Optical tweezer array system, method of designing metasurfaces therein, and particle array trapping method

Abstract

The present disclosure relates to an optical tweezer array system, a method for designing a metasurface therein, and a particle array capturing method. The optical tweezer array system comprises: a light source, wherein the light source is configured to emit a light beam; a vacuum cavity, wherein a window of the vacuum cavity is transparent to the light beam, the vacuum cavity is arranged on an exit light path of the light source, and the vacuum cavity is configured to load particles to be captured inside the vacuum cavity; and a metasurface, which is arranged on the exit light path of the light source, and is configured to modulate the light beam so that the light beam forms an optical tweezer array in the vacuum cavity to capture the particles at optical tweezer positions of the optical tweezer array.

Description

Technical Field

[0001] This disclosure relates to the fields of optical technology and quantum manipulation, specifically to an optical tweezers array system, a method for designing metasurfaces in an optical tweezers array system, and a particle array trapping method. Background Technology

[0002] In fields such as quantum computing, quantum simulation, and precision measurement, there is a need to control the spatial position and movement of particles such as atoms and molecules. These particles are typically confined within a large, high-vacuum glass cavity to isolate them from environmental interference. Under these conditions, achieving manipulation requires a tool and method that can precisely manipulate the particles inside the vacuum cavity through a glass window. Optical tweezers can utilize the gradient force generated by the interaction of light and particles to form an optical trap, thereby restricting or adjusting the position of particles in space.

[0003] When multiple particles need to be manipulated simultaneously, multiple optical tweezers are required, i.e., multiple optical tweezers need to form an optical tweezers array to complete the operation. Related technologies include methods for generating optical tweezers such as acousto-optic deflectors and liquid crystal spatial light modulators (LSLs). However, these methods often encounter problems when generating large-scale optical tweezers arrays. Acousto-optic deflectors are limited by acoustic diffraction resolution and modulation interference, making it difficult to achieve large-scale optical tweezers arrays. Liquid crystal spatial light modulators are also limited by the finite number of pixels, making it difficult to achieve large-scale optical tweezers arrays. Furthermore, the spot size generated by these methods is too large, requiring the use of large-size, high numerical aperture microscope objectives for focusing, which introduces optical losses, and the field of view of the microscope objectives also limits scalability.

[0004] Of particular note is that, because atoms or molecules are confined within a high-vacuum cavity, the optical system must operate over long working distances through the cavity's glass window. This not only requires the optical system to have a longer working distance, but the refraction, aberrations, and optical field distortion introduced by the glass window itself further increase the complexity of optical path design and calibration. Therefore, devices using these methods require complex control electronics and microscopy systems, making compact integration difficult and resulting in complex and unstable systems. Thus, improvements are needed in the generation method of optical tweezers arrays. Summary of the Invention

[0005] According to a first aspect of this disclosure, an optical tweezers array system is provided. The optical tweezers array system includes: a light source, a vacuum cavity, and a metasurface. The light source is configured to emit a light beam. A window of the vacuum cavity is transparent to the light beam, and the vacuum cavity is disposed in the exit light path of the light source. The vacuum cavity is configured to load particles to be captured within it. The metasurface is disposed in the exit light path of the light source. The metasurface is configured to modulate the light beam such that the light beam forms an optical tweezers array within the vacuum cavity to capture particles at the optical tweezers positions of the optical tweezers array.

[0006] In some embodiments, the power of the light source and the wavelength of the light beam are adjusted according to the diffraction efficiency of the metasurface, the Airy disk intensity utilization rate of the metasurface, the optical path loss rate of the optical tweezers array system, and the number of optical tweezers in the optical tweezers array system, such that the well depth of each optical tweezer in the optical tweezers array is greater than or equal to a first preset threshold, so that the loading rate of the optical tweezers array is greater than or equal to a preset loading rate, wherein the Airy disk intensity utilization rate is the ratio of the total light intensity of the light beam diffracted by the metasurface into the optical tweezers array to the total light intensity of all diffracted light diffracted by the metasurface.

[0007] In some embodiments, the equivalent temperature of the first preset threshold in the energy space is 0.27 mK.

[0008] In some embodiments, a microscope is not included between the metasurface and the optical tweezers position of the optical tweezers array.

[0009] In some embodiments, the metasurface is located within the vacuum cavity.

[0010] In some embodiments, the metasurface does not operate in a vacuum environment.

[0011] In some embodiments, the metasurface is located between the vacuum cavity and the light source.

[0012] In some embodiments, the first radius of the microstructured region of the metasurface is greater than or equal to tan(θ)×(L1+d / n1+L2), where θ is the angle corresponding to the numerical aperture required to focus the optical tweezers to the design size of the optical tweezers array, L1 is the distance between the metasurface and the outer surface of the vacuum cavity, d is the thickness of the wall of the vacuum cavity, n1 is the window refractive index of the wall of the vacuum cavity, and L2 is the spacing distance between the trapped particles and the inner surface of the vacuum cavity.

[0013] In some embodiments, the distance between the metasurface and the outer surface of the vacuum cavity is less than or equal to 10 cm.

[0014] In some embodiments, the optical tweezers array system further includes a beam-splitting mirror disposed between the light source and the metasurface. The beam-splitting mirror includes a mirror surface at a predetermined angle to the outgoing light path of the light source, and a central aperture on the mirror surface. The projection of the aperture onto the metasurface is circular. The beam-splitting mirror is configured to reflect light beyond a second radius from the center of the light beam at a distance perpendicular to the direction of travel of the light beam.

[0015] In some embodiments, the optical tweezers array system further includes a microscope disposed in the outgoing light path of the vacuum cavity. The microscope is configured to receive light emitted from the vacuum cavity, the light including light for forming the optical tweezers array and fluorescence emitted by particles captured by the optical tweezers array.

[0016] In some embodiments, one or more lenses of the microscope are configured such that portions of light emitted from the metasurface that are not focused into optical tweezers by the metasurface do not converge onto any lens of the microscope.

[0017] In some embodiments, the optical tweezers array system further includes: a rotating waveplate disposed between the light source and the metasurface, and a polarizing beam splitter disposed between the rotating waveplate and the metasurface. The rotating waveplate is configured to change the phase of the light beam; the rotating waveplate and the polarizing beam splitter are configured to adjust the intensity of the light beam.

[0018] In some embodiments, the surface of the metasurface near the light source is coated with an antireflective film.

[0019] According to a second aspect of this disclosure, a method is provided for designing a metasurface in an optical tweezers array system, the metasurface comprising a plurality of cells arranged in an array, the optical tweezers array system being the optical tweezers array system according to any one of the foregoing embodiments. The method includes: determining, based on a target light intensity distribution of the optical tweezers array at a target plane, the phase shift that each cell constituting the metasurface needs to cause to light incident on the metasurface; and determining parameters for each cell based on the phase shift that each cell needs to cause.

[0020] In some embodiments, the metasurface is located between the vacuum cavity and the light source. Determining the phase shift that each cell constituting the metasurface needs to cause to the light incident on the metasurface, based on the target light intensity distribution of the optical tweezers array at the target plane, includes: setting an initial light intensity distribution and an initial phase for the light emitted from the metasurface; calculating a first light intensity distribution and a first phase for the light propagating to the outer surface of the vacuum cavity based on the initial light intensity distribution and the initial phase; calculating a second light intensity distribution and a second phase for the light propagating to the inner surface of the vacuum cavity based on the first light intensity distribution and the first phase; calculating a third phase for the light propagating to the target plane based on the second light intensity distribution and the second phase; calculating a third light intensity distribution and a fourth phase for the light propagating backward from the target plane to the inner surface of the vacuum cavity based on the target light intensity distribution and the third phase; calculating a fourth light intensity distribution and a fifth phase for the light propagating backward from the inner surface of the vacuum cavity to the outer surface of the vacuum cavity based on the third light intensity distribution and the fourth phase; and calculating a fifth phase for the light propagating backward from the outer surface of the vacuum cavity based on the fourth light intensity distribution and the fifth phase. The process of calculating the sixth phase of light propagating backward to the metasurface and updating the initial phase to the sixth phase is repeated. This process continues until the absolute value of the difference between two consecutive calculated sixth phases is less than a preset value.

