Method for generating a spatial light modulator tensor for atomic array rearrangement

Abstract

Provided is a method for generating a spatial light modulator tensor for atomic array rearrangement, comprising: constructing an initial pixel plane complex amplitude field on a pixel plane of a spatial light modulator based on target light illumination parameters and performing a WGS single-step iteration; obtaining a pixel plane steady-state complex amplitude field based on convergence of the WGS single-step iteration to a fixed point; calculating a partial derivative of a WGS single-step operator with respect to the pixel plane steady-state complex amplitude field to obtain a steady-state Jacobian matrix; calculating a partial derivative of the WGS single-step operator with respect to positions of all optical traps to obtain a position partial derivative matrix; and obtaining a complex amplitude sensitivity matrix based on the steady-state Jacobian matrix and the position partial derivative matrix, and obtaining a complex amplitude sensitivity matrix Hermitian Gram matrix as the spatial light modulator tensor. In this way, the path planning of atomic rearrangement can be optimized using the spatial light modulator tensor, the accuracy of the generated hologram and the generation speed of the hologram are improved, and a better atomic rearrangement effect is obtained.

Description

Technical Field

[0001] This application relates to the field of quantum computing technology, and more specifically, to a method for generating spatial light modulator tensors for atomic array rearrangement, an electronic device, and a computer-readable storage medium. Background Technology

[0002] Neutral atoms (such as or Quantum computing is one of the most promising quantum computing routes. Its core advantages are: the same type of atoms have natural uniformity (no manufacturing tolerances and parameter dispersion), the hyperfine ground state coherence time is extremely long (up to 10 seconds, far exceeding the operation time of typical quantum gates), and it allows the realization of high-fidelity fully connected two-qubit gates between two qubits by physically moving atomic qubits.

[0003] This technology captures individual cold atoms with optical tweezers and achieves quantum entanglement gates through Rydberg excitation. Typically, a large-scale programmable optical tweezers array is realized using a spatial light modulator (SLM). The SLM modulates the phase of the incident laser light through individual liquid crystal pixels on a liquid crystal panel. After Fourier transform by a lens, an optical tweezers array is formed on the focal plane, thereby fixing individual cold atoms in individual optical traps by the optical tweezers array.

[0004] During the loading of cold atoms into optical traps constructed from optical tweezers arrays, the probability of each optical trap being occupied by a single atom follows an independent Bernoulli distribution (typical occupancy rate) due to atomic number density fluctuations and photo-induced collision blocking mechanisms. This means that for a quantum array, for example, containing 100 physical bits, the probability of forming a completely defect-free target array after natural random loading is extremely low (approximately). ).

[0005] Therefore, before each quantum computation, an atomic array rearrangement mechanism must be introduced. This involves identifying the current defect state through camera fluorescence imaging, implementing motion planning using low-level control algorithms, and frequently refreshing the hologram to drive the SLM to change the optical trap positions in real time, physically transforming the scattered atoms into a specified defect-free target configuration. Here, the SLM (e.g., comprising 1024×1024 pixels) can simultaneously control the real-time movement of atoms trapped in multiple optical traps by applying a phase delay to each liquid crystal pixel.

[0006] In existing hologram generation methods, such as those using the WGS (Weighted Gerchberg-Saxton) algorithm, spatial crosstalk between optical traps is neglected. That is, during the WGS iterative convergence process, because the spatial light modulator uniformly modulates all light waves through the hologram, moving any optical trap will physically leak light through wavefront superposition, affecting the intensity of all other optical traps. This non-local coupling can lead to a significant deterioration in the intensity uniformity of the focal plane when the optical traps move at high speeds, potentially causing atomic detachment and heating. It can also cause a phase jump that instantaneously eliminates atomic coherence, and the speed is limited.

[0007] For example, the latency of standard WGS (100 iterations) is greater than 10ms and phase continuity is not guaranteed; the latency of linear phase difference (LPI) is about 1ms, which satisfies phase continuity, but the intensity error is large; the latency of a one-step generation scheme of convolutional neural network (CNN) is about 0.5ms, but phase continuity is not guaranteed, and a large amount of training data is required, resulting in poor generalization performance; the latency of sparse WPGS is about 4ms, and it only satisfies partial phase continuity and has no optimality guarantee.

[0008] Therefore, it is desirable to provide a scheme based on optical trap displacement to measure holographic changes. Summary of the Invention

[0009] This application provides a method for generating a spatial light modulator tensor for atomic array rearrangement. By generating a spatial light modulator tensor that measures the change in steady-state hologram caused by optical trap displacement, the path planning for atomic rearrangement can be optimized, the accuracy and generation speed of the generated hologram can be improved, and thus a better atomic rearrangement effect can be obtained.

[0010] According to one aspect of this application, a method for generating a spatial light modulator tensor for atomic array rearrangement is provided, comprising: constructing an initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on target illumination parameters, and performing WGS single-step iteration using a WGS single-step operator on the initial pixel plane complex amplitude field to obtain a pixel plane complex amplitude field for the corresponding iteration round; obtaining the pixel plane complex amplitude field for the corresponding iteration round as a pixel plane steady-state complex amplitude field based on the convergence of the WGS single-step iteration to a fixed point; calculating the partial derivative of the WGS single-step operator with respect to the pixel plane steady-state complex amplitude field to obtain a steady-state Jacobian matrix; calculating the partial derivative of the WGS single-step operator with respect to the positions of all optical traps to obtain a position partial derivative matrix; and obtaining a complex amplitude sensitivity matrix by the total differential of the fixed-point condition of the WGS single-step operator based on the steady-state Jacobian matrix and the position partial derivative matrix, and obtaining the Hermitian Gram matrix of the complex amplitude sensitivity matrix as the spatial light modulator tensor.

