A topological resonant cavity and a method for preparing a high-dimensional energy-time entangled source

Abstract

The present invention provides a topological resonant cavity and a method for preparing a high-dimensional energy-time entanglement source, comprising a topological straight waveguide and a triangular resonant cavity; wherein the topological straight waveguide comprises two valley photonic crystals distributed and arranged on both sides of the waveguide interface, and the structural parameters of the valley photonic crystals 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; wherein the triangular resonant cavity adopts one of the valley photonic crystals, which is arranged in the distribution arrangement of another valley photonic crystal. The topological resonant cavity is prepared based on a silicon-based chip, has excellent dispersion control capability, can optimize the generation efficiency of the four-wave mixing process, and realize high-dimensional energy-time entanglement.

Description

Technical Field

[0001] The present invention relates to the field of quantum communication, and in particular to a topological resonant cavity and a method for preparing a high-dimensional energy-time entangled source. Background Art

[0002] Quantum entanglement source is an indispensable part of quantum system. Based on the resonant cavity structure composed of third-order nonlinearity, the four-wave mixing process in the cavity is an effective solution to generate high-dimensional quantum entanglement source. The four-wave mixing process refers to the pump light (frequency ω p ) interacts with nonlinear materials to generate signal light (frequency ω S ) and idle light (frequency ω i ) is a nonlinear process. This process needs to satisfy the energy conservation condition (ω p =ω S +ω i ) and the momentum conservation condition and are the wave vectors corresponding to the pump light, signal light and idle light respectively.

[0003] Currently, researchers mainly use nonlinear optical crystals to prepare energy-time entangled photon pairs. However, nonlinear crystals are often large in size, incompatible with CMOS processes, and cannot be integrated on silicon-based chips. The generated entangled photon pairs are not bright enough, which is not conducive to building an integrated entangled source. In addition, in practical applications such as quantum sensing, communication, and imaging, many quantum entangled sources with the same characteristics are usually required. However, defects and irregularities are inevitable in the nano-processing process, and defects limit the scalability of such quantum entangled sources. Summary of the invention

[0004] In view of the defects in the prior art, the purpose of the present invention is to provide a topological resonant cavity and a method for preparing a high-dimensional energy-time entangled source.

[0005] According to one aspect of the present invention, a topological resonant cavity is provided, comprising a topological straight waveguide and a triangular resonant cavity, wherein:

[0006] The topological straight waveguide comprises a waveguide interface, and a first valley photonic crystal and a second valley photonic crystal distributed and arranged on both 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 to generate a topological band gap, thereby adjusting the working bandwidth of the topological straight waveguide.

[0007] The triangular resonant cavity adopts any one of the first valley photonic crystal and the second valley photonic crystal, and is arranged in a distribution arrangement of another valley photonic crystal different from the triangular resonant cavity.

[0008] Preferably, the unit cells of the first valley photonic crystal and the second valley photonic crystal are composed of two triangular holes of different sizes, and the symmetry of the two valley photonic crystals is spatially inverted.

[0009] Preferably, the structural parameters include the lattice constant a of the unit cell, the side lengths d1 and d2 of the triangular hole, and the perimeter L of the triangular resonant cavity.

[0010] Preferably, a pair of topological boundary states appear on the boundary between the first valley photonic crystal and the second valley photonic crystal, and the topological boundary states have opposite transmission directions;

[0011] The pump light is input from one port of the topological straight waveguide, and the generated signal light, idle light and remaining pump light are output from another port of the topological straight waveguide;

[0012] During the input and output process, the pump light that meets the resonant wavelength condition enters the triangular resonant cavity, and the pump light of other wavelengths cannot be coupled into the triangular resonant cavity.

[0013] Preferably, the resonance condition of the triangular resonant cavity is: the wavelength of the light retained in the cavity needs to satisfy that the optical path L around the cavity is equal to an integer multiple of the wavelength, that is, nL = m·λ m , where λ m represents the pump light wavelength that meets the resonance wavelength condition, m represents the quality factor of the topological resonant cavity obtained by calculation in the mth resonance mode, and n represents an integer.

[0014] Preferably, the pump light is coupled into the triangular resonant cavity by the topological straight waveguide. Due to the third-order nonlinear coefficient χ (3) , a nonlinear four-wave mixing process occurs in the triangular resonant cavity, that is, two pump light photons generate one signal light photon and one idle light photon; this process satisfies the energy matching condition ω p is the incident pump light frequency, ω s and ω i are the generated signal optical frequency and idle optical frequency respectively.