[0021] In some embodiments, calculating the first light intensity distribution and first phase at the outer surface of the vacuum cavity, calculating the second light intensity distribution and second phase at the inner surface of the vacuum cavity, and calculating the third phase at the target plane includes: reading the matrix representing the light before propagation in blocks to obtain multiple first matrices; performing a Fast Fourier Transform (FFT) on each first matrix to obtain a second matrix corresponding to each first matrix; calculating the third matrix after propagation for each second matrix; performing an Inverse Fast Fourier Transform (IFFT) on each third matrix to obtain a fourth matrix corresponding to each third matrix; combining all fourth matrices into a matrix representing the light after propagation; and determining the light intensity distribution and / or phase of the light after propagation based on the matrix of the light after propagation, wherein the obtained second matrix and the obtained fourth matrix are stored in a non-transitory storage medium; and / or calculating the light propagating backward from the target plane to the target plane. The method involves calculating the third light intensity distribution and fourth phase at the inner surface of a vacuum cavity, calculating the fourth light intensity distribution and fifth phase of light propagating backward from the inner surface of the vacuum cavity to the outer surface of the vacuum cavity, and calculating the sixth phase of light propagating backward from the outer surface of the vacuum cavity to the metasurface. This includes: reading the matrix representing the light before backward propagation in blocks to obtain multiple fifth matrices; performing a Fast Fourier Transform (FFT) on each fifth matrix to obtain a sixth matrix corresponding to each fifth matrix; calculating a seventh matrix after backward propagation for each sixth matrix; performing an Inverse Fast Fourier Transform (IFFT) on each seventh matrix to obtain an eighth matrix corresponding to each seventh matrix; combining all eighth matrices into a matrix representing the light after backward propagation; and determining the light intensity distribution and / or phase of the light after backward propagation based on the matrix of the light after backward propagation. The obtained sixth and eighth matrices are stored in a non-transitory storage medium.

[0022] In some embodiments, the metasurface is located within the vacuum cavity. Determining the phase shift that each cell constituting the metasurface needs to cause to the light incident on the metasurface based on the target light intensity distribution of the optical tweezers array at the target plane includes: setting an initial light intensity distribution and an initial phase for the light emitted from the metasurface; calculating a seventh phase of the light propagating to the target plane based on the initial light intensity distribution and the initial phase; calculating an eighth phase of the light propagating backward from the target plane to the metasurface based on the target light intensity distribution and the seventh phase; updating the initial phase to the eighth phase; and repeating the operation of calculating the seventh phase of the light propagating to the target plane based on the initial light intensity distribution and the initial phase, calculating the eighth phase of the light propagating backward from the target plane to the metasurface based on the target light intensity distribution and the seventh phase, and updating the initial phase to the eighth phase, until the absolute value of the difference between two adjacent calculated eighth phases is less than a preset value.

[0023] In some embodiments, calculating the seventh phase of light propagating to the target plane includes: reading the matrix representing the light before propagation in blocks to obtain multiple first matrices; performing a Fast Fourier Transform (FFT) on each first matrix to obtain a second matrix corresponding to each first matrix; calculating a third matrix after propagation for each second matrix; performing an Inverse Fast Fourier Transform (IFFT) on each third matrix to obtain a fourth matrix corresponding to each third matrix; combining all fourth matrices into a matrix representing the light after propagation; and determining the intensity distribution and / or phase of the propagated light based on the matrix of the propagated light, wherein the obtained second matrix and the obtained fourth matrix are stored in a non-transitory storage medium; and / or calculating the light from... The eighth phase propagated from the target plane to the metasurface includes: reading the matrix representing the light before backpropagation in blocks to obtain multiple fifth matrices; performing a Fast Fourier Transform (FFT) on each fifth matrix to obtain a sixth matrix corresponding to each fifth matrix; calculating a seventh matrix after backpropagation for each sixth matrix; performing an Inverse Fast Fourier Transform (IFFT) on each seventh matrix to obtain an eighth matrix corresponding to each seventh matrix; combining all the eighth matrices into a matrix representing the light after backpropagation; and determining the intensity distribution and / or phase of the light after backpropagation based on the matrix of the light after backpropagation. The obtained sixth and eighth matrices are stored in a non-transitory storage medium.

[0024] According to a third aspect of this disclosure, a particle array capture method is provided, comprising: capturing a plurality of particles at the optical tweezer positions of the optical tweezer array using an optical tweezer array system as described above, to form a particle array.

[0025] In some embodiments, capturing multiple particles at the optical tweezers positions of the optical tweezers array using the optical tweezers array system as described above includes: loading the particles to be captured into a vacuum cavity, wherein the particles are in a gaseous state; cooling the particles using a magneto-optical trap to bring the temperature of the particles below or equal to a preset temperature; activating a light source to emit a light beam to form an optical tweezers array in the vacuum cavity; and observing the captured particles by laser-cooled fluorescence imaging.

[0026] Other features and advantages of this disclosure will become clearer from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0027] The accompanying drawings, which form part of this specification, illustrate embodiments of this disclosure and, together with the specification, serve to explain the principles of this disclosure.

[0028] This disclosure will become clearer with reference to the accompanying drawings and the following detailed description, wherein:

[0029] Figure 1 A schematic diagram of an optical tweezers array system according to some embodiments of the present disclosure is shown;

[0030] Figure 2 A schematic diagram of an optical tweezers array system according to some embodiments of the present disclosure is shown;

[0031] Figure 3 A schematic diagram of an optical tweezers array system according to some embodiments of the present disclosure is shown;

[0032] Figure 4 A schematic diagram of a beam-splitting mirror in an optical tweezers array system according to some embodiments of the present disclosure is shown;

[0033] Figure 5 A flowchart illustrating a method for designing metasurfaces in an optical tweezers array system according to some embodiments of the present disclosure is shown;

[0034] Figure 6 A flowchart illustrating step S120 of a method for designing a metasurface in an optical tweezers array system according to some embodiments of the present disclosure is shown.

[0035] Figure 7 A flowchart illustrating step S122A of a method for designing a metasurface in an optical tweezers array system according to some embodiments of the present disclosure is shown.

[0036] Figure 8 A flowchart illustrating step S125A of a method for designing a metasurface in an optical tweezers array system according to some embodiments of the present disclosure is shown.

[0037] Figure 9 A flowchart illustrating step S120 of a method for designing a metasurface in an optical tweezers array system according to some embodiments of the present disclosure is shown.

[0038] Figure 10 A flowchart illustrating a method of using an optical tweezers array system according to some embodiments of the present disclosure is shown. Detailed Implementation

[0039] Various exemplary embodiments of the present disclosure will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present disclosure.

[0040] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this disclosure or its application or use. Those skilled in the art will understand that they merely illustrate exemplary ways that can be used to implement this disclosure, and are not exhaustive.

[0041] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0042] This disclosure presents an optical tweezers array system for capturing particles.

[0043] like Figure 1 and Figure 2 As shown, in some embodiments of this disclosure, the optical tweezers array system may include: a light source 10, a vacuum cavity 20, and a metasurface 30.

[0044] The light source 10 can be configured to emit a light beam. A vacuum cavity 20 can be positioned in the exit light path of the light source 10, and the window of the vacuum cavity 20 is transparent to the light beam emitted by the light source 10. Particles to be captured by the optical tweezers array can be loaded inside the vacuum cavity 20. A metasurface 30 can be positioned in the exit light path of the light source. Specifically, in... Figure 1 In some embodiments shown, the metasurface 30 may be located between the vacuum cavity 20 and the light source 10. In such... Figure 2 In some of the embodiments shown, the metasurface 30 may be located within the vacuum cavity 20. The metasurface 30 may be configured to modulate the light beam emitted by the light source 10 such that the beam forms an optical tweezers array within the vacuum cavity 20, thereby trapping particles at the optical tweezers positions of the optical tweezers array.

[0045] In some embodiments, the light beam emitted by the light source 10 may be a laser. In some specific embodiments, the light intensity range may be between 1W and 150W, and the laser wavelength may be between 800nm ​​and 1100nm. For example, the light source may be configured to emit an 852nm laser with a power of 30W.

[0046] In some embodiments, the vacuum cavity 20 can be a closed optical cavity, with the window of the vacuum cavity 20 transparent to the light beam emitted by the light source 10. Particles to be captured can be introduced into the vacuum cavity 20 under vacuum conditions and pre-cooled, thereby capturing the particles at the optical tweezers position after the light source is activated. In some specific embodiments, the window of the vacuum cavity 20 can be formed of glass, with a glass thickness error of less than or equal to 50 micrometers, a peak-to-valley (PV) value of less than or equal to 60 nanometers, and a surface roughness of less than or equal to 0.5 nanometers, thereby suppressing aberrations and ensuring that the wavefront error of the glass surface (the optical path difference between the outgoing wavefront of the optical system and the ideal spherical wave) is less than or equal to one-tenth of the working wavelength, thus avoiding optical tweezers array distortion. Alternatively, the window can also be formed of other transparent materials, without limitation.

