A device for generating entangled photons based on photonic crystals

Abstract

A device for generating entangled photons based on photonic crystals relates to the field of photon entanglement source technology. It includes a dielectric material layer with several lattices etched with paired elliptical holes. These lattices are periodically arranged on the dielectric material layer, each with the same structure and a period of 'a'. A single lattice unit is horizontally or vertically shifted a distance 'a' to completely overlap with the previous period, forming an array. The length and width of each lattice are both the length of a first period, as determined by requirements. Two through-hole elliptical holes are provided on each lattice, with the axial direction of the holes deflected upwards to the same side, and the upper and lower edges of the same elliptical hole deflected. When a linearly polarized single photon is incident perpendicularly on the device, a superposition state of left- and right-handed rotating light with opposite orbital angular momentum is generated, i.e., the entangled state of the single photon. By combining vertical and horizontal polarization with photonic crystals having different topological charges at the gamma point, all four Bell states can be generated, providing a possibility for angular momentum entanglement in quantum optics.

Description

Technical Field

[0001] This invention relates to the field of photon entanglement source technology, and in particular to a device for generating entangled photons based on a photonic crystal. Background Technology

[0002] Quantum entanglement, as a fundamental physical effect, has a wide range of applications, such as quantum imaging, quantum communication, and information computing. Entangled photons in space or angular domains are an essential resource for quantum applications.

[0003] Early methods for generating entangled photons largely relied on nonlinear crystals, but the large size and low generation efficiency of nonlinear crystals significantly impacted device miniaturization and efficiency. The research and development of optical metasurfaces offer new possibilities for generating entangled photons. Optical metasurfaces, composed of nanostructures, are thin-layer materials with subwavelength scale structures, allowing for precise control of the phase, amplitude, and polarization state of incident light in real space. By designing the geometry and material properties of the metasurface, the characteristics of photons can be modulated, thereby efficiently generating entangled photons in very thin layers. Existing technologies utilize photonic crystals to directly construct two-photon frequency and path super-entangled sources. For example, Chinese patent publications CN 111443548A and CN 111562708A disclose "Nonlinear Photonic Crystals and Their Two-Photon Frequency and Path Super-Entangled Generation Methods" and "Two-Photon Frequency and Discrete Path Super-Entangled Generation Methods of Nonlinear Photonic Crystals," respectively. However, these technologies primarily utilize nonlinear photonic crystals to directly construct two-photon frequency and path super-entangled sources.

[0004] The literature (DOI 10.1126 / science.aat9042) describes how each unit cell of a metasurface is rotated at a certain angle to form a PB phase plate. This causes circularly polarized light incident on the metasurface to generate a PB phase, resulting in cross-polarization and orbital angular momentum. If a linearly polarized single photon is incident on such a surface, a superposition state of left- and right-handed photons with opposite orbital angular momentum can be generated, i.e., an entangled state. This achieves entanglement of the spin and orbital angular momentum degrees of freedom of photons under both single-photon and two-photon incidence conditions. It offers advantages such as ultrathinness, small size, and high generation rate compared to nonlinear crystals.

[0005] The aforementioned methods utilize material nonlinear effects and spatial phase modulation of metasurfaces to obtain entangled states. However, research on obtaining entangled states using periodic photonic crystals is still limited. In recent years, the study of bound states in the continuous spectrum (BIC) and the discovery of the polarization distribution in the k-space of photonic crystals have enabled periodic photonic crystals to achieve PB phase modulation in k-space through polarization vortices around BIC points, providing a basis for using photonic crystals to control the polarization and phase of light. Currently, studies have reported the realization of highly polarized circularly polarized light and the optical spin Hall effect in photonic crystals fabricated with periodic structures. However, there are still few applications of obtaining entangled states using photonic crystals via single photons. Photonic crystals offer advantages such as flexible control over the optical field, ease of fabrication using mature etching methods, and the absence of a geometric center. These advantages can be leveraged to improve photonic crystal efficiency by reducing radiation channels and implementing multi-mode coupling. Summary of the Invention