[0015] Preferably, when the frequencies ω of the signal light and the idle light S and ω i and arrival time t S and t i Satisfying the uncertainty relation Δ(ωs +ω i )Δ(t s -t i )<1, the signal light and the idle light are energy-time entangled.

[0016] 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 resonance peaks, and the signal light (|1> S ,|2> S ,|3> S ...) and idle light (|1> I ,|2> I ,|3> I …) satisfies the two-party entanglement relationship; the signal light and idle light generated by the four-wave mixing process can be distributed at any resonant frequency, and the distribution in the frequency dimension is high-dimensional, that is, high-dimensional energy-time entanglement.

[0017] Preferably, the pump light frequency ω P , signal light ω s and idle light i The frequencies are all within the working bandwidth of the topological straight waveguide; the pump light, signal light and idle light all have the topological protection characteristics of the topological boundary state and are robust to structural defects at corners.

[0018] According to a second aspect of the present invention, a method for preparing a high-dimensional energy-time entangled source based on the above-mentioned topological resonant cavity is provided, comprising:

[0019] Adjust the structural parameters of valley photonic crystals to achieve topological boundary states;

[0020] Incident pump light ω p The pump light that is incident on the topological straight waveguide interface and meets the resonant wavelength condition is coupled into the triangular resonant cavity;

[0021] Incident pump light ω p After the triangular resonant cavity undergoes a nonlinear spontaneous four-wave mixing process, a signal light ω of a high-dimensional energy-time entangled two-photon state is generated. s and idle light i .

[0022] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0023] 1. The topological resonant cavity in the embodiment of the present invention is prepared based on valley photonic crystals, forming a topological straight waveguide and a triangular resonant cavity; by adjusting the structural parameters of the valley photonic crystals, the entire topological resonant cavity has excellent dispersion control capability, and the expected working bandwidth of the topological straight waveguide is obtained, thereby providing rich spectrum resources.

[0024] 2. The topological resonant cavity in the embodiment of the present invention can improve the generation efficiency of the four-wave mixing process and realize broadband high-dimensional energy-time entanglement by optimizing the quality factor of the triangular resonant cavity.

[0025] 3. The topological resonant cavity and the method for preparing a high-dimensional energy-time entangled source in the embodiments of the present invention undergo a four-wave mixing process in the triangular resonant cavity. The generated signal light and idle light frequencies may be distributed on different resonant peaks. The signal light and the idle light satisfy the energy-time entanglement relationship, thereby realizing the acquisition of high-dimensional quantum entanglement.

[0026] 4. The topological resonant cavity and the method for preparing a high-dimensional energy-time entangled source in the embodiments of the present invention generate high-dimensional entangled photon pairs in the topological resonant cavity. Therefore, the entangled photon pairs are topologically protected and are robust to structural defects such as corners. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0028] Figure 1 A schematic diagram of the design of a triangular resonant cavity capable of generating a high-dimensional energy-time entanglement source and a topological waveguide for coupling in one embodiment of the present invention;

[0029] Figure 2 A schematic diagram of a valley photonic crystal structure of a topological resonant cavity that generates high-dimensional energy-time entanglement and a corresponding energy band structure in one embodiment of the present invention;

[0030] Figure 3 It is a schematic diagram of the energy conservation condition and momentum conservation condition of the four-wave mixing process in one embodiment of the present invention, and the principle of high-dimensional entanglement generated by four-wave mixing in the resonant cavity;

[0031] Figure 4 The transmission spectrum of a topological resonant cavity that generates high-dimensional energy-time entanglement in one embodiment of the present invention;

[0032] Figure 5 The electric field distribution at the resonant frequency of a topological resonant cavity that generates high-dimensional energy-time entanglement in one embodiment of the present invention;

[0033] Figure 6 The first embodiment of the present invention is a flow chart of a method for preparing a high-dimensional energy-time entangled source based on a topological resonant cavity. DETAILED DESCRIPTION

[0034] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0035] Reference Figure 1 As shown, 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 includes two valley photonic crystals VPC1 and VPC2 distributed and arranged on both sides of the waveguide interface, and the structural parameters of the valley photonic crystals are adjustable; the dispersion relation at the waveguide interface is adjusted 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 of the valley photonic crystals and is arranged in the distributed arrangement of another valley photonic crystal.