[0047] Metasurfaces are planar optical elements based on subwavelength structures that can precisely control the phase, amplitude, and polarization of incident light at the nanoscale. Their core principle is to achieve localized modulation of the light wavefront by designing nanostructures with different geometries and arrangements (such as silicon nitride or titanium dioxide nanopillars). Compared to traditional optical elements (such as acousto-optic deflectors and liquid crystal spatial light modulators), metasurfaces offer advantages such as high numerical aperture, high pixel density, compactness, integrability, strong scalability, and a high damage threshold.

[0048] To reduce the probability of collisions between particles and the background gas, thereby ensuring the long-term coherence of the qubits, the particle array is placed in an ultra-high vacuum environment, namely, vacuum cavity 20. Therefore, the primary technical challenge in using optical tweezers generated by metasurface 30 for particle trapping is to achieve effective compatibility between the metasurface and the ultra-high vacuum cavity, ensuring that the optical tweezers can be efficiently and with low loss projected into the particle trapping region within the cavity.

[0049] In some embodiments, the metasurface 30 may operate outside of a vacuum environment. Specifically, such as Figure 1 As shown, the metasurface 30 may not be located within the vacuum cavity 20. For example, the environment in which the metasurface 30 is located may be an air environment or other non-vacuum environment. Compared to the scheme where the metasurface 30 is placed in the vacuum cavity 20, the scheme where the metasurface does not need to operate in a vacuum environment can avoid the influence of the metasurface on the ultra-high vacuum system, avoid the deposition and contamination of the metasurface by the particles to be captured in the vacuum cavity, and avoid electromagnetic interference of the electromagnetic environment of the metasurface to the captured particles. This can improve the working stability, adjustment convenience, and stability of the metasurface when performing quantum computing gate operations on particles. At the same time, it can also greatly alleviate the temperature rise problem caused by the heating of the metasurface by the ultra-high power laser required for projecting large-scale optical tweezers arrays.

[0050] In some embodiments, such as Figure 2 As shown, metasurface 30 can operate in a vacuum environment. Specifically, metasurface 30 can be located within vacuum cavity 20. Compared to a solution where metasurface 30 is located outside vacuum cavity 20, the metasurface within the vacuum cavity does not need to compensate for aberrations caused by the vacuum cavity glass. Furthermore, because it is placed in a vacuum, the working distance between the metasurface and the optical tweezers array to be focused can be shorter. To achieve the same numerical aperture, the required metasurface size can be smaller, the required processing technology can be lower, and the processing cost can be reduced.

[0051] Furthermore, compared to the approach of adding a microscope objective between the vacuum cavity 20 and the metasurface 30, the optical tweezers array system according to this disclosure does not require a microscope objective. The light source is directly projected onto the metasurface and modulated to focus within the vacuum cavity, forming an optical tweezers array. This results in a smaller size, lower cost, and easier optical alignment. It avoids reflection loss, scattering loss, absorption loss, aberrations, and field-of-view limitations caused by increased optical interfaces, thereby improving the power, number of optical tweezers, and capture stability.

[0052] According to the scheme of this disclosure, a metasurface is placed outside a vacuum cavity. To compensate for aberrations such as spherical aberration introduced by the window (typically a few millimeters thick glass) of the vacuum cavity 20, a second aspect of this disclosure later provides a method for designing a metasurface 30 in an optical tweezers array system. And to simultaneously achieve long working distances (e.g., as... Figure 3 As shown, L1 is 2 mm of air, d is 3 mm of glass, and L2 is 10 mm of vacuum. With a high numerical aperture (e.g., greater than 0.5), the size of metasurface 30 can be increased accordingly (e.g., diameter greater than or equal to 20 mm). This places higher demands on the fabrication consistency and large-area uniformity of phase distribution of the metasurface 30 nanostructure, and consequently increases the fabrication cost and difficulty.

[0053] When fabricating large-area optical tweezers metasurfaces (such as silicon nitride), the primary challenge compared to small-size fabrications is stitching error. To achieve large-area patterning of large samples, the design pattern can be divided into hundreds of independent writing fields, relying on high-precision displacement stages for field-by-field positioning and exposure. When using a zigzag path for sequential exposure, the physical distance and time interval between the first and last writing fields increase significantly. Within this time span, unavoidable slight temperature fluctuations in the process chamber (e.g., ±0.1℃) can cause thermal expansion / contraction of the sample and thermal drift of the displacement stage. This drift accumulates as the exposure process progresses, resulting in relative positional distortions of up to nearly 100 nanometers between writing fields that are far apart. Errors caused by such slow thermal drift are difficult to correct in real time using conventional alignment marks within the writing fields. These factors significantly amplify stitching errors. To achieve nanometer-level fabrication precision for large-area patterns, the temperature stability of the process environment must be controlled at an extremely high level, with changes of less than 0.02℃ per hour. The requirements for environmental control, equipment capabilities, and process stability are far higher than for small-area fabrication.

[0054] The second step is the removal of the chromium mask. Due to the high structure and small linewidth, the traditional wet etching combined with ultrasound would damage the pattern. Therefore, static wet etching without ultrasound can be used. However, with the area increased to 3.8cm × 3.8cm and the pattern size increased, the area of ​​residual chromium in non-patterned areas (such as sample edges) significantly increased. The size of the available wet etching vessels is limited by the process equipment and cannot be scaled up proportionally to the sample size, leading to an increased risk of chromium residue. Therefore, a combined dry and wet etching process can be used: first, a gentle, controlled wet etching process is used to remove most of the chromium, and then a dry etching process is used to precisely remove the remaining chromium layer across the entire surface. This process does not damage the silicon nitride structure.

[0055] Finally, when the wafer size is changed from small to large, both the etching rate and morphology change significantly. Due to the increased total area of ​​the patterned region, the consumption and local concentration distribution of reactive gases change, directly leading to differences in the etching rate across different areas of the wafer. This difference further causes micro-morphology problems such as inconsistent sidewall tilt and uncontrolled undercutting. If an etching program optimized for small wafers is directly applied, the different local electric field and temperature distribution on the sample surface will cause a shift in the process window, making it impossible to obtain consistent etching results. Therefore, to achieve uniformity and controllable morphology in large-wafer processes, etching program parameters (such as gas flow rate and power) can be adjusted. After experiments with small-sized patterns, full-size patterns can be used for verification, thus requiring considerable experience with the process parameters.

[0056] Back Figure 1 and Figure 2 In some embodiments, the particles to be captured can be atoms (e.g., alkali metal atoms, alkaline earth metal atoms), ions or molecules, or objects at the nanoscale to microscale, such as spheres with radii between ten nanometers and one thousand nanometers or spheres between one micrometer and ten micrometers, without limitation.

[0057] In some embodiments, the power of the light source and the wavelength of the beam can be adjusted according to the diffraction efficiency of the metasurface, the Airy spot light intensity utilization rate of the metasurface, the optical path loss rate of the optical tweezers array system, and the number of optical tweezers in the optical tweezers array system, so that the well depth of each optical tweezer in the optical tweezers array is greater than or equal to a first preset threshold, and the loading rate of the optical tweezers array is greater than or equal to a preset loading rate.

[0058] In some embodiments, the first preset threshold for the well depth has an equivalent temperature of 0.27 mK in energy space, thereby allowing a rubidium atom loading rate greater than or equal to 80%. The loading rate is the ratio of the number of optical tweezers trapping particles to the total number of optical tweezers in the array. The equivalent temperature in energy space is obtained by the ratio of the energy of the optical tweezers to the Boltzmann constant. In the context of this disclosure, well depth refers to the energy of the potential well formed by the optical tweezers and is numerically described by its equivalent temperature in energy space.

[0059] In some specific embodiments, the average power of each optical tweezer can be 0.8mW, corresponding to an equivalent temperature of 0.472mK at the well depth, which is higher than the first preset threshold of 74%, so that the particles have a lower probability of leaving the optical tweezers, thereby leaving a margin for particle loading and improving the success rate.

[0060] In some embodiments, the ratio of the trap depth to the optical power of each optical tweezer at various wavelengths is shown in Table 1 below, and the power required by the light source can be determined based on the table below.

[0061]

[0062] Table 1

[0063] In some embodiments, an optical tweezers array with more than 10,000 optical tweezers can be optionally formed. In some specific embodiments, the number of optical tweezers in the array can be 18,225, and it can capture more than 10,000 atoms.