[0006] The purpose of this invention is to address the problem of existing metasurface technologies requiring a geometric center for incident beams, and to provide a device based on photonic crystals to generate entangled photons. This device uses a single photon incident on the photonic crystal to generate entangled states of orbital angular momentum and spin angular momentum. By designing a periodic lattice structure, the phase and polarization of photons are controlled using the properties of momentum space, thus achieving the generation of entangled photon pairs. Due to the translational symmetry caused by the periodic lattice, the topological vortex point exists in momentum space; therefore, the incident beam does not need to be aligned with the vortex center in real space.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] A device for generating entangled photons based on photonic crystals includes: a dielectric material layer, on which a plurality of lattices with paired elliptical holes are provided, the plurality of lattices being periodically arranged on the dielectric material layer, each lattice having the same structure and a lattice period of 'a', and a single lattice unit being horizontally or vertically translated a distance 'a' to completely overlap with the previous period to form an array; the length and width of the lattice are both the length of the first period set according to requirements, and the lattice has two through elliptical holes, the axial direction of the elliptical holes being deflected upwards to the same side, and the upper and lower edges of the same elliptical hole being deflected; when a linearly polarized single photon is incident perpendicularly on the device, a superposition state of left- and right-handed rotating light with opposite orbital angular momentum is generated, that is, the entangled state of the single photon.

[0009] Furthermore, the cross-sectional shape of the lattice can be a regular quadrilateral.

[0010] Furthermore, the length and width of the lattice can both be 400-720nm, preferably 560nm; the thickness of the lattice is 400-600nm, preferably 600nm.

[0011] Furthermore, the semi-major axis of the elliptical hole can be 90-150 nm, preferably 120 nm, and the semi-minor axis of the elliptical hole can be 60-110 nm, preferably 80 nm.

[0012] Furthermore, the geometric centers of the two elliptical holes on the same lattice are 280 nm apart.

[0013] Furthermore, the distance between the upper and lower edges of the same elliptical hole is 15–45 nm, preferably 15 nm.

[0014] Furthermore, the number of lattice periods is at least 15 to avoid edge effects.

[0015] All of these parameters are adjusted according to the wavelength and the specific dielectric properties of the material. The cross-sectional shape of the crystal lattice can also be a regular hexagon. Depending on the design of different crystal lattice shapes, the shape of the through holes on the crystal lattice is adaptively adjusted to slightly break the symmetry while satisfying rotational symmetry. The ideal periodic structure is infinitely large, but in practical applications, the number of lattice periods is at least 15 to avoid edge effects.

[0016] The working principle of this invention is as follows:

[0017] Bound states (BICs) in the continuous spectrum are a common phenomenon in photonic crystals. In the momentum space of the BIC band structure of a photonic crystal, a BIC point corresponds to a polarization singularity. At this point, the polarization of a plane wave cannot be defined, therefore light cannot radiate in the form of a plane wave, resulting in an optical mode with an infinitely high quality factor Q. Every point in k-space outside of a BIC point corresponds to a specific polarization state of far-field radiation. These polarization states have a specific distribution in k-space and form a vortex around the BIC point, thus defining the topological charge number, or orbital number q, of the BIC point. This polarization distribution allows the photonic crystal to behave as a resonator with different polarizations for momentum in different planes. Therefore, a photonic crystal can serve as a highly anisotropic polarized optical device and can easily achieve the same effect as a metasurface (which modulates the phase of light in real space) through k-space optical field manipulation.

[0018] When a circularly polarized beam of light is incident perpendicularly on a photonic crystal at a frequency slightly deviating from the BIC point on the energy band, the beam can be decomposed into plane waves with different k-components. If it is a Gaussian beam, it corresponds to a circle centered at the gamma point in momentum space. These plane waves with different k-components will couple with the corresponding polarization states in k-space, producing a spin-orbit coupling effect. Part of the transmitted or reflected light will be cross-polarized, causing the left-hand and right-hand circularly polarized light to reverse. At the same time, it carries twice the orbital angular momentum of the polarization state near the gamma point, which is twice the number of times it orbits the gamma point. The orbital angular momentum carried by the left-hand and right-hand circularly polarized light has opposite signs: l = -2q for the left-hand circularly polarized light and l = 2q for the right-hand circularly polarized light.

[0019] When incident linearly polarized light, it can be considered as a superposition of left- and right-handed polarized light. Due to cross-polarization, it will produce left-handed light with l = -2q and right-handed light with l = 2q, respectively. To generate a photonic crystal that allows the angular momentum of photons to become entangled with their orbital angular momentum, l = ±1 is required, i.e., q = ±1 / 2. The topological charge of the BIC corresponding to the gamma point of the photonic crystal is a positive integer. To generate a topological charge of q = ±1 / 2 at the gamma point, it is necessary to slightly break the rotational symmetry of the periodic unit cell of the photonic crystal while maintaining the mirror symmetry of the unit cell. This splits the positive integer topological charge into half-charges symmetrically distributed on both sides of the kx axis. At the same time, the mirror symmetry in the z direction is broken, causing the two half-charges to be translated, moving one half-charge to the gamma point.