[0036] This embodiment is a resonant cavity that directly generates topologically protected high-dimensional energy-time entangled photon pairs. It has excellent dispersion control capabilities and can improve the generation efficiency of the four-wave mixing process by optimizing the quality factor of the triangular resonant cavity, thereby achieving broadband high-dimensional energy-time entanglement.

[0037] In a preferred embodiment of the present invention, the topological resonant cavity is composed of two valley photonic crystals (VPCs), namely VPC1 and VPC2, the unit cell of the VPC is composed of two triangular holes of different sizes, wherein the lattice symmetry of VPC1 and VPC2 is spatially inverted. Figure 2 As shown, the preferred lattice constant is a = 350nm. For VPC1, the preferred side length of the small triangular hole in the upper left corner is d1 = 0.3a, and the preferred side length of the large triangular hole in the lower right corner is d2 = 0.7a; for VPC2, the preferred side length of the large triangular hole in the upper left corner is d2 = 0.7a, and the preferred side length of the small triangular hole in the lower right corner is d1 = 0.3a. When the unit cells of VPC1 and VPC2 are arranged according to Figure 2When the arrangement is carried out according to the schematic diagram on the left in (a), a valley photonic crystal is formed. When the triangular holes in the unit cell are of the same size (d1=d2), the TE mode of the photonic crystal at the K point and the K′ point has a photonic Dirac cone, and the Dirac cone is protected by the time reversal and space reversal symmetry of the original lattice. When the initial unit cell is deformed into VPC1 and VPC2, the sign of the Berry curvature near the K and K′ points is opposite. Interchanging the sizes of the two holes will change the sign of the Berry curvature at the K and K′ points, which means that the two valley photonic crystals have different band topologies. The sign of the valley Chern number reflects the sign of the Berry curvature, and the difference in the valley Chern number represents the number of K (K′) valley boundary states. If the difference in the size of the two holes is very small, the valley Chern number can be quantized to 1 / 2 or -1 / 2. Therefore, according to the state-boundary correspondence principle, an interface can have at most one topological boundary state at each valley.

[0038] 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 obtained is as follows: Figure 2 As shown in (b). From the dispersion curve, we can see that a pair of topological boundary states appear in the photonic band gap with a frequency of 182-201THz. The pair of topological boundary states are located at k x >0 and k x <0, they have opposite valley spins, corresponding to opposite transport directions.

[0039] In a preferred embodiment of the present invention, both ports of the topological straight waveguide can be used as the input of pump light, and the generated signal light, idle light and remaining pump light are output from the other port. During the input and output process, the pump light that meets the resonant wavelength condition enters the triangular resonant cavity, and the pump light of other wavelengths cannot be coupled into the resonant cavity. Specifically, the resonant wavelength condition is: the wavelength of the light retained in the topological resonant cavity needs to satisfy the optical path L around the triangular resonant cavity is equal to an integer multiple of the wavelength, that is, nL = m·λ m , where λ m represents the pump light wavelength that satisfies the resonant wavelength condition, and n is an integer.

[0040] In a preferred embodiment of the present invention, due to the third-order nonlinear coefficient χ (3) , a nonlinear four-wave mixing process occurs in the triangular resonant cavity, and two pump light photons generate one signal light photon and one idle light photon. Figure 3 As shown, due to the resonant characteristics of the triangular resonant cavity, four-wave mixing can only occur at the resonant wavelength.

[0041] In a preferred embodiment of the present invention, the simulated topological resonant cavity transmission spectrum is as follows: Figure 4As shown in the figure, in the working bandwidth of the topological boundary state, there can be a number of equally spaced resonant modes. The pump light at this frequency can be coupled into the triangular resonant cavity, and the interval between each resonant mode is 0.9 THz. Due to the resonant condition of the resonant cavity, the wavelength of the light retained in the cavity must satisfy: the optical path L around the cavity is equal to an integer multiple of the wavelength, that is, nL = m·λ m , where λ m represents the wavelength of the pump light that can resonate, and m represents the quality factor (Q value) of the topological resonator obtained by calculation, which is 2×10 5 , n represents an integer.