[0064] In some embodiments, the metasurface diffraction efficiency can be the ratio of the intensity of light whose direction of travel is altered by the metasurface diffraction to the total intensity of light incident on the metasurface. In some embodiments, the light incident on the metasurface can be divided into three categories upon exiting the metasurface: the first category is reflected light that is reflected back along the incident light path; the second category is unmodulated light that is not diffracted by the optical microstructures on the metasurface and exits in a direction parallel to the incident light path; and the third category is modulated diffracted light whose direction of travel is altered by the optical microstructures on the metasurface. The diffraction efficiency can be the ratio of the intensity of the modulated diffracted light to the intensity of the incident light. The modulated diffracted light can converge at the target plane to form an optical tweezers array. In some specific embodiments, the metasurface diffraction efficiency can be greater than or equal to 67.5% to effectively utilize the power of the light source and avoid the unmodulated light affecting the effect of the optical tweezers array.

[0065] In some embodiments, the surface of the metasurface near the light source can be coated with an antireflection film to reduce reflected light and increase the utilization rate of light intensity. In some specific embodiments, the antireflection film can be a broadband antireflection film, thereby making the transmittance of 850nm laser greater than or equal to 99.5%, that is, the ratio of the intensity of reflected light to the intensity of incident light is less than or equal to 0.5%.

[0066] The Airy disk intensity utilization rate can be defined as the ratio of the total intensity of the light diffracted by the metasurface into an optical tweezers array to the total intensity of all diffracted light from the metasurface in modulated diffracted light; that is, the ratio of the total intensity of the optical tweezers array to the total intensity of all modulated diffracted light. In some specific embodiments, the Airy disk intensity utilization rate can be greater than or equal to 87% to reduce the influence of stray light such as speckle (a granular structure resulting from random phase superposition due to imperfect surface smoothness when light waves pass through a medium) on the optical tweezers array. Specifically, the percentage of speckle with a Strell ratio (the ratio of the intensity of the maximum intensity point in the actual aberration-free condition to that in the ideal aberration-free condition) greater than or equal to 0.8 (i.e., reaching the diffraction limit) can be 99.7%. Specifically, stray light may converge in areas outside the optical tweezers region of the optical tweezers array, forming potential wells in these areas. These potential wells may also trap particles, causing particles to be trapped outside the target region. Increasing the Airy disk intensity utilization rate can reduce the number of particles mistakenly trapped outside the target region. In some specific embodiments, the Airy spot intensity utilization rate can be greater than or equal to 87%, thereby reducing the number of traps formed by stray light and the capture probability.

[0067] The optical path loss rate of an optical tweezers array system can be the loss caused by various optical components or structures in the system to light intensity. For example, it can include the loss to light intensity caused by beam shaping and truncation, and the losses from light absorption and scattering by elements that control light intensity, windows in the vacuum cavity, and other devices. In some specific embodiments, the loss rate of beam truncation can be less than or equal to 13.5%, and the loss rate of other devices can be less than or equal to 10%.

[0068] In some embodiments, the metasurface 30 is located between the vacuum cavity 20 and the light source 10, and the first radius of the microstructured region of the metasurface can be greater than or equal to tan(θ)×(L1+d / n1+L2), where θ is... Figure 3The angle subtended by the optical tweezers array relative to the optical path, as shown, can specifically be the angle corresponding to the numerical aperture required for the designed size of the optical tweezers array when the optical tweezers are focused. L1 is the distance between the metasurface 30 and the outer surface of the vacuum cavity 20, d is the thickness of the wall of the vacuum cavity 20, n1 is the refractive index of the window of the wall of the vacuum cavity 20, and L2 is the distance between the trapped particle and the inner surface of the vacuum cavity 20. Specifically, the light beam enters the interior of the vacuum cavity 20 through the window of the wall of the vacuum cavity 20. It is easy to understand that, in the case where the vacuum cavity has multiple inner or outer surfaces that are not on the same plane, unless otherwise specified, the inner surface of the vacuum cavity referred to herein refers to the surface of the window of the vacuum cavity wall that contacts the internal environment of the vacuum cavity, and the outer surface of the vacuum cavity referred to herein refers to the surface of the window of the vacuum cavity wall that contacts the external environment.

[0069] In some specific embodiments, θ can be greater than or equal to 45°, i.e., the first radius can be greater than or equal to (L1+d / n1+L2) to ensure that the numerical aperture of the formed optical tweezers array is sufficiently large. The spacing between the captured particles and the inner surface of the vacuum cavity 20 can be greater than or equal to 10 mm to reduce the interference of the electric field on the surface of the vacuum cavity 20 on the captured particles. The thickness of the vacuum cavity wall can be greater than or equal to 3.5 mm to reduce the deformation of the vacuum cavity 20 (it is easy to understand that the air environment will exert pressure on the vacuum cavity 20, which is a vacuum environment inside, thus causing deformation). In some embodiments, the size of the metasurface can be 19.5 mm.

[0070] In some embodiments, the distance between the metasurface 30 and the outer surface of the vacuum cavity 20 can be less than or equal to 10 cm. In some embodiments, the distance between the metasurface 30 and the outer surface of the vacuum cavity 20 can be further reduced, for example, to 5 cm, 1 cm, or 5 mm. In some specific embodiments, the distance between the metasurface 30 and the outer surface of the vacuum cavity 20 can be less than or equal to 2.5 mm. This can reduce the influence of the air region between the metasurface 30 and the vacuum cavity 20 on the modulated light, while increasing the integration of the entire system and reducing its size. Specifically, the greater the distance between the outer surface of the vacuum cavity 20 and the metasurface 30, the longer the working distance between the metasurface 30 and the optical tweezers array to be focused. As mentioned above, the first radius of the microstructured region of the metasurface can be greater than or equal to tan(θ)×(L1+d / n1+L2). In some specific embodiments, when L1=9mm, d=3.5mm, n1=1.5, and tan(θ)=0.75, the metasurface radius can be greater than 10.375mm when L2=2.5mm; greater than 6mm when L2=10mm; greater than 46mm when L2=50mm; and greater than 83.5mm when L2=100mm.

[0071] Similarly, in some embodiments, the metasurface 30 is located within the vacuum cavity 20, and the first radius of the microstructured region of the metasurface can be greater than or equal to tan(θ) × L³, where θ is as follows: Figure 3 The angle of the optical tweezers array relative to the optical path shown can specifically be the angle corresponding to the numerical aperture required for the design size of the optical tweezers array when the optical tweezers are focused. L3 is the spacing distance between the trapped particles and the metasurface 30.

[0072] In some embodiments, such as Figure 3 As shown, the optical tweezers array system may further include a beam-splitting mirror 40 disposed between the light source and the metasurface. Wherein, as... Figure 4 As shown, the beam-splitting reflector 40 may include a mirror surface, which may be set at a preset angle to the outgoing light path of the light source. The center of the mirror surface may have a hole, and the projection of the hole onto the metasurface may be circular. Figure 4 Region A in the diagram shows an oblique perspective view of the beam-splitting mirror 40, where the dashed lines represent the perspective structure. Figure 4 Region B in the diagram shows a side perspective view of the beam-splitting mirror 40, with the shaded area representing the perspective structure of the internal aperture.

[0073] The beam-splitter 40 can be configured to reflect light beyond a second radius r at a distance from the center of the beam in a direction perpendicular to the beam's travel direction. This allows for adjustment of the beam's spot radius to obtain a beam that matches the metasurface. In some embodiments, after the beam-splitter 40 adjusts the beam to the second radius in a direction perpendicular to the beam's travel direction, the radius of the beam in the direction perpendicular to the beam's travel direction upon reaching the metasurface 30 can be greater than or equal to the first radius of the microstructured metasurface 30 described above. It is understood that an excessively large second radius results in excessive light intensity loss due to truncation of the light spot as it passes through the metasurface 30, while an excessively small second radius leads to a decrease in image quality. In some specific embodiments, the light intensity truncation loss rate can be less than or equal to 13.5%. In some specific embodiments, the second radius can be equal to the overall size of the metasurface.

[0074] In some embodiments, light reflected off the optical path by the beam-splitting mirror 40 can be reflected towards a water-cooled absorber to prevent this portion of the light from irradiating the metasurface 30 or the vacuum cavity 20 and generating a thermal effect. In some specific embodiments, the temperature rise of the metasurface 30 during continuous operation can be less than or equal to 15°C. In some specific embodiments, the beam-splitting mirror can reflect 4W of light intensity (13% of the incident light) that does not reach the metasurface to the water-cooled absorber.

[0075] In some embodiments, such as Figure 3As shown, the optical tweezers array system may further include a microscope 50 disposed in the outgoing light path of the vacuum cavity 20. The microscope 50 may be configured to receive light emitted from the vacuum cavity 20, which may include light used to form the optical tweezers array and fluorescence emitted by particles captured by the optical tweezers array.

