CN115729012A - Topological resonant cavity and preparation method of high-dimensional energy-time entanglement source - Google Patents
Topological resonant cavity and preparation method of high-dimensional energy-time entanglement source Download PDFInfo
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Abstract
The invention provides a topological resonant cavity and a preparation method of a high-dimensional energy-time entanglement source, which comprises a topological straight waveguide and a triangular resonant cavity; the topological straight waveguide comprises two valley photonic crystals which are distributed and arranged on two sides of a waveguide interface, and the structural parameters of the valley photonic crystals are adjustable; adjusting the dispersion relation at the waveguide interface by adjusting the structural parameters to generate a topological band gap and adjust the working bandwidth of the topological straight waveguide; the triangular resonant cavity adopts one valley photonic crystal and is arranged in the distribution arrangement of the other valley photonic crystal. The topological resonant cavity is prepared on the basis of a silicon-based chip, has excellent dispersion regulation and control capability, can optimize the generation efficiency of a four-wave mixing process, and realizes high-dimensional energy-time entanglement.
Description
Technical Field
The invention relates to the field of quantum communication, in particular to a topological resonant cavity and a preparation method of a high-dimensional energy-time entanglement source.
Background
Quantum entanglement sources are an integral part of quantum systems. Base ofThe resonant cavity structure formed by three-order nonlinearity generates a four-wave mixing process in the cavity, and is an effective scheme for generating a high-dimensional quantum entanglement source. The four-wave mixing process refers to the pumping light (frequency is omega) in the third-order nonlinear material p ) Interacts with nonlinear material to generate signal light (with frequency omega) S ) And idle light (frequency omega) i ) The non-linear process of (2). The process needs to satisfy the energy conservation condition (ω) p ＝ω S +ω i ) And condition of conservation of momentum
And
the wave vectors corresponding to the pump light, the signal light and the idle light respectively.
At present, researchers mainly use nonlinear optical crystals to prepare energy-time entangled photon pairs, however, nonlinear crystals are often large in size, incompatible with CMOS (complementary metal oxide semiconductor) processes, and cannot realize integration on a silicon-based chip, and the generated entangled photon pairs are not enough in brightness and are not beneficial to constructing an integrated entangled source. Furthermore, in practical applications such as quantum sensing, communication and imaging, many quantum entanglement sources with the same characteristics are usually required. However, defects and irregularities are unavoidable during nanofabrication, which limits the scalability of such quantum entanglement sources.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a topological resonant cavity and a preparation method of a high-dimensional energy-time entanglement source.
According to an aspect of the present invention, there is provided a topological resonant cavity comprising a topological straight waveguide and a triangular resonant cavity, wherein:
the topological straight waveguide comprises a waveguide interface, a first valley photonic crystal and a second valley photonic crystal which are distributed and arranged on two sides of the waveguide interface, the structural parameters of the first valley photonic crystal and the second valley photonic crystal are adjustable, the dispersion relation at the waveguide interface is adjusted by adjusting the structural parameters, a topological band gap is generated, and the working bandwidth of the topological straight waveguide is adjusted;
the triangular resonant cavity adopts any one of the first valley photonic crystal and the second valley photonic crystal, and is arranged in the distribution arrangement of the other valley photonic crystal different from the triangular resonant cavity.
Preferably, the unit cells of the first and second valley photonic crystals are formed by two triangular holes with different sizes, and the symmetry of the two valley photonic crystals is inverted spatially.
Preferably, the structural parameters include a lattice constant a of the unit cell, and a side length d of the triangular hole 1 And d 2 And the perimeter L of the triangular resonator cavity.
Preferably, a pair of topological boundary states appears on the boundaries of the first and second valley photonic crystals, the topological boundary states having opposite transmission directions;
pump light is input from one port of the topological straight waveguide, and generated signal light, idle light and residual pump light are output from the other port of the topological straight waveguide;
in the input and output processes, the pump light meeting the resonance wavelength condition enters the triangular resonant cavity, and the pump light with the other wavelengths cannot be coupled into the triangular resonant cavity.
Preferably, the resonance condition of the triangular resonant cavity is as follows: the wavelength of the light remaining in the cavity is such that the optical path length L around the cavity is equal to an integer multiple of the wavelength, i.e. nL = m · λ m Wherein λ is m And the wavelength of the pump light meeting the resonance wavelength condition is shown, m represents the quality factor of the topological resonant cavity obtained by calculating the mth resonance mode, and n represents an integer.