[0042] In a preferred embodiment of the present invention, the electric field distribution of the topological resonant cavity at the resonant frequency is as follows: Figure 5 As shown, it can be seen that at this frequency, the pump light is coupled into the inside of the triangular resonant cavity, and the energy is mainly distributed at the boundary of the triangular resonant cavity.

[0043] In a preferred embodiment of the present invention, when the frequency of the pump light is equal to the frequency of the resonant mode, the pump light is coupled into the triangular resonant cavity, and a four-wave mixing effect occurs in the topological microcavity to generate signal light and idle light. The process satisfies the relationship between energy conservation and momentum conservation, that is, and The Hamiltonian of four-wave mixing can be expressed as:

[0044] H=H L +H NL (1)

[0045] Among them, H L and H NL are the linear Hamiltonian and the nonlinear Hamiltonian, respectively.

[0046]

[0047] where ω j is the frequency at the resonance peak, and are the photon creation and annihilation operators at the resonant frequency, respectively.

[0048]

[0049] γ0 is the effective coupling coefficient, ω p ,ω s and ω i are the frequencies of pump light, signal light and idle light respectively, and are the generation operators of signal light and idle light respectively, and are the annihilation operators of the signal light and the idle light, respectively, kp , k s and k i are the wave vectors corresponding to the pump light, signal light and idle light, respectively, x is the transmission path length, and hc represents the Hermitian conjugation. The two-photon state generated by four-wave mixing is:

[0050]

[0051] ω s and ω i are the frequencies of the signal light and the idle light, respectively, A(ω s ,ω i ) is the joint spectral amplitude (JSA) of the signal light and the idle light, and are the generation operators of signal light and idle light respectively, |0> is the vacuum state.

[0052] In a preferred embodiment of the present invention, a nonlinear four-wave mixing process occurs in the triangular resonant cavity, two pump light photons generate one signal light photon and one idle light photon, and the process satisfies the energy conservation condition (2ω P =ω S +ω I ) and the momentum conservation condition The generated signal light and idle light are distributed as follows Figure 2 As shown, they are located on both sides of the pump light. S and ω I ) and arrival time (t S and t I ) satisfies the uncertainty relation, the signal light and the idle light are energy-time entangled. For the energy-time entangled two-photon state, the inequality Δ(ω s +ω i )Δ(t s -t i )<1.

[0053] 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 resonance peaks. S ,|2> S ,|3> S ...) and idle light (|1> I ,|2〉 I ,|3> I …) satisfies the entanglement relationship between the two parties, but the distribution in the frequency dimension is high-dimensional, so it is also called high-dimensional energy-time entanglement. Among them, the arrival time refers to the time point when the signal light and the idle light arrive after transmitting the same length of path.

[0054] In a preferred embodiment of the present invention, the pump light frequency ω P , signal light ω s and idle light i The frequencies of the topological straight waveguides are all within the working bandwidth of the topological straight waveguides; the pump light, signal light, and idle light all have the topological protection characteristics of the topological boundary states and are robust to structural defects at corners. The bandwidth of the high-dimensional quantum entangled photon pairs generated in the topological resonant cavity can be as high as 20 THz, providing rich spectrum resources.

[0055] Based on the same inventive concept, in other embodiments of the present invention, a method for preparing a high-dimensional energy-time entangled source based on a topological resonant cavity is provided, see Figure 6 The process includes:

[0056] S100, adjusting the structural parameters of the valley photonic crystal to achieve topological boundary states;

[0057] S200, incident pump light ω p When the pump light is incident on the topological straight waveguide interface and meets the resonant wavelength condition, it can be coupled into the triangular resonant cavity.

[0058] S300, incident pump light ω p After the nonlinear spontaneous four-wave mixing process in the triangular resonant cavity, the signal light ω of the high-dimensional energy-time entangled two-photon state is generated. s and idle light i .

[0059] In this embodiment, a four-wave mixing process occurs in the resonant cavity, and the generated signal light and idle light frequencies may be distributed on different resonant peaks. Each pair of signal light and idle light satisfies the energy-time entanglement relationship, and high-dimensional quantum entanglement is obtained. The high-dimensional entangled photon pairs generated in this embodiment are generated in the topological resonant cavity, so the entangled photon pairs are topologically protected and robust to structural defects such as corners.