[0076] Specifically, microscope 50 can observe the image of the optical tweezers array to confirm the state of the optical tweezers array, and after loading particles, can observe the fluorescence of the particles captured by the optical tweezers array, thereby obtaining the calculation results of quantum computing using the captured particles.

[0077] In some embodiments, one or more lenses of the microscope 50 may be configured such that portions of light emitted from the metasurface 30 that are not focused into optical tweezers by the metasurface 30 do not converge onto any lens in the microscope 50. In some embodiments, the lens material in the microscope 50 may be fused silica, and the surface may be coated with a film with a high damage threshold, for example, a loss threshold greater than 200 W / cm². 2 This prevents the lens surface in microscope 50 from being damaged by thermal lensing. Specifically, in some embodiments, 7W of incident light is not focused into optical tweezers by metasurface 30, thus entering microscope 50 as parallel light. This configuration avoids the light from damaging the microscope through thermal effects.

[0078] In some embodiments, the optical tweezers array system may further include: a rotating waveplate disposed between the light source 10 and the metasurface 30, and a polarization beam splitter (not shown) disposed between the rotating waveplate and the metasurface.

[0079] The rotating waveplate can be configured to change the phase of the light beam; the rotating waveplate and the polarization beam splitter can be configured to adjust the intensity of the light beam. Specifically, the polarization direction of the light beam can be changed by rotating the waveplate, so that the polarization beam splitter can change the intensity of the emitted beam according to the polarization direction of the light beam. In some embodiments, the angle of the rotating waveplate can be controlled (e.g., by electrically rotating the waveplate) in relation to the particle loading process in the vacuum cavity 20, thereby preventing fluctuations in optical power from affecting the stability of the trap depth of the optical tweezers.

[0080] Compared to methods using acousto-optic modulators to control light intensity, this disclosure employs a rotating waveplate and a polarizing beam splitter to reduce modulation losses and increase light intensity utilization. In some specific embodiments, the intensity control loss of the rotating waveplate and polarizing beam splitter can be less than or equal to 1%, while acousto-optic modulators typically have losses greater than 10%.

[0081] Easy to understand Figure 3 The aforementioned devices can also be applied to similar applications. Figure 2The technical solution of the metasurface 30 being located in the vacuum cavity 20 is not described in detail here.

[0082] This disclosure also proposes a method for designing metasurfaces in an optical tweezers array system. The metasurface may comprise multiple cells arranged in an array, and the optical tweezers array system is any of the optical tweezers array systems described in the foregoing embodiments. Figure 5 As shown, the method may include: step S120, determining the phase shift that each cell constituting the metasurface needs to cause to the light incident on the metasurface based on the target light intensity distribution of the optical tweezers array at the target plane; step S160, determining the parameters of each cell based on the phase shift that each cell needs to cause.

[0083] Metasurfaces comprise multiple subwavelength structures at the micrometer, nanometer, or smaller scale. Depending on their arrangement and shape, these structures can influence the phase, amplitude, and polarization of incident light, thus modulating the wavefront. Such structures are referred to as cells. Cells can be arranged in an array on a substrate; the array can be square, rectangular, or any other shape, without limitation.

[0084] In some embodiments, a cell may include a cylinder, and the parameters of the cell may include: the shape of the cylinder, the height of the cylinder, the characteristic dimensions of the cylinder in a plane perpendicular to the height, the refractive index of the cylinder, and the cell period. For example, the shape of the cylinder may include a circle, a square, a rectangle, a polygon, etc. The height of the cylinder is the distance from the surface of the cylinder opposite to the substrate to the surface of the substrate. The characteristic dimensions of the cylinder in a plane perpendicular to the height can be selected according to the shape of the cylinder. For example, in a polygonal cylinder, it may be the length of each side of the polygon; in a circular cylinder, it may be the diameter of the circle; and in a square cylinder, it may be the side length of the square. The cell period is the spacing between multiple cells arranged in a selected direction. In a two-dimensional plane, different periods may exist in different directions, which is not limited here.

[0085] In some embodiments, in step S120, based on the target light intensity distribution of the optical tweezers array at the target plane, light can be reversed from the target plane to the metasurface by methods such as angular spectral diffraction, so as to obtain the phase shift that each cell needs to cause to the light incident on the metasurface.

[0086] like Figure 6As shown, in some embodiments, the metasurface is located between the vacuum cavity and the light source. Step S120 may include: Step S121A, setting the initial light intensity distribution and initial phase of the light emitted from the metasurface; Step S122A, calculating the first light intensity distribution and first phase of the light propagating to the outer surface of the vacuum cavity based on the initial light intensity distribution and initial phase; Step S123A, calculating the second light intensity distribution and second phase of the light propagating to the inner surface of the vacuum cavity based on the first light intensity distribution and first phase; Step S124A, calculating the third phase of the light propagating to the target plane based on the second light intensity distribution and second phase; Step S125A, calculating the third phase of the light propagating to the target plane based on the target light intensity distribution... Step S126A: Based on the third intensity distribution and the fourth phase, calculate the third intensity distribution and the fourth phase of light propagating backward from the target plane to the inner surface of the vacuum cavity; Step S127A: Based on the fourth intensity distribution and the fifth phase, calculate the sixth phase of light propagating backward from the outer surface of the vacuum cavity to the metasurface, and update the initial phase to the sixth phase; and repeat steps S122A to S127A until the absolute value of the difference between two adjacent calculated sixth phases is less than a preset value.

[0087] In step S121A, the initial intensity distribution of the light emitted from the metasurface can be set according to the expected parameters of the entire optical system. In some specific embodiments, it can be set according to one or more of the following: the working distance of the optical system incident on the metasurface (i.e., the distance between the metasurface and the optical tweezers in the direction of light propagation), the numerical aperture (i.e., the sine of the arctangent of the ratio of the metasurface radius to the working distance), the entrance pupil diameter (i.e., the diameter of the cell-containing region of the metasurface), and the spot diameter (i.e., the diameter of the spot of light incident on the metasurface). For example, the light intensity can be set to be uniformly distributed within the range of the entrance pupil diameter. The initial phase can be given in any way, for example, a random phase can be used as the initial phase.

[0088] In step S122A, the light intensity distribution and phase at the outer surface of the vacuum cavity, i.e. the first light intensity distribution and the first phase, can be obtained by angular spectral diffraction based on the initial light intensity distribution and the initial phase.

[0089] The light before propagation can be represented by the complex electric field matrix of the light emitted from the metasurface. Here, the complex electric field is a complex number of the form Aexp(iφ), where A represents the amplitude, φ represents the phase, exp is an exponential function, i is the imaginary unit, and the square of the amplitude is the light intensity. Each element of the complex electric field matrix can represent light at different spatial locations, i.e., the spatial distribution.

[0090] Angular spectral diffraction can transform the complex electric field matrix from a spatial position distribution to a spatial frequency distribution using methods such as Fourier transform. That is, each element of the complex electric field matrix can represent light at different spatial frequencies. Multiplying the complex electric field matrix of the spatial frequency distribution of light by the propagation operator matrix yields the complex electric field matrix of the propagated light with the same spatial frequency distribution. Then, by using inverse Fourier transforms or similar methods, the complex electric field matrix of the propagated light is transformed from a spatial frequency distribution to a spatial position distribution, revealing the distribution of the propagated light at different spatial locations. The intensity distribution and phase of the propagated light at these different spatial locations constitute the first intensity distribution and the first phase.

[0091] Similarly, steps S123A and S124A can be performed in a manner similar to step S122A, calculating the second light intensity distribution and the second phase at the inner surface of the vacuum cavity based on the first light intensity distribution and the first phase, and calculating the third phase at the target plane based on the second light intensity distribution and the second phase.

[0092] In some specific embodiments, such as Figure 7 As shown, step S122A may include (steps S123A and S124A are the same): step S122A1, reading the matrix representing the light before propagation in blocks to obtain multiple first matrices; step S122A2, performing a Fast Fourier Transform (FFT) on each first matrix to obtain a second matrix corresponding to each first matrix; step S122A3, calculating the third matrix after propagation for each second matrix; step S122A4, performing an Inverse Fast Fourier Transform (IFFT) on each third matrix to obtain a fourth matrix corresponding to each third matrix; step S122A5, combining all fourth matrices into a matrix representing the light after propagation; and step S122A6, determining the intensity distribution and / or phase of the light after propagation based on the matrix of the light after propagation.