[0020] In summary, under such circumstances, when a linearly polarized single photon is incident perpendicularly on a photonic crystal, a superposition state of left- and right-handed rotating light with opposite orbital angular momentum can be generated, i.e., the entangled state of the single photon.

[0021] Compared with the prior art, the present invention has the following outstanding technical effects:

[0022] This invention constructs a periodic lattice arrangement structure. This structure allows incident linearly polarized single photons to exit in a superposition of left- and right-handed rotations with opposite orbital angular momentum. By using linearly polarized single photon states of a specific frequency as incident light and measuring the density matrix of the exiting photons, the entanglement state of the exiting photons can be determined. All four Bell states can be generated by combining vertical and horizontal polarization with photonic crystals that have different topological charges at the gamma point.

[0023] The entangled photon generation device provided by this invention features a simple structure, flexible design, and convenient fabrication. Its structure can be easily realized using existing micro-nano fabrication techniques. This invention, through the design of a special photonic crystal structure, can efficiently manipulate the polarization state of light, including converting from linear polarization to circular polarization, and finely controlling the polarization state. Due to the phase difference introduced by the elliptical aperture and the bandgap effect of the photonic crystal, photons within a specific frequency range acquire orbital angular momentum while undergoing cross-polarization, such as making |σ... ± Circular polarized light becomes This results in entangled states. By adjusting the parameters and structure of the crystal lattice, the bandgap characteristics of the photonic crystal can be easily changed, thereby enabling precise control of the frequency, phase, and polarization of entangled photon pairs.

[0024] Experiments show that left- and right-handed circularly polarized light passing through a photonic crystal can produce left- and right-handed circularly polarized light with opposite orbital angular momentum. Furthermore, since horizontal and vertical polarization can be decomposed into... and The superposition of circularly polarized light, through vertical and horizontal polarization, allows it to combine with photonic crystals at the gamma point that have different topological charges, forming different entangled states. The device designed in this invention utilizes the superposition of left- and right-handed circularly polarized light, making angular momentum entanglement possible in quantum optics. This invention can be applied to fields such as quantum communication, quantum sensing, and quantum computing. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of a device embodiment for generating entangled photons based on a photonic crystal.

[0026] Figure 2 This is a schematic diagram of the lattice structure in an embodiment of a device for generating entangled photons based on a photonic crystal.

[0027] Figure 3 This is a longitudinal cross-sectional schematic diagram of a crystal lattice in an embodiment of a device that generates entangled photons based on a photonic crystal;

[0028] Figure 4 This is a top view schematic diagram of a crystal lattice in an embodiment of a device for generating entangled photons based on a photonic crystal;

[0029] Figure 5 The image shows the energy band diagram of the photonic crystal in the embodiment.

[0030] Figure 6 The diagram shows the eigenpolarization of the electric field in k-space, where the vortex center at (0,0) corresponds to the BIC point.

[0031] Figure 7 This is the eigenpolarization diagram of the electric field in k-space after slightly breaking the symmetry;

[0032] Figure 8 The phase distribution diagram is shown after the vortex that once encircles the polarization axis around the center is transformed into a vortex that encircles the center 0.5 times.

[0033] Figure 9 The diagrams show the electric field intensity and phase distribution of left-handed and right-handed light in a photonic crystal. (a) shows the change in electric field intensity distribution before and after incident light; (b) shows the electric field intensity distribution across the xy section after incident light; (c) shows the spatial phase distribution of left-handed light; and (d) shows the phase distribution of right-handed light. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the following embodiments will be used in conjunction with the accompanying drawings to further illustrate the invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0035] like Figures 1-4 As shown in the embodiment of the present invention, a device for generating entangled photons based on a photonic crystal includes a dielectric material layer 1, on which a plurality of lattices 2 are disposed; the plurality of lattices 2 are arranged periodically on the dielectric material layer 1, and each lattice 2 has the same structure; the length and width of the lattice 2 are set according to requirements, and can be 400-720 nm. In a preferred embodiment, the length and width a of the lattice 2 are 560 nm; different materials and different structural parameters will result in different operating wavelengths. Depending on the period and the material used, the required incident light wavelength will change accordingly, resulting in different wavelengths of entangled photons. The thickness of the lattice 2 can be 400-600 nm. In a preferred embodiment, the thickness of the lattice 2 is 600 nm.