[0060] The robustness in topological photonics is combined with the preparation of integrated quantum entangled sources on silicon-based chips to solve the high loss problem faced in the preparation and transmission of quantum entangled sources, and realize the content of topological photonics from a new quantum perspective. The high-dimensional energy-time entangled source prepared using silicon-based chip photonic crystals is topologically protected and robust to defects such as corners. It will bring innovative improvements to the performance of quantum systems and greatly enrich the practical application scenarios of quantum systems, such as quantum walks, robust quantum light sources, low-loss integrated quantum devices, and the realization of quantum teleportation.

[0061] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various modifications or variations within the scope of the claims, which does not affect the essence of the present invention. The above preferred features can be used in any combination without conflicting with each other.

Claims

1. A topological resonant cavity, characterized in that: It includes a topological straight waveguide and a triangular resonant cavity, where: The topological straight waveguide comprises a waveguide interface, and a first valley photonic crystal and a second valley photonic crystal distributed and arranged on both 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 to generate a topological band gap, thereby adjusting the working bandwidth of the topological straight waveguide. The triangular resonant cavity adopts any one of the first valley photonic crystal and the second valley photonic crystal, and is arranged in a distribution arrangement of another valley photonic crystal different from the triangular resonant cavity; A pair of topological boundary states appear at the boundary between the first valley photonic crystal and the second valley photonic crystal, and the topological boundary states have opposite transmission directions; The pump light is input from one port of the topological straight waveguide, and the generated signal light, idle light and remaining pump light are output from another port of the topological straight waveguide; During the input and output process, the pump light that meets the resonant wavelength condition enters the triangular resonant cavity, and the pump light of other wavelengths cannot be coupled into the triangular resonant cavity; The resonance condition of the triangular resonant cavity is: the wavelength of the light retained in the cavity needs to satisfy the optical path L around the cavity is equal to an integer multiple of the wavelength, that is, nL = m·λ m , where λ m represents the pump light wavelength that meets the resonant wavelength condition, m represents the quality factor of the topological resonant cavity obtained by calculation in the mth resonant mode, and n represents an integer; The pump light is coupled into the triangular resonant cavity by the topological straight waveguide. Due to the third-order nonlinear coefficient χ (3) , a nonlinear four-wave mixing process occurs in the triangular resonant cavity, that is, two pump light photons generate one signal light photon and one idle light photon; this process satisfies the energy matching condition ω p is the incident pump light frequency, ω s and ω i are the generated signal optical frequency and idle optical frequency respectively; When the frequencies of the signal light and the idle light ω S and ω i and arrival time t S and t i Satisfying the uncertainty relation Δ(ω s +ω i )Δ(t s -t i )<1, the signal light and the idle light are energy-time entangled; 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 resonance peaks. S ,|2> S ,|3> S ...) and idle light (|1> I ,|2> I ,|3> I …) satisfies the two-party entanglement relationship; the signal light and idle light generated by the four-wave mixing process can be distributed at any resonant frequency, and the distribution in the frequency dimension is high-dimensional, that is, high-dimensional energy-time entanglement.

2. A topological resonant cavity according to claim 1, characterized in that: The unit cells of the first valley photonic crystal and the second valley photonic crystal are composed of two triangular holes of different sizes, and the symmetry of the two valley photonic crystals is spatially inverted.

3. A topological resonant cavity according to claim 2, characterized in that: The structural parameters include the lattice constant a of the unit cell, the side lengths d1 and d2 of the triangular hole, and the perimeter L of the triangular resonant cavity.

4. A topological resonant cavity according to claim 1, characterized in that: Pump light frequency ω P , signal light ω s and idle light i The frequencies are all within the working bandwidth of the topological straight waveguide; the pump light, signal light and idle light all have the topological protection characteristics of the topological boundary state and are robust to structural defects at corners.

5. A method for preparing a high-dimensional energy-time entangled source based on the topological resonant cavity according to any one of claims 1 to 4, characterized in that: include: Adjust the structural parameters of valley photonic crystals to achieve topological boundary states; Incident pump light ω p The pump light that is incident on the topological straight waveguide interface and meets the resonant wavelength condition is coupled into the triangular resonant cavity; Incident pump light ω p After the triangular resonant cavity undergoes a nonlinear spontaneous four-wave mixing process, a signal light ω of a high-dimensional energy-time entangled two-photon state is generated. s and idle light i .

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