[0093] By reading in blocks, performing FFT, and then propagating and performing IFFT, each resulting second and fourth matrix can be stored in non-transitory storage medium before being combined, thereby reducing the amount of data written to video memory and / or main memory simultaneously. Specifically, for example, the matrix can be divided into 50 blocks, thus reducing the amount of data written simultaneously to 1 / 50. In some operations where the amount of data written is proportional to the square of the matrix size, the amount of data written simultaneously can be reduced to 1 / 2500. This allows for large-scale three-segment media computations to be performed on existing computing devices.

[0094] In some specific embodiments, in step S122A1, reading multiple first matrices in blocks may include: dividing the first representation matrix representing the complex electric field of the light before propagation into multiple blocks, each block having all columns and one or more rows of the first representation matrix. In step S122A2, obtaining the second matrix may include: reading each block and performing an FFT on the read block, transposing the FFT-processed block and storing it in a non-transitory storage medium, and combining all blocks to obtain the second representation matrix; dividing the second representation matrix into multiple blocks, each block having all columns and one or more rows of the second representation matrix, reading each block and performing an FFT on the read block, and combining all blocks after the FFT to obtain a third representation matrix, which is the aforementioned second matrix. The second representation matrix may also be stored in a non-transitory storage medium. In step S122A3, multiplying the third representation matrix by the propagation matrix yields a fourth representation matrix, which is the aforementioned third matrix. In step S122A4, the fourth representation matrix is ​​divided into multiple blocks, each block having all columns and one or more rows of the fourth representation matrix. Each block is read and an IFFT is performed on the read block. The IFFT-processed block is transposed and stored in a non-transitory storage medium. All blocks are combined to obtain the fifth representation matrix. The fifth representation matrix is ​​then divided into multiple blocks, each block having all columns and one or more rows of the fifth representation matrix. Each block is read and an IFFT is performed on the read block. The fifth representation matrix can also be stored in a non-transitory storage medium. In step S122A5, all blocks after the IFFT are combined to obtain the sixth representation matrix representing the complex electric field of the propagated light. The sixth representation matrix is ​​the aforementioned fourth matrix.

[0095] In step S125A, the target light intensity distribution can be combined with the third phase to form the complex electric field matrix of the target optical tweezers. This complex electric field matrix is ​​then propagated backward to the inner surface of the vacuum cavity to obtain the third light intensity distribution and the fourth phase. Similarly, in steps S126A and S127A, a similar approach to step S125A can be used to calculate the fourth light intensity distribution and the fifth phase based on the third light intensity distribution and the fourth phase, and to calculate the sixth phase based on the fourth light intensity distribution and the fifth phase, as well as the sixth phase based on the fourth light intensity distribution and the fifth phase, as well as the sixth phase based on the fourth light intensity distribution and the fifth phase, as well as the sixth phase. This updates the initial phase to the sixth phase, ensuring that the updated light emitted from the metasurface approaches the target light intensity distribution after propagation.

[0096] In some specific embodiments, such as Figure 8As shown, step S125A may include (steps S126A and S127A are the same): Step S125A1, reading the matrix representing the light before back propagation in blocks to obtain multiple fifth matrices; Step S125A2, performing a Fast Fourier Transform (FFT) on each fifth matrix to obtain a sixth matrix corresponding to each fifth matrix; Step S125A3, calculating the seventh matrix after back propagation for each sixth matrix; Step S125A4, performing an Inverse Fast Fourier Transform (IFFT) on each seventh matrix to obtain an eighth matrix corresponding to each seventh matrix; Step S125A5, combining all the eighth matrices into a matrix representing the light after back propagation; and Step S125A6, determining the intensity distribution and / or phase of the light after back propagation based on the matrix of the light after back propagation.

[0097] The obtained sixth and eighth matrices can be stored in a non-transitory storage medium and then combined, thereby reducing the amount of data written to video memory and / or main memory at the same time.

[0098] Multiplying the electric field matrix of the spatial frequency distribution by the backpropagation operator matrix yields the electric field matrix of the spatial frequency distribution after backpropagation. Similarly, steps S125A1-S125A5 can be completed in a manner similar to the aforementioned steps S122A1-S122A5. Furthermore, the second and fifth representation matrices can also be stored in a non-transitory storage medium and then combined.

[0099] Steps S122A to S127A can be executed multiple times until the absolute value of the difference between two adjacent calculated sixth phases is less than a preset value, that is, the initial light intensity distribution and the finally updated initial phase can obtain the target light intensity distribution after propagation.

[0100] In some specific embodiments, the distance from the target plane to the inner surface of the vacuum cavity can be 9 mm, and the refractive index can be the refractive index of vacuum. The thickness of the window in the vacuum cavity can be 3.5 mm, and the refractive index can be the refractive index of Pyrex glass. The distance from the outer surface of the vacuum cavity to the metasurface can be 2.5 mm, and the refractive index can be the refractive index of air.

[0101] In some embodiments, the preset value for the difference between the sixth phases can be 0.1 rad. In some specific embodiments, 100 iterations can be performed to satisfy this condition. In some embodiments, the phase matrix can be a large matrix of 11628 × 11628.

[0102] The propagation path of metasurface light is divided into three segments of the medium and calculated independently, which can effectively handle abrupt changes in the refractive index of the interface.

[0103] like Figure 9As shown, in some embodiments, the metasurface is located inside a vacuum cavity. Step S120 may include: step S121B, setting an initial light intensity distribution and an initial phase of the light emitted from the metasurface; step S122B, calculating a seventh phase of the light propagating to the target plane based on the initial light intensity distribution and the initial phase; step S123B, calculating an eighth phase of the light propagating backward from the target plane to the metasurface based on the target light intensity distribution and the seventh phase, and updating the initial phase to the eighth phase; and repeating the operations of steps S122B to S123B until the absolute value of the difference between two adjacent calculated eighth phases is less than a preset value.

[0104] As is easily understood, steps S121B to S123B can be based on similar... Figure 6 The operations from steps S121A to S127A are performed. Specifically, they can be performed according to similar... Figure 7 Step S122B can be executed in the manner described in steps S122A1 to S122A6, and can be performed according to a similar manner. Figure 8 Step S123B is executed in the manner described in steps S125A1 to S125A6, which will not be elaborated here.

[0105] Back Figure 5 In step S160, the parameters of each cell can be determined based on the required phase shift for each cell. The relationship between the phase shift and the cell parameters can be predetermined or determined in other ways. By determining the parameters of each cell, the desired metasurface can be obtained.

[0106] In some embodiments, prior to step S160, the metasurface design method may further include determining the correlation between cell parameters and the phase shift caused by the cells to light, which can be accomplished using electromagnetic simulation methods such as the finite-difference time-domain method or rigorous coupled-wave analysis. A series of cell parameters can be determined such that the phase shift caused by the parameters of all cells to light covers the entire range of phases between 0 and 2π, and the transmittance of the cells to light is greater than or equal to a preset threshold. In this way, ensuring that the range of phase shift caused by the cells to light covers the entire range of phases between 0 and 2π allows all required phases to be achieved through different feature sizes, and ensuring that the transmittance of light is greater than or equal to the preset threshold avoids poor cell light transmission that could affect the generation of optical tweezers.

[0107] This disclosure also proposes a particle array capture method, which may include: using an optical tweezers array system according to any of the foregoing embodiments to capture multiple particles at the optical tweezers positions of the optical tweezers array to form a particle array.

[0108] In some embodiments, capturing multiple particles at the optical tweezers positions of the optical tweezers array using the optical tweezers array system according to any of the foregoing embodiments may include: step S220, loading the particles to be captured into a vacuum cavity; step S240, cooling the particles using a magneto-optical trap to bring the particle temperature below or equal to a preset temperature; step S260, activating a light source to emit a beam of light to form an optical tweezers array in the vacuum cavity; and step S280, observing the captured particles using laser-cooled fluorescence imaging.

[0109] In step S220, the particles loaded into the vacuum chamber can be in a gaseous state.

[0110] In some embodiments, the pressure inside the vacuum chamber can be maintained at less than or equal to 10. -9 A vacuum with a pressure of Pa.

[0111] In step S240, the temperature of the particles can be pre-cooled to 100 μK or below using a magneto-optical trap to facilitate capture by the optical tweezers array.