Preferably, the pump light is coupled into the triangular resonant cavity by the topological straight waveguide due to a third-order nonlinear coefficient χ of a valley photonic crystal silicon material (3) A nonlinear four-wave mixing process occurs in the triangular resonant cavity, namely two pump light photons generate a signal light photon and an idle light photon; this processSatisfy the energy matching condition
ω p For the frequency, omega, of the incident pump light s And omega i Respectively, the generated signal light frequency and the idle light frequency.
Preferably, the frequencies ω of the signal light and the idle light S And omega i And time of arrival t S And t i Satisfy the uncertainty relation delta (omega) s +ω i )Δ(t s -t i )<At 1, there is an energy-time entanglement between the signal light and the idle light.
Preferably, when a four-wave mixing process occurs in the triangular resonant cavity, the frequencies of the signal light and the idle light generated by the four-wave mixing process can be distributed on different resonant peaks, and the signal light (| 1)> S ，|2> S ，|3> S \8230;) and idle light (| 1)> I ，|2> I ，|3> I 8230), satisfies the entanglement relationship of two parties; the signal light and idle light generated by this four-wave mixing process can be distributed at any resonant frequency, with the distribution in the frequency dimension being high-dimensional, i.e., high-dimensional energy-time entanglement.
Preferably, the pump light frequency ω P Signal light omega s And an idle light omega i All located within the operating bandwidth of said topologically straight waveguide; the pump light, the signal light and the idle light have the topological protection characteristic of a topological boundary state, and have robustness on structural defects of corners.
According to a second aspect of the present invention, there is provided a method for preparing a high-dimensional energy-time entanglement source based on the topological resonant cavity, comprising:
adjusting the structural parameters of the valley photonic crystal to realize a topological boundary state;
incident pump light omega p The pump light which is normally incident to a topological straight waveguide interface and meets the resonance wavelength condition is coupled into the triangular resonant cavity;
incident pump light omega p After the triangular resonant cavity is subjected to a nonlinear spontaneous four-wave mixing process, signal light omega in a high-dimensional energy-time entangled two-photon state is generated s And an idle light omega i 。
Compared with the prior art, the invention has at least one of the following beneficial effects:
1. the topological resonant cavity in the embodiment of the invention is prepared on the basis of valley photonic crystals, and a topological straight waveguide and a triangular resonant cavity are formed; by adjusting the structural parameters of the valley photonic crystal, the whole topological resonant cavity has excellent dispersion regulation and control capability, and the expected working bandwidth of the topological straight waveguide is obtained, so that abundant spectrum resources are provided.
2. The topological resonant cavity in the embodiment of the invention can improve the generation efficiency of the four-wave mixing process by optimizing the quality factor of the triangular resonant cavity, and realize high-dimensional energy-time entanglement of a broadband.
3. According to the topological resonant cavity and the high-dimensional energy-time entanglement source preparation method, a four-wave mixing process is generated in the triangular resonant cavity, the frequency of generated signal light and idle light can be distributed on different resonant peaks, the signal light and the idle light meet the energy-time entanglement relation, and the acquisition of high-dimensional quantum entanglement is realized.
4. According to the topological resonant cavity and the high-dimensional energy-time entanglement source preparation method, the generated high-dimensional entangled photon pairs are generated in the topological resonant cavity, so that the entangled photon pairs are protected by topology and have robustness on structural defects such as corners and the like.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic diagram of a triangular resonator cavity and a topological waveguide design for coupling that can generate a high-dimensional energy-time entanglement source according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a valley photonic crystal structure and corresponding band structure of a topological resonator for producing high-dimensional energy-time entanglement in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of the energy and momentum conservation conditions of the four-wave mixing process and the high-dimensional entanglement of the resonant cavity caused by the four-wave mixing according to an embodiment of the present invention;
FIG. 4 is a transmission spectrum of a topological resonator that produces high dimensional energy-time entanglement in an embodiment of the present invention;
FIG. 5 is an electric field distribution at a resonant frequency of a topological resonator that produces high dimensional energy-time entanglement in an embodiment of the present invention;
FIG. 6 is a flow chart of a method for preparing a high-dimensional energy-time entanglement source based on a topological resonant cavity in an example of the invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.
Referring to fig. 1, the present invention provides an embodiment, a topological resonant cavity, including a topological straight waveguide and a triangular resonant cavity; wherein the topological straight waveguide comprises two valley photonic crystals VPC distributed and arranged on two sides of the waveguide interface 1 And VPC 2 The structural parameters of the valley photonic crystal are adjustable; adjusting the dispersion relation at the interface of the waveguide by adjusting the structural parameters to generate a topological band gap and adjust the working bandwidth of the topological straight waveguide; the triangular resonant cavity adopts one kind of valley photonic crystal and is arranged in the distribution arrangement of the other kind of valley photonic crystal.
