end array detectors with lower readout noise and dark counts, in accordance with

equation 2, below. In certain embodiments, a confocal scanning technique can be employed. In certain embodiments, a wide field of view can be captured. The control unit 490 can process the fluorescent response from the array of pixels 430 and generate a full ESR spectrum for each pixel. By one or more processors and/or other circuits in control unit 490, the spectrum can be fit with a sum of Lorentzian dips, and contrasts from the fits can be used as an intensity map for uniquely addressable NVs. In certain embodiments, the control unit 490 can also include one or more memories

NY02:757642.1 coupled to the one or more processors and/or other circuits including computer code, which when executed can cause the one or more processors to perform desired functions.

By comparing an image of an NV being resonantly driven with an image of an NV being off-resonantly driven, only the lowered fluorescence from the resonantly excited center is seen in the subtraction of the two images as shown in Fig l c. The signal to noise ratio of this subtracted image can be approximately given by « . ^mC ( 1) σ ^γτη{Μ -\) + γτη(\™0) where γ is the fluorescence rate, τ is the acquisition time, η is the collection efficiency, C is the fractional decrease of the total fluorescence on resonance, and M is the total number of emitters in a collection volume. For imaging with a two- dimensional CCD array, substitution of equation 1 into an analytical solution can provide a shot-noise-limited measurement error on the center of a two-dimensional Gaussian as:

where s is the standard deviation of the Gaussian distribution, N is the total number of signal photons collected, and a is the pixel size divided by the magnification.

Assuming no resonance lines and after an acquisition time of approximately 5 s, an NV center can be distinguished from a cluster of approximately 100 centers with a resolution Δχ of approximately 30 nm.

For purposes of illustration and not limitation, certain non-limiting examples of the disclosed subject matter will now be described in detail.

in one exemplary embodiment, a scanning confocal technique can be employed. For example, and not limitation, a confocal scan can include a 13 by 13 pixilated image over a square area of approximately 800 nm x 800 nm including two NV centers. With reference to Fig. 5, an exemplary ESR spectrum 510 can be generated. For each pixel, the microwave field can be scanned over three separate frequencies; the first resonant with one NV- center, the second being off resonant from both centers, and the third being resonant with the second NV center. One of ordinary skill in the art will appreciate that the order of frequencies can be varied.

NY02:757642.1 With the three intensity plots 520, each at different frequencies, the differences 530 between the intensity plots for each center can be generated. Using, e.g., a least squares method fitting routine 540, each NV center can be resolved 550. As illustrated in Fig, 5, the NV centers were resolved 195 nm apart with a resolution of 35 nm. In certain embodiments, the number of frequency steps per pixel can correspond to the number of NV centers contained within the scanning area.

Additionally, in certain embodiments, a full ESR spectrum can be generated for each pixel.

For purposes of illustration, and not limitation, a two-dimensional confocal scan with a total of m NV centers can be given by:

J(x, y, ω) = ; Ι,α, [1 - D. (P_RF , P_PUMP , <a)N, (x, y)] , (3) where / is intensity, a is collection efficiency; D,- is electron spin resonance dips; P_RF is power of the radio-frequency field; pump is the power of the optical 532 nm pump field; ω is the crystal field splitting frequency, and V is a two-dimensional Gaussian distribution with general defining parameters. In certain embodiments, a symmetric Gaussian (that is, with σ_χ = σ_γ ) can also be used for fitting the subtracted data. A confocal scan taken off resonance can be subtracted from a confocal scan taken on resonance to isolate only the photons emitted from the NVs with frequencies ω,, given by:

Ι(χ, )', ω₀ ) - I(x, y, a>_i) = I-afi, (P_RF , P_PUMP )N_t (x, y) (4)

Di can be given by:

Di(P_RF , P_pump , ce) = ^^Y' ^{l iy} , (5)

(r,- / 2) + (ω - ω_ί) where Qi( _RF, pump), H(PRF, pump), and a>. = ω₀ ± B · μ_{ , N,{x,y) can be given by:

A confocal scan can be performed and/or an emCCD array can be used to detect fluorescent responses of the nitrogen vacancy centers. In one embodiment, for example, for each pixel in the array, a microwave field applied can dwell upon

NY02:?57642. ] three separate frequencies: ω_{-1 ;} ω₀, and ω₊₁. Three intensity plots can be recorded, each corresponding to one of the three separate frequencies. That is, for each frequency, the array of pixels can record an intensity measurement at each pixel. By doing the subtraction I(x, y, a>₀)— I(x, y, (o_±1 ) , the same NV center can be isolated twice. In certain embodiments, the dwell time for each microwave emission can be approximately 200 ms.