[0036] Each lattice 2 has two through elliptical holes 3; the semi-major axis of the elliptical hole 3 is l a It can be 90–150 nm, with a semi-short axis of l b The value can be 60-110 nm; in a preferred embodiment, the semi-major axis of the elliptical hole 3 is designed to be 120 nm and the semi-minor axis to be 80 nm.

[0037] The elliptical aperture 3 is deflected θ (the specific angle is determined by the subsequent 15nm offset) upwards to the same side. The distance between the upper and lower edges of the same elliptical aperture 3 is 15-45nm (that is, the upper elliptical aperture and the lower elliptical aperture are offset by 15-45nm, but they are connected). The deflection is to break the lattice symmetry, so that... Figure 6 The momentum space topology shown becomes Figure 5 To produce The entangled state. In a preferred embodiment, the upper and lower edges of the same elliptical hole 3 are deflected by d = 15 nm.

[0038] The distance between the geometric centers of the two elliptical holes 3 is set to 280 nm.

[0039] The operating frequency of a device depends on the dielectric constant of the material used and the etching parameters, ranging from 150 to 250 THz. Different dielectric materials have different absorption rates in different frequency bands, and therefore different applicable wavelengths. The wavelength and etching parameters should be selected based on the properties of the dielectric material.

[0040] In use: A circularly polarized light beam at the device's operating wavelength is incident normally onto the surface of dielectric material layer 1 (which is made of a photonic crystal). In the momentum space of the BIC band structure of the photonic crystal, the BIC point corresponds to a polarization singularity. Each point in k-space (excluding the BIC point) corresponds to a specific polarization state of far-field radiation. These polarization states have a specific distribution in k-space and simultaneously form a vortex around the BIC point. This allows us to define the topological charge number, or the orbital number q, of the BIC point. This polarization distribution allows the photonic crystal to behave as a resonator with different polarizations for momentum in different planes. Therefore, the photonic crystal can function as a highly anisotropic polarized device and can easily produce the same effect as the metasurface used to manipulate the phase of light in real space through optical field manipulation in k-space.

[0041] The energy band diagram of the photonic crystal is as follows: Figure 5 As shown, the red solid diamond marks the quasi-BIC point, the gray solid line is the energy band it belongs to, and the frequency at the red dashed line is the frequency of the incident light. The incident light at this frequency is used to excite the quasi-BIC mode in the photonic crystal.

[0042] k-space electric field eigenpolarization, such as Figure 6 and 7 As shown, the arrow points to the azimuth angle, and the vortex center at (0,0) corresponds to the BIC point.

[0043] After slightly breaking the symmetry, the vortex that once encircles the center of the polarization major axis becomes 0.5 times, corresponding to a half-integer topological charge, producing something like... Figure 8 The phase distribution diagram is shown.

[0044] Photonic crystal band structure diagram as shown Figure 5 As shown, a circularly polarized light beam |σ ±(± represents left-hand and right-hand rotation) When light with a frequency slightly deviating from the BIC point (i.e., light with a frequency slightly lower than the BIC point is incident perpendicularly) is incident on a photonic crystal (as shown by the dashed line at the quasi BIC), the beam can be decomposed into plane waves with different k-components. If it is a Gaussian beam, it corresponds to a circle centered at the gamma point in momentum space. These plane waves with different k-components will couple with the corresponding polarization states in k-space, producing a spin-orbit coupling effect. Part of the transmitted or reflected light will be cross-polarized, causing the left-hand and right-hand circularly polarized light to reverse. At the same time, it carries twice the orbital angular momentum of the polarization state near the gamma point, and the orbital angular momentum carried by the left-hand and right-hand circularly polarized light has opposite signs: left-handed light has l = -2q, and right-handed light has l = 2q, producing a spin-orbit coupling effect. Figure 8 The vortex phase distribution shown, even if |σ ± Circular polarized light becomes A vortex beam. The left-handed far-field field intensity distribution and phase distribution are as follows: Figure 9 As shown.

[0045] Figure 9 Figure (a) in the figure can show the change in electric field intensity distribution before and after incident; Figure 9 Figure (b) in the figure can show the electric field intensity distribution of the xy section after incident, and the color bar is the electric field intensity (red is high and blue is low); Figure 9 Figure (c) shows the spatial distribution of the phase of the left-handed optical system. Figure 9 Figure (d) shows the right-handed optical phase distribution. The color bar represents the phase, ranging from -π to π.