The embodiment is a resonant cavity for directly generating a topology-protected high-dimensional energy-time entangled photon pair, has excellent dispersion regulation and control capability, and can improve the generation efficiency of a four-wave mixing process and realize broadband high-dimensional energy-time entanglement by optimizing the quality factor of a triangular resonant cavity.
In a preferred embodiment of the present invention, the topological cavity is composed of two Valley Photonic Crystals (VPCs), each VPC 1 And VPC 2 The VPC cell is formed by two triangular holes of different sizes, wherein the VPC cell is formed by two triangular holes of different sizes 1 And VPC 2 Is spatially inverted. As shown in fig. 2, the preferred lattice constant is a =350nm for VPC 1 The preferred side length of the small triangular hole at the upper left corner is d 1 =0.3a, preferred side length of large triangular hole in lower right corner is d 2 =0.7a; for VPC 2 The preferred side length of the large triangular hole at the upper left corner is d 2 =0.7a, preferred side length of small triangular hole in lower right corner is d 1 =0.3a. When the handle VPC 1 And VPC 2 When the unit cells of (a) are arranged as shown schematically in the left side of fig. 2, a valley photonic crystal is formed. When the triangular holes in the unit cell are the same size (d) 1 ＝d 2 ) In the TE mode of the photonic crystal at K point and K' point, photon Dirac cones are provided, and the Dirac cones are protected by the time reversal and space reversal symmetry of the original crystal lattice. When the initial cell is deformed to VPC 1 And VPC 2 When the Berry curvature signs near points K and K 'are opposite, interchanging the dimensions of the two holes changes the Berry curvature signs at points K and K', which means that the two valley photonic crystals have different band topologies. The sign of the valley old number reflects the sign of the Berry curvature, and the difference of the valley old number indicates the number of K (K') valley boundary states. If the size difference of the two holes is small, the valley old number may be quantized to 1/2 or-1/2. Therefore, according to the body state-boundary correspondence principle, at most one topological boundary state can exist in each valley of one interface.
In a preferred embodiment of the present invention, the dispersion curve corresponding to the valley photonic crystal is calculated by finite element simulation software, and the result is shown in fig. 2 (b). As can be seen from the dispersion curve, a pair of topological boundary states appears in the photonic bandgap with the frequency of 182-201THz, and the pair of topological boundary states are respectively positioned at k x >0 and k x <At 0, they have opposite valley spins, corresponding to opposite transmission directions.
In a preferred embodiment of the inventionBoth ports of the topological straight waveguide can be used as the input of pump light, and the generated signal light, idle light and the rest of the pump light are output from the other port. In the input and output processes, the pump light meeting the resonance wavelength condition enters the triangular resonant cavity, and the pump light with other wavelengths cannot be coupled into the resonant cavity. Specifically, the resonance wavelength conditions are: the wavelength of the light retained in the topological resonant cavity needs to satisfy that the optical path L around the triangular resonant cavity is equal to integral multiple of the wavelength, namely nL = m.lambda m Wherein λ is m Denotes the wavelength of the pump light satisfying the resonance wavelength condition, and n is an integer.
In a preferred embodiment of the present invention, the third-order nonlinear coefficient χ is due to the valley photonic crystal silicon material (3) And a nonlinear four-wave mixing process occurs in the triangular resonant cavity, and two pump light photons generate a signal light photon and an idle light photon. As shown in fig. 3, four-wave mixing is only possible at the resonant wavelength due to the resonant characteristics of the triangular resonator.
In a preferred embodiment of the present invention, the simulated transmission spectrum of the topological resonant cavity is as shown in fig. 4, and resonant modes distributed at equal intervals can appear in the working bandwidth of the topological boundary state, the pump light at the frequency can be coupled into the triangular resonant cavity, and the interval of each resonant mode is 0.9THz. Due to the resonance condition of the resonant cavity, i.e. the wavelength of the light remaining in the cavity, it is necessary to satisfy: the optical path length L around the cavity is equal to an integer multiple of the wavelength, i.e. nL = m · λ m Wherein λ is m Represents the wavelength of the pump light which can resonate, m represents the quality factor (Q value) of the topological resonant cavity obtained by calculating the mth resonant mode and is 2 multiplied by 10 5 And n represents an integer.
In a preferred embodiment of the invention, the electric field distribution of the topological resonator at the resonant frequency is shown in fig. 5, where it can be seen that the pump light is coupled into the inside of the triangular resonator, with the energy being distributed mainly at the boundaries of the triangular resonator.