In another exemplary embodiment, a wide-field imaging technique can be employed, in which an entire image, I(r,w), can be acquired simultaneously using a two-dimensional detector array. In this embodiment, total acquisition time can be significantly reduced relative to the confocal scanning technique described above.

For purposes of example, and not limitation, an emCCD array with a magnification of approximately 200x and a laser with power of approximately 1.25 kW/cm² can be used over a 60 um diameter field. The emCCD and magnification optics can be arranged such that each pixel of the emCCD array can correspond to 85 nra of a sample. As such, each diffraction-limited spot can be fully encapsulated in an image of approximately 7 x 7 pixels. Each capture can have an exposure time of, for example, 450 ms. Microwave emission can step between 2.65 GHz to 2.9 GHz, and the number of steps can be, for example, approximately 51. For example, the emCCD can capture one frame for each of 51 steps in a microwave frequency sweep. In certain embodiments, this can be repeated and averaged, e.g., approximately 10 times.

With reference to Fig. 6, the intensity of each NV can be plotted as a function of microwave frequency applied, depicting the ESR spectrum 610 across a large field of view. An image 620 can be generated over a wide field of view illustrated resolvable NV center areas. Moreover, within each resolved area, individual NVs can be resolved using a few frequency points that are resonant with the areas of interest, as illustrated in reconstructed graph 630.

In certain embodiments of the disclosed subject matter, pulsed measurements can be used over a wide fi eld of view. For example, in connection with, e.g., an intensified CCD (iCCD), dynamic decoupling techniques such as Rabi, Ramsey and/or Echo measurements of many NV centers can be utilized during confocal excitation and collection. In connection with such embodiments, such measurements can also be performed in parallel over a wide field of view using an iCCD or, in general, any array of detectors sensitive enough to detect single photons.

N ¥02:757642.1 In another exemplary embodiment, the techniques disclosed herein above can be used in connection with Forster resonance energy transfer (FRET) techniques to obtain nm-scale resolution. For example, a fluorophore with an absorption spectrum at least partially overlapping with the emission spectrum of the NV centers can be provided to a sample. The fluorescent response of the NV center can non-radiatively excite the fluorophore if the NV is within a certain distance of the fluorophore. The fluorescent response of the fluorophore can be detected, and proximity information between the NV and the fluorophore can be resolved. Such an energy transfer from the NV to the fluorophore can occur by a dipole-dipole coupling effect. For the FRET phenomenon described herein, transfer of more than 50% of the energy can occur, for example, when the distance between the two molecules fall within a Forster distance, which can be approximately 10 nm in length. Accordingly, the techniques disclosed herein can provide for resolution of the proximity of a NV and a fluorophore to on the order of tens of nanometers or less.

Additionally or alternatively, in connection with FRET techniques, the techniques disclosed herein can enable the determination of an orientation of a magnetic dipole of a molecule coupled to a fluorophore. Due to the strong magnetic moment of the electron, any nearby magnetic fields can induce a Zeeman splitting of the m_s = +1 and the m_s = -1 ground state levels. Such a Zeeman effect can be optically detected. Alternatively, sensitive measurement of magnetic fields with the NV centers can include a pulsed scheme such as spin-echo or dynamic decoupling techniques as disclosed herein.

Moreover, the techniques disclosed herein can further enable the probing of a local environment. For example, the presence of a local magnetic field, electric field, or inhomogeneous pH can alter the fluorescent response of the NV centers. Accordingly, changes in these environmental characteristics can be determined by observing differences in the fluorescent response of the NVs. Changes in the electron spin orientation or the charge state of the NV- can be measured by the fluorescence brightness and spectrum.

As described above in connection with certain embodiments, a control unit 490 is provided to process the fluorescent response from the array of pixels 430 and generate a full ESR spectrum for each pixel and fit the spectrum with a sum of Lorentzian dips, such that contrasts from the fits can be used as an intensity map for

NY02:757642. i uniquely addressable NVs. In these embodiments, the control unit 490 plays a significant role in enabling the resolution of nitrogen vacancy centers, e.g., below the diffraction limit. For example, the presence of the control unit 490 provides the ability to provide near real-time feedback to, e.g., the tunable microwave emitter, the light source, and provides the ability to isolate unique NV centers. Such techniques could not be preformed merely in the mind or with pen and paper.