[0046] When incident linearly polarized light is incident on a linearly polarized light source, the linearly polarized light can be considered as a superposition of left- and right-polarized light. Superposition state will be formed due to cross-polarization To generate a photonic crystal that allows the angular momentum and orbital angular momentum of photons to become entangled, l = ±1, or q = ±1 / 2, is required. The topological charge of the BIC corresponding to the gamma point of the photonic crystal is a positive integer. To generate a topological charge of q = ±1 / 2 at the gamma point, while maintaining the mirror symmetry of the periodic unit cell of the photonic crystal, it is necessary to slightly break the rotational symmetry by rotating the elliptical air column towards the central axis and tilting it slightly in the vertical direction. This splits the positive integer topological charge into half-charges symmetrically distributed on both sides of the kx-axis. Simultaneously, the mirror symmetry in the z-direction is broken, causing the two half-charges to translate, moving one half-charge to the gamma point as follows: Figure 7 As shown. Figure 9 As shown, the incident light propagates along the z-direction, and the planar field intensity distribution parallel to the propagation direction is as follows. Figure 9 As shown in Figure (a), the electric field intensity of the cross section perpendicular to the propagation direction after passing through the photonic crystal is as follows: Figure 9As shown in Figure (b), the phase distribution in the xy plane under left- and right-handed polarization is as follows: Figure 9 Figures (c) and (d) show that when a linearly polarized single photon is incident perpendicularly on a photonic crystal, a superposition state of left- and right-handed optical rotation with opposite orbital angular momentum can be generated. In the case of a single photon, it is a single-photon entangled state in which the orbital angular momentum degree of freedom and the spin degree of freedom are entangled.

[0047] In actual manufacturing, the present invention may include a substrate. The lattice thickness and substrate thickness have little impact on the product function, but mainly have a slight impact on the operating wavelength.

[0048] The above are merely embodiments of the present invention. The invention is not limited to the fields covered by these embodiments. Commonly known structures and characteristics in the solutions are not described in detail here. Those skilled in the art are aware of all common technical knowledge in the field prior to the application date or priority date, are able to access all existing technologies in that field, and have the ability to apply conventional experimental methods prior to that date. Those skilled in the art can, under the guidance of this application, improve and implement this solution in combination with their own capabilities. Some typical known structures or methods should not be obstacles for those skilled in the art to implement this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the structure of the present invention. These should also be considered within the scope of protection of the present invention, and will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A device for generating entangled photons based on a photonic crystal, characterized in that... include: A dielectric material layer is provided with a plurality of lattices etched with paired elliptical holes. The plurality of lattices are periodically arranged on the dielectric material layer. Each lattice has the same structure and a lattice period of 'a'. After a single lattice unit is horizontally or vertically shifted by a distance 'a', it completely overlaps with the previous period to form an array. The length and width of the lattice are both the length of the first period set according to the requirements. The lattice has two through elliptical holes. The axial direction of the elliptical holes is deflected upward to the same side, and the upper and lower edges of the same elliptical hole are deflected. When a linearly polarized single photon is incident perpendicularly on the device, a superposition state of left and right rotating light with opposite orbital angular momentum is generated, that is, the entangled state of the single photon.

2. The device for generating entangled photons based on a photonic crystal as described in claim 1, characterized in that... The cross-sectional shape of the lattice is a regular quadrilateral.

3. The device for generating entangled photons based on a photonic crystal as described in claim 2, characterized in that... The length and width of the lattice are both 400-720 nm; the thickness of the lattice is 400-600 nm.

4. The device for generating entangled photons based on a photonic crystal as described in claim 3, characterized in that... The lattice has a length and width of 560 nm and a thickness of 600 nm.

5. The device for generating entangled photons based on a photonic crystal as described in claim 1, characterized in that... The semi-major axis of the elliptical aperture is 90–150 nm, and the semi-minor axis of the elliptical aperture is 60–110 nm.

6. The device for generating entangled photons based on a photonic crystal as described in claim 5, characterized in that... The semi-major axis of the ellipse is 120 nm, and the semi-minor axis of the ellipse is 80 nm.

7. The device for generating entangled photons based on a photonic crystal as described in claim 1, characterized in that... The geometric centers of two elliptical holes on the same lattice are 280 nm apart.

8. The device for generating entangled photons based on a photonic crystal as described in claim 1, characterized in that... The distance between the upper and lower edges of the same elliptical hole is 15–45 nm.

9. The device for generating entangled photons based on a photonic crystal as described in claim 8, characterized in that... The distance between the upper and lower edges of the same elliptical hole is 15nm.

10. The device for generating entangled photons based on a photonic crystal as described in claim 1, characterized in that... The number of lattice periods is at least 15 to avoid edge effects.

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