[0112] In step S260, the particles are irradiated using an optical tweezers array to complete the capture. In some embodiments, the particles can be loaded into the optical tweezers of the array during the red-detuned optical molasses cooling stage. Here, red detuning refers to the tuning of the laser light frequency to a level lower than the quantum system resonant frequency of the particles. During the red-detuned optical molasses stage, the average velocity of the particles is initially reduced through a Doppler cooling mechanism, and then further cooled to a sub-Doppler temperature by a polarization gradient cooling (PGC) mechanism. When the kinetic energy of the particles decreases below the dipole well depth of the optical tweezers, they can be trapped at the bottom of the well, completing the loading process. It should be noted that during the red-detuned loading process, the near-resonant cooling light within the well induces strong light-assisted two-body collisions, causing paired particles entering the same optical tweezers to be simultaneously heated and escape (i.e., a collision blocking effect). Therefore, the single-atom loading rate of optical tweezers based on the red-detuned mechanism is typically limited to a theoretical upper limit of approximately 50%. In some embodiments, the detuning of the cooling light can be 40 MHz, and the intensity of the cooling light can be 2.5 I. sat The intensity of the repump light can be 0.4 I. sat , where I sat It is the saturation light intensity of a particle transitioning between states.

[0113] Alternatively, in some embodiments, particles can be loaded into optical tweezers during a blue-detuned Λ-enhanced gray-molasses cooling stage. Blue detuning refers to the tuning of the laser's optical frequency to a frequency higher than the quantum system resonant frequency of the particles. In this stage, the combination of cooling and repumping light effectively cools the particles; more importantly, during loading into the micro-volume of the optical tweezers, the blue-detuned light induces repulsive light-assisted inelastic collisions between particles within the same potential well. Specifically, when two particles approach each other in the optical tweezers' potential well, the blue-detuned light resonates and excites them to a repulsive molecular potential surface. During this inelastic collision, the magnitude of the kinetic energy released and gained by the particles is deterministic, and this energy change is controlled by the amount of blue detuning. By precisely adjusting the matching relationship between the amount of blue detuning and the depth of the optical tweezers' potential well, the kinetic energy generated by the collision can be such that only one particle overcomes the potential barrier and flies out of the optical tweezers, while the other particle remains in the potential well after energy distribution or dissipation. This deterministic 'one-in, one-out' loading mechanism successfully breaks the parity constraint (i.e., collision blocking effect) of pairwise loss in the red detuning mechanism, thus effectively exceeding the theoretical limit of 50% loading rate. In some embodiments, based on this blue detuning inelastic collision mechanism, a significant improvement in single-atom loading rate (e.g., reaching 80% or higher) can be achieved, thereby greatly optimizing the initialization efficiency of the entire optical tweezers array. In some embodiments, the detuning of the cooling light can be 45 MHz, and the intensity of the cooling light can be 2.5 I. sat The intensity of the repump light can be 0.4I. sat , where I sat It is the saturation light intensity of a particle transitioning between states.

[0114] In step S280, the trapped particles can be observed using red detuning polarization gradient cooling (RPGC) fluorescence imaging. Red detuning refers to the laser's frequency being tuned below the resonant frequency of the particle's quantum system. Polarization gradient cooling, also known as Sisyphus cooling, involves causing the particle to lose kinetic energy by climbing a potential energy slope, and then being pumped by light to the bottom of another potential energy valley, repeating this process continuously. During this process, the spontaneous fluorescence emitted by the particle during the climbing and pumping can be used to observe the particle's state.

[0115] In some embodiments, the standard deviation of the generated optical tweezers array can be less than or equal to 20% to optimize the capture effect, wherein the standard deviation of the optical tweezers array is the ratio of the standard deviation of the trap depth of each optical tweezer in the optical tweezers array to the average value of the trap depth of each optical tweezer in the optical tweezers array.

[0116] In some specific embodiments, the spacing between the light spots of the optical tweezers in each optical tweezers array can be greater than or equal to 4.3 μm, the diameter of the waist of a single optical tweezer can be greater than or equal to 0.9 μm, and the standard deviation of the generated optical tweezers array can be less than or equal to 13% to achieve large-scale particle array capture.

[0117] According to the technical solution disclosed herein, an optical tweezers array system and a particle array trapping method based thereon can be provided. The optical tweezers array system includes: a light source, a vacuum cavity transparent to the light beam, and a metasurface. The light source is configured to emit a light beam. The vacuum cavity is disposed in the outgoing light path of the light source and is configured to load particles to be trapped inside it. The metasurface is disposed between the vacuum cavity and the light source. The metasurface is configured to modulate the light beam, causing the beam to form an optical tweezers array within the vacuum cavity, thereby trapping particles at the optical tweezers positions of the array. This allows for the generation of large-scale optical tweezers arrays with more than ten thousand optical tweezers, enabling efficient trapping of large-scale particle arrays, suitable for atomic and molecular manipulation in fields such as quantum computing, quantum simulation, and precision measurement.

[0118] The foregoing has described one or more exemplary embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0119] The terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, product, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, product, or apparatus. Without further limitation, the presence of other identical or equivalent elements in the process, method, product, or apparatus that includes said elements is not excluded. For example, the use of terms such as "first" or "second" to denote names does not indicate any particular order.

[0120] The same or similar parts between the various embodiments of this disclosure can be referred to mutually, and each embodiment focuses on describing the differences from other embodiments. In the description of this disclosure, the reference to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," "exemplary," etc., means that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this disclosure, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this disclosure and the features of the different embodiments or examples.

[0121] Additionally, when used in this disclosure, the terms “here,” “above,” “below,” “below,” “in the following,” “overall,” and similar terms should refer to the entirety of this disclosure and not any particular part thereof. Furthermore, unless expressly stated otherwise or otherwise understood in the context in which they are used, conditional language used herein, such as “may,” “possibly,” “for example,” “like,” etc., is generally intended to express that certain embodiments include, while other embodiments do not, certain features, elements, and / or states. Therefore, such conditional language is not generally intended to imply that one or more embodiments require features, elements, and / or states in any way, or whether such features, elements, and / or states are included or performed in any particular embodiment.

[0122] The above description is merely an embodiment of one or more embodiments of this disclosure and is not intended to limit the scope of the one or more embodiments of this disclosure. Various modifications and variations can be made to the one or more embodiments of this disclosure by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of the claims.

Claims

1. An optical tweezers array system, the optical tweezers array system comprising: A light source, wherein the light source is configured to emit a light beam; A vacuum cavity, wherein the window of the vacuum cavity is transparent to the light beam, the vacuum cavity is disposed in the exit light path of the light source, and wherein the vacuum cavity is configured to load particles to be captured inside it; A metasurface, wherein the metasurface is disposed in the outgoing light path of the light source; The metasurface is configured to modulate the light beam such that the light beam forms an optical tweezers array within the vacuum cavity to trap particles at the optical tweezers positions of the optical tweezers array.

2. The optical tweezers array system according to claim 1, wherein, The power of the light source and the wavelength of the light beam are adjusted according to the diffraction efficiency of the metasurface, the Airy disk intensity utilization rate of the metasurface, the optical path loss rate of the optical tweezers array system, and the number of optical tweezers in the optical tweezers array system, so that the well depth of each optical tweezer in the optical tweezers array is greater than or equal to a first preset threshold, so that the loading rate of the optical tweezers array is greater than or equal to a preset loading rate. The Airy disk intensity utilization rate is the ratio of the total light intensity of the light beam diffracted by the metasurface into the optical tweezers array to the total light intensity of all diffracted light diffracted by the metasurface.

3. The optical tweezers array system according to claim 2, wherein, The equivalent temperature of the first preset threshold in the energy space is 0.27 mK.

4. The optical tweezers array system according to claim 1, wherein, The area between the metasurface and the optical tweezers position of the optical tweezers array does not include a microscope.

5. The optical tweezers array system according to claim 1, wherein, The metasurface is located inside the vacuum cavity.

6. The optical tweezers array system according to claim 1, wherein, The metasurface does not operate in a vacuum environment.

7. The optical tweezers array system according to claim 6, wherein, The metasurface is located between the vacuum cavity and the light source.

8. The optical tweezers array system according to claim 7, wherein, The first radius of the microstructured region of the metasurface is greater than or equal to tan(θ)×(L1+d / n1+L2), where θ is the angle corresponding to the numerical aperture required to focus the optical tweezers to the size of the optical tweezers array, L1 is the distance between the metasurface and the outer surface of the vacuum cavity, d is the thickness of the wall of the vacuum cavity, n1 is the window refractive index of the wall of the vacuum cavity, and L2 is the spacing distance between the trapped particles and the inner surface of the vacuum cavity.

9. The optical tweezers array system according to claim 7, wherein, The distance between the metasurface and the outer surface of the vacuum cavity is less than or equal to 10 cm.

10. The optical tweezers array system according to claim 1, further comprising: A beam-splitting reflector is disposed between the light source and the metasurface, wherein the beam-splitting reflector includes a mirror surface, the mirror surface forming a predetermined angle with the outgoing light path of the light source, and the mirror surface has a hole at its center, the projection of the hole onto the metasurface being circular. The beam-splitting mirror is configured to reflect light away from the optical path at a distance beyond a second radius from the center of the beam, perpendicular to the direction of travel of the beam.