In a preferred embodiment of the invention, the pump light is coupled to the resonant mode when the frequency of the pump light is equal to the frequency of the resonant modeInside the triangular resonant cavity, a four-wave mixing effect occurs in the topological microcavity to generate signal light and idle light, and the process meets the relation of energy conservation and momentum conservation, namely
And with
The Hamiltonian of the four-wave mixing can be expressed as:
H＝H L +H NL (1)
wherein H L And H NL Linear and non-linear hamiltonian quantities, respectively.
Wherein omega j Is the frequency at the resonance peak and is,
and
respectively, the generation and annihilation operators of photons at the resonant frequency.
γ 0 Is the effective coupling coefficient, ω p 、ω s And ω i The frequencies of the pump light, the signal light and the idle light respectively,
and
generating operators for the signal light and the idle light respectively,
and
annihilation operators, k, of signal light and idler light, respectively p ，k s And k i Wave vectors corresponding to the pump light, the signal light and the idle light respectively, x is the length of a transmission path, and h.c. represents hermitian conjugation. The two-photon states produced by four-wave mixing are:
ω s and omega i Frequencies of signal light and idle light, A (omega) s ,ω i ) The combined Spectral Amplitude of the signal light and the idler light (JSA),
and
operators for signal light and idle light, |0>Is in a vacuum state.
In a preferred embodiment of the invention, a nonlinear four-wave mixing process occurs in the triangular resonator, two pump photons produce a signal photon and an idle photon, and the process satisfies the energy conservation condition (2 ω) P ＝ω S +ω I ) And condition of conservation of momentum
The generated signal light and the idle light are distributed on both sides of the pump light as shown in fig. 2. Frequency of signal light and idle light (omega) S And omega I ) And time of arrival (t) S And t I ) When the uncertainty relationship is satisfied, there is an energy-time entanglement between the signal light and the idle light. For energy-time entangled two-photon states, the inequality Δ (ω) is usually satisfied s +ω i )Δ(t s -t i )<1。
In a preferred embodiment of the present invention, the frequencies of the signal light and the idle light generated by the four-wave mixing process may be distributed on different resonant peaks, i.e., |1> S ，|2> S ，|3> S \8230;) and idle light (| 1)> I ，|2〉 I ，|3> I 8230), satisfies the two-dimensional entanglement relationship, but the distribution in the frequency dimension is high-dimensional, and is therefore also referred to as high-dimensional energy-time entanglement. The reaching time refers to a time point reached after the signal light and the idle light transmit the same length path.
In a preferred embodiment of the invention, the pump light frequency ω is P Signal light omega s And an idle light omega i Are all located within the operating bandwidth of the topologically straight waveguide; the pump light, the signal light and the idle light have the topological protection characteristic of a topological boundary state, and have robustness on structural defects of corners. The high-dimensional quantum entangled photon bandwidth generated in the topological resonant cavity can be up to 20THz, providing abundant spectral resources.
Based on the same inventive concept, in other embodiments of the present invention, a method for preparing a topological resonant cavity based high-dimensional energy-time entanglement source is provided, and referring to fig. 6, the process includes:
s100, adjusting the structural parameters of the valley photonic crystal to realize a topological boundary state;
s200, pump light omega is incident p The pump light which is normally incident to the topological straight waveguide interface and meets the resonance wavelength condition can be coupled into the triangular resonant cavity.
S300, pump light omega is incident p After nonlinear spontaneous four-wave mixing process in the triangular resonant cavity, signal light omega with high dimensional energy-time entangled two-photon state is generated s And an idle light omega i 。
In the embodiment, a four-wave mixing process occurs in the resonant cavity, the frequencies of the generated signal light and the idle light may be distributed on different resonant peaks, and each pair of the signal light and the idle light satisfies an energy-time entanglement relationship, so that the acquisition of high-dimensional quantum entanglement is realized. The high-dimensional entangled photon pair generated by the embodiment is generated in the topological resonant cavity, so that the entangled photon pair is protected topologically and has robustness to structural defects such as corners and the like.
Robustness in topological photonics is combined with preparation of an integrated quantum entanglement source on a silicon-based chip, the problem of high loss in the preparation and transmission processes of the quantum entanglement source is solved, and the content of the topological photonics is realized from a new quantum angle. The high-dimensional energy-time entanglement source prepared by the silicon-based chip photonic crystal is topologically protected and has robustness on defects such as corners and the like. Revolutionary promotion can be brought to the performance of the quantum system, and the practical application scenes of the quantum system are greatly enriched, such as quantum walking, robust quantum light sources, low-loss integrated quantum devices, realization of quantum invisible states and the like.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The above-described preferred features may be used in any combination without conflict with each other.