The presently disclosed subject matter is not to be limited in scope by the specific embodiments herein. Indeed, various modifications of the disclosed subject matter in addition to those described herein will become apparent to those skilled in the art from the foregoing description and the accompanying figures. Such modifications are intended to fall within the scope of the appended claims.

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Claims

1. A method for resolving at least one nitrogen vacancy center, comprising:

providing at least one diamond structure with one or more nitrogen vacancy centers within a focal location, each being in either a dark state or a bright state;

applying a magnetic field across the at least one diamond structure; optically exciting the one or more nitrogen vacancy centers;

switching at least one nitrogen vacancy center from the dark state to the bright state or from the bright state to the dark state by applying at least one microwave pulse to the one or more nitrogen vacancy centers;

detecting a fluorescent response of each nitrogen vacancy center; and resolving at least one of the nitrogen vacancy centers based on the fluorescent response of each nitrogen vacancy center, the fluorescent response of each nitrogen vacancy center corresponding to its orientation relative to the magnetic field.

2. The method of claim 1, wherein the optically exciting includes directing a continuous wave of pump light at approximately 532 ran to the nitrogen vacancy center.

3. The method of claim 1, wherein the optically exciting includes applying a pulse of pump light at approximately 532 nm to the nitrogen vacancy center prior to applying the at least one microwave pulse, and applying a pulse of pump light at approximately 532 nm to the nitrogen vacancy center subsequent to applying the at least one microwave pulse.

4. The method of claim 1, wherein the providing at least one diamond structure with one or more nitrogen vacancy centers further comprises providing a plurality of nitrogen vacancy centers, at least some having differing orientations with respect to the magnetic field, whereby a spin sublevel of each nitrogen vacancy center experi ences a Zeeman splitting corresponding to the orientation of the nitrogen vacancy center with respect to the magnetic field.

5. The method of claim 4, wherein applying at least one microwave pulse further comprises tuning a first microwave pulse to a field splitting frequency of a

NY02:757642.1 first one of the nitrogen vacancy centers, thereby modulating the fluorescent response of the first one of the nitrogen vacancy centers.

6. The method of claim 5, wherein applying at least one microwave pulse further comprises tuning at least a second microwave pulse to a field splitting frequency of a second one of the nitrogen vacancy centers, thereby modulating the fluorescent response of the second one of the nitrogen vacancy centers.

7. The method of claim 6, wherein applying at least one microwave pulse farther comprises:

applying the first microwave pulse at a first frequency, the first frequency tuned to the field splitting frequency of the first one of the nitrogen vacancy centers;

applying the second microwave pulse at a second frequency, the second frequency tuned to the field splitting frequency of the second one of the nitrogen vacancy centers; and

applying at least a third microwave pulse at a third frequency, the third frequency tuned a frequency not corresponding to a field splitting frequency of either the first or the second one of the nitrogen vacancy centers.

8. The method of claim 6, wherein detecting the fluorescent response of each nitrogen vacancy center further comprises:

generating a first intensity plot of a first fluorescent response corresponding to the first frequency;

generating a second intensity plot of a second fluorescent response corresponding to the second frequency; and

generating at least a third intensity plot of a third fluorescent response corresponding to the third frequency.

9. The method of claim 8, wherein resolving the at least one nitrogen vacancy center includes determining the position of the first one of the nitrogen vacancy centers by subtracting the first and third intensity plots from the second intensity plot.

10. The method of claim 1, wherein applying at least one microwave pulse further includes continuously varying a frequency of a microwave emission.

1 1. The method of claim 1 , wherein the switching at least one nitrogen vacancy center and the detecting a florescent response further comprises applying a

NY02:757642.5 plurality of microwave pulses and detecting a plurality of fluorescent responses, corresponding to the plurality of microwave pulses, to obtain a full electron spin resonance spectrum for a plurality of locations of a sample; and wherein resolving at least one nitrogen vacancy center further comprises:

fitting the electronic spin resonance spectrum with a sum of Lorentzian dips;

generating an intensity map for the nitrogen vacancy center using contrasts from the fitted electron spin resonance spectrum.