11. The optical tweezers array system according to claim 1, further comprising: A microscope is disposed in the outgoing light path of the vacuum cavity, wherein the microscope is configured to receive light emitted from the vacuum cavity, the light emitted from the vacuum cavity including light for forming the optical tweezers array and fluorescence emitted by particles captured by the optical tweezers array.

12. The optical tweezers array system according to claim 11, wherein, One or more lenses of the microscope are configured such that portions of light emitted from the metasurface that are not focused into optical tweezers by the metasurface do not converge onto any lens of the microscope.

13. The optical tweezers array system according to claim 1, further comprising: A rotating waveplate is disposed between the light source and the metasurface, wherein the rotating waveplate is configured to change the phase of the light beam; A polarization beam splitter is disposed between the rotating waveplate and the metasurface. The rotating waveplate and the polarizing beam splitter are configured to adjust the light intensity of the beam.

14. The optical tweezers array system according to claim 1, wherein, The surface of the metasurface closest to the light source is coated with an antireflective film.

15. A method for designing a metasurface in an optical tweezers array system, said optical tweezers array system being the optical tweezers array system according to any one of claims 1-4, 10-14, wherein the metasurface comprises a plurality of cells arranged in an array, the method comprising: Based on the target light intensity distribution of the optical tweezers array at the target plane, determine the phase shift that each cell constituting the metasurface needs to cause to the light incident on the metasurface; The parameters of each cell are determined based on the phase shift required for each cell.

16. The method according to claim 15, wherein, The metasurface is located between the vacuum cavity and the light source. Based on the target light intensity distribution of the optical tweezers array at the target plane, the phase shift that each cell constituting the metasurface needs to cause to the light incident on the metasurface includes: The initial intensity distribution and initial phase of the light emitted from the metasurface are set. Based on the initial light intensity distribution and the initial phase, calculate the first light intensity distribution and the first phase at the outer surface of the vacuum cavity where the light propagates. Based on the first light intensity distribution and the first phase, calculate the second light intensity distribution and the second phase at the inner surface of the vacuum cavity where the light propagates. Based on the second light intensity distribution and the second phase, calculate the third phase at the point where the light propagates to the target plane. Based on the target light intensity distribution and the third phase, calculate the third light intensity distribution and the fourth phase as the light propagates backward from the target plane to the inner surface of the vacuum cavity. Based on the third light intensity distribution and the fourth phase, calculate the fourth light intensity distribution and the fifth phase as light propagates backward from the inner surface of the vacuum cavity to the outer surface of the vacuum cavity. Based on the fourth light intensity distribution and the fifth phase, a sixth phase is calculated, in which light propagates backward from the outer surface of the vacuum cavity to the metasurface, and the initial phase is updated to the sixth phase. The process of repeatedly calculating the first light intensity distribution and first phase at the outer surface of the vacuum cavity based on the initial light intensity distribution and the initial phase, calculating the second light intensity distribution and second phase at the inner surface of the vacuum cavity based on the first light intensity distribution and the first phase, calculating the third phase at the target plane based on the second light intensity distribution and the second phase, calculating the third light intensity distribution and fourth phase at the inner surface of the vacuum cavity based on the target light intensity distribution and the third phase, calculating the fourth light intensity distribution and fifth phase at the outer surface of the vacuum cavity based on the third light intensity distribution and the fourth phase, and calculating the sixth phase at the outer surface of the vacuum cavity based on the fourth light intensity distribution and the fifth phase, and updating the initial phase to the sixth phase, continues until the absolute value of the difference between two consecutive calculated sixth phases is less than a preset value.

17. The method according to claim 16, wherein, Calculating the first light intensity distribution and first phase at the outer surface of the vacuum cavity, calculating the second light intensity distribution and second phase at the inner surface of the vacuum cavity, and calculating the third phase at the target plane, including: The matrix representing the light before propagation is read in blocks to obtain multiple first matrices. Perform a Fast Fourier Transform (FFT) on each first matrix to obtain the second matrix corresponding to each first matrix. Calculate the third matrix after propagation for each second matrix. Perform an inverse fast Fourier transform (IFFT) on each third matrix to obtain the fourth matrix corresponding to each third matrix. Combine all the fourth matrices into a matrix representing the propagated light, and The intensity distribution and / or phase of the propagated light are determined based on the matrix of the propagated light. The obtained second and fourth matrices are stored in a non-transitory storage medium; and / or Calculating the third intensity distribution and fourth phase of light propagating backward from the target plane to the inner surface of the vacuum cavity, calculating the fourth intensity distribution and fifth phase of light propagating backward from the inner surface of the vacuum cavity to the outer surface of the vacuum cavity, and calculating the sixth phase of light propagating backward from the outer surface of the vacuum cavity to the metasurface, including: The matrix representing the light before backpropagation is read in blocks to obtain multiple fifth matrices. Perform a Fast Fourier Transform (FFT) on each fifth matrix to obtain the sixth matrix corresponding to each fifth matrix. Calculate the seventh matrix after backpropagation for each sixth matrix. Perform an inverse fast Fourier transform (IFFT) on each seventh matrix to obtain the eighth matrix corresponding to each seventh matrix. Combine all the eighth matrices into a matrix representing the light after backward propagation, and The intensity distribution and / or phase of the back-propagated light are determined based on the matrix of the back-propagated light. The sixth and eighth matrices obtained are stored in a non-transitory storage medium.

18. The method according to claim 15, wherein, The metasurface is located within the vacuum cavity. Based on the target light intensity distribution of the optical tweezers array at the target plane, the phase shift that each cell constituting the metasurface needs to cause to the light incident on the metasurface includes: The initial intensity distribution and initial phase of the light emitted from the metasurface are set. Based on the initial light intensity distribution and the initial phase, calculate the seventh phase at the target plane where the light propagates. Based on the target light intensity distribution and the seventh phase, calculate the eighth phase of light propagating backward from the target plane to the metasurface, and update the initial phase to the eighth phase. The process of repeatedly calculating the seventh phase of light propagation to the target plane based on the initial light intensity distribution and the initial phase, calculating the eighth phase of light propagation from the target plane to the metasurface based on the target light intensity distribution and the seventh phase, and updating the initial phase to the eighth phase, continues until the absolute value of the difference between two adjacent calculated eighth phases is less than a preset value.

19. The method according to claim 18, wherein, Calculating the seventh phase of light propagating to the target plane includes: The matrix representing the light before propagation is read in blocks to obtain multiple first matrices. Perform a Fast Fourier Transform (FFT) on each first matrix to obtain the second matrix corresponding to each first matrix. Calculate the third matrix after propagation for each second matrix. Perform an inverse fast Fourier transform (IFFT) on each third matrix to obtain the fourth matrix corresponding to each third matrix. Combine all the fourth matrices into a matrix representing the propagated light, and The intensity distribution and / or phase of the propagated light are determined based on the matrix of the propagated light. The obtained second and fourth matrices are stored in a non-transitory storage medium; and / or Calculating the eighth phase of light propagating backward from the target plane to the metasurface includes: The matrix representing the light before backpropagation is read in blocks to obtain multiple fifth matrices. Perform a Fast Fourier Transform (FFT) on each fifth matrix to obtain the sixth matrix corresponding to each fifth matrix. Calculate the seventh matrix after backpropagation for each sixth matrix. Perform an inverse fast Fourier transform (IFFT) on each seventh matrix to obtain the eighth matrix corresponding to each seventh matrix. Combine all the eighth matrices into a matrix representing the light after backward propagation, and The intensity distribution and / or phase of the back-propagated light are determined based on the matrix of the back-propagated light. The sixth and eighth matrices obtained are stored in a non-transitory storage medium.

20. A method for capturing particles using an array, comprising: Using the optical tweezers array system according to any one of claims 1-14, multiple particles are captured at the optical tweezers positions of the optical tweezers array to form a particle array.

21. The particle array capture method according to claim 20, wherein, Using the optical tweezers array system according to any one of claims 1-14 to trap a plurality of particles at the optical tweezers position of the optical tweezers array comprises: The particles to be captured are loaded into a vacuum cavity, wherein the particles are in a gaseous state; The particles are cooled using a magneto-optical trap so that the temperature of the particles is lower than or equal to a preset temperature. The light source is activated to emit a beam of light, forming an array of optical tweezers in the vacuum cavity; The captured particles were observed using laser-cooled fluorescence imaging.

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