Claims (10)
1. A topological resonator comprising a topological straight waveguide and a triangular resonator, wherein:
the topological straight waveguide comprises a waveguide interface, a first valley photonic crystal and a second valley photonic crystal which are distributed and arranged on two sides of the waveguide interface, the structural parameters of the first valley photonic crystal and the second valley photonic crystal are adjustable, the dispersion relation at the waveguide interface is adjusted by adjusting the structural parameters, a topological band gap is generated, and the working bandwidth of the topological straight waveguide is adjusted;
the triangular resonant cavity adopts any one of the first valley photonic crystal and the second valley photonic crystal, and is arranged in the distribution arrangement of the other valley photonic crystal different from the triangular resonant cavity.
2. The topological resonant cavity of claim 1, wherein the unit cell of said first and second valley photonic crystals is formed by two triangular holes with different sizes, and the symmetry of the two valley photonic crystals is spatially inverted.
3. The topological resonator according to claim 2, wherein said structural parameters comprise lattice constant a of unit cell, side length d of triangular hole 1 And d 2 And the perimeter L of the triangular resonator cavity.
4. The topological resonant cavity of claim 1, wherein a pair of topological boundary states appears at the boundaries of said first valley photonic crystal and said second valley photonic crystal, said topological boundary states having opposite propagation directions;
pump light is input from one port of the topological straight waveguide, and generated signal light, idle light and residual pump light are output from the other port of the topological straight waveguide;
in the input and output processes, the pump light meeting the resonance wavelength condition enters the triangular resonant cavity, and the pump light with the other wavelengths cannot be coupled into the triangular resonant cavity.
5. The topological resonant cavity of claim 4, wherein the resonance condition of said triangular resonant cavity is: the wavelength of the light remaining in the cavity is such that the optical path length L around the cavity is equal to an integer multiple of the wavelength, i.e. nL = m · λ m Wherein λ is m And the wavelength of the pump light meeting the resonance wavelength condition is shown, m represents the quality factor of the topological resonant cavity obtained by calculating the mth resonance mode, and n represents an integer.
6. The topological resonant cavity of claim 4, wherein the pump light is coupled into the triangular resonant cavity by the topological straight waveguide due to a third-order nonlinearity χ of the valley photonic crystal silicon material (3) The non-linear four-wave mixing process occurs in the triangular resonant cavity, i.e. two pump light photon generationGenerating a signal photon and an idle photon; the process satisfies energy matching conditions
ω p For the frequency, omega, of the incident pump light s And ω i Respectively, the generated signal light frequency and the idle light frequency.
7. A topological cavity resonator according to claim 4 or 5, characterized in that when the frequencies ω of the signal light and the idle light are equal S And ω i And time of arrival t S And t i Satisfies the uncertainty relation Δ (ω) s +ω i )Δ(t s -t i )<At 1, there is an energy-time entanglement between the signal light and the idle light.
8. The topological resonant cavity of claim 6, wherein when a four-wave mixing process occurs in the triangular resonant cavity, frequencies of signal light and idle light generated by the four-wave mixing process can be distributed on different resonant peaks, and the signal light (| 1)> S ，|2> S ，|3> S \8230;) and idle light (| 1)> I ，|2> I ，|3> I 8230meet the entanglement relationship of two parties; the signal light and idle light generated by this four-wave mixing process can be distributed at any resonant frequency, with the distribution in the frequency dimension being high-dimensional, i.e., high-dimensional energy-time entanglement.
9. A topological resonator according to claim 4 or 5, characterized in that the pump light frequency ω is P Signal light omega s And an idle light omega i Are all located within the operating bandwidth of the topologically straight waveguide; the pump light, the signal light and the idle light have the topological protection characteristic of a topological boundary state, and have robustness on structural defects of corners.
10. A method for preparing a high-dimensional energy-time entanglement source based on the topological resonant cavity of any one of claims 1 to 9, comprising:
adjusting the structural parameters of the valley photonic crystal to realize a topological boundary state;
incident pump light omega p The pump light which is normally incident to the interface of the topological straight waveguide and meets the resonant wavelength condition is coupled into the triangular resonant cavity;
incident pump light omega p After the triangular resonant cavity is subjected to a nonlinear spontaneous four-wave mixing process, signal light omega in a high-dimensional energy-time entangled two-photon state is generated s And an idle light omega i 。
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