12. The method of claim 1, wherein the focal location is a diffraction- limited area.

13. The method of claim 1, further comprising:

providing at least one fluorophore having an emission spectrum at least partially overlapping with an emission spectrum of the one or more nitrogen vacancy centers, wherein a fluorescent response of one of the nitrogen vacancy centers optically excites the fluorophore if the one of the nitrogen vacancy centers is within a threshold distance of fluorophore; and

detecting a fluorescent response of the fluorophore corresponding to the optical excitation of the one of the nitrogen vacancy centers.

14. The method of claim 13, further comprising determining a distance of one of the nitrogen vacancy centers from the fluorophore based on at least the fluorescent response of the one of the nitrogen vacancy centers and the fluorescent response of the fluorophore.

15. The method of claim 13, further comprising determining an orientation of a magnetic dipole of a molecule, the fluorophore coupled to the molecule, based on at least the fluorescent response of the one of the nitrogen vacancy centers and the fluorescent response of the fluorophore.

16. The method of claim 1, wherein the at least one diamond structure is exposed to an environment, wherein applying at least one microwave pulse includes applying two or more microwave pulses, each microwave pulse having a different frequency, and wherein detecting the fluorescent response of each nitrogen vacancy center includes detecting a fluorescent response corresponding to each microwave pulse, the method further comprising determining, based on the fluorescent response of each nitrogen vacancy center, a characteristic of the environment.

NY02:757642.1

17. The method of claim 16, wherein the characteristic of the environment includes local magnetic field, local electric field, or pH.

8. A system for resolving at least one nitrogen vacancy center within a focal location using an applied magnetic field, comprising:

a light source, operatively configured to excite the at least one nitrogen vacancy center in the presence of the applied magnetic field, thereby inducing the at least one nitrogen vacancy center to produce a fluorescent response;

a photodetector arranged to detect the fluorescent response, if any; a tunable microwave emitter arranged to apply at least one microwave pulse to the at least one nitrogen vacancy center; and

a control unit, coupled to the photodetector and the tunable microwave emitter, configured to adjust the frequency of the tunable microwave emitter, and configured to resolve the at least one nitrogen vacancy center based on the fluorescent response, the fluorescent response corresponding to its orientation relative to the magnetic field.

19. The system of claim 18, wherein the photodetector includes an array of pixels, and wherein the photodetector is further arranged to detect an intensity map of the fluorescent response across the array of pixels.

20. The system of claim 19, further comprising far- field optics to direct the fluorescent response to the photodetector.

21. The system of claim 20, wherein the focal location includes a diffraction-limited area, and wherein the array of pixels corresponds to at least the diffraction-limited area.

22. The system of claim 21, wherein the control unit is further configured to:

adjust the frequency of the tunable microwave emitter to a first frequency, the first frequency corresponding to an m_s = +1 spin sublevel field splitting frequency of the at least one nitrogen vacancy center;

adjust the frequency of the tunable microwave emitter to a second frequency, the second frequency corresponding to a zero field splitting frequency of the at least one nitrogen vacancy center; and

NY02:757642.1 adjust the frequency of the tunable microwave emitter to at least a third frequency, the third frequency corresponding to an m_s = -1 spin sublevel field splitting frequency of the at least one nitrogen vacancy center,

23. The system of claim 22, wherein the control unit is further configured to:

receive from the photodetector a first intensity plot of a first fluorescent response corresponding to the first frequency;

receive from the photodetector a second intensity plot of a second fluorescent response corresponding to the second frequency; and

receive from the photodetector at least a third intensity plot of a third fluorescent response corresponding to the third frequency; and

wherein the first, second, and third intensity plots include a

measurement of int ensity of the fluorescent response over the array of pixels.

24. The system of claim 23, wherein the control unit is further configured to resolve the at least one nitrogen vacancy center based on by subtracting the first and third intensity plots from the second intensity plot.

25. The system of claim 18, wherein the light source includes a laser adapted to continuously irradiate the at least one nitrogen vacancy center with approximately 532 nm light.

26. The system of claim 18, wherein the light source is coupled to the control unit, and wherein the light source includes a laser adapted to apply a pulse of pump light at approximately 532 nm to the at least one nitrogen vacancy center prior to application of the at least one microwave pulse, and adapted to apply a pulse of pump light at approximately 532 nm to the nitrogen vacancy center subsequent to application of the at least one microwave pulse.

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