[0011] In the above method for generating the tensor of a spatial light modulator for atomic array rearrangement, constructing the initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters includes: obtaining the target illumination parameters, which include: a set of target amplitudes of each optical trap in the pre-configured target array, a set of positions of each optical trap, an initial hologram, a uniformity convergence accuracy threshold, a set of weights of the iterative initial states of each optical trap, a laser wavelength, and a focal length of the pre-Fourier lens.

[0012] In the above method for generating the tensor of a spatial light modulator for atomic array rearrangement, constructing the initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters includes: multiplying the initial hologram based on the liquid crystal pixel coordinates of the liquid crystal panel of the spatial light modulator with an imaginary unit and using the result as the exponent of the natural constant to obtain the initial pixel plane complex amplitude field.

[0013] In the above method for generating the tensor of a spatial light modulator for atomic array rearrangement, constructing the initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters includes: multiplying the position of each optical trap in the target array on the focal plane of the spatial light modulator by a phase period constant and then dividing by the laser wavelength and the focal length of the pre-Fourier lens to obtain the frequency of each optical trap.

[0014] In the above-described method for generating spatial light modulator tensors for atomic array rearrangement, performing WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field for the corresponding iteration round includes: dividing the pixel plane complex amplitude field of the current round by its magnitude to obtain a phased pixel plane complex amplitude field; performing a forward Fourier transform on the phased pixel plane complex amplitude field to obtain a focal plane complex amplitude field on the focal plane; at each optical trap position in the target array, dividing the focal plane complex amplitude field by its magnitude and multiplying it by the target amplitude and the weight of the current round to obtain an amplitude-constrained focal plane complex amplitude field; and performing an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field to obtain the pixel plane complex amplitude field for the next round.

[0015] In the above method for generating spatial light modulator tensors for atomic array rearrangement, performing WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round further includes: dividing the target amplitude of each optical well by the modulus of the focal plane complex amplitude at the position of each optical well and multiplying it by the weight of each optical well in the current round to obtain the weight of each optical well in the next round.

[0016] In the above method for generating spatial light modulator tensors for atomic array rearrangement, calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane to obtain the steady-state Jacobian matrix includes: calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a small perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to obtain the steady-state Jacobian matrix.

[0017] In the above-described method for generating the spatial light modulator tensor for atomic array rearrangement, the calculation of the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a micro-perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to obtain the steady-state Jacobian matrix includes: constructing a phased steady-state complex amplitude field of the pixel plane based on the phased operation in the WGS single-step operator and obtaining the Jacobian coefficients of each optical well corresponding to the phased steady-state complex amplitude field of the pixel plane; constructing a focal plane tangent space projection operator for projecting the complex perturbation vector onto the imaginary part direction of the focal plane based on the complex perturbation vector acting on the phased steady-state complex amplitude field of the pixel plane; and multiplying the Jacobian coefficients of each optical well, the focal plane tangent space projection operator, and the plane wave factor for plane wave modulation to obtain the steady-state Jacobian matrix.

[0018] In the above method for generating spatial light modulator tensors for atomic array rearrangement, after obtaining the steady-state Jacobian matrix, the method further includes: probing the non-zero elements of the steady-state Jacobian matrix column by column with probe vectors that are non-zero only in the neighborhood of the optical trap to extract the non-zero elements of the steady-state Jacobian matrix and obtain a sparsified steady-state Jacobian matrix.

[0019] In the above-described method for generating the spatial light modulator tensor for atomic array rearrangement, calculating the partial derivatives of the WGS single-step operator with respect to the positions of all optical traps to obtain the position partial derivative matrix includes: modulating the phased pixel plane steady-state complex amplitude field pixel by pixel with the lateral and longitudinal coordinates of the pixel plane of the spatial light modulator to obtain a lateral coordinate modulation field and a longitudinal coordinate modulation field; performing a Fourier transform on the lateral coordinate modulation field and the longitudinal coordinate modulation field and sampling at the frequency of each optical trap to obtain the lateral component modulation spectrum sample value and the longitudinal component modulation spectrum sample value of each optical trap; multiplying the lateral component modulation spectrum sample value and the longitudinal component modulation spectrum sample value of each optical trap by a frequency-coordinate mapping constant to combine the position partial derivative components of each optical trap along the lateral and longitudinal directions; and flattening the position partial derivative components of each optical trap along the lateral and longitudinal directions into column vectors of the pixel plane complex amplitude field and concatenating them according to the lateral and longitudinal coordinate order of the optical traps to obtain the position partial derivative matrix.

[0020] In the above method for generating the spatial light modulator tensor for atomic array rearrangement, obtaining the complex amplitude sensitivity matrix from the total differential of the fixed-point condition of the WGS single-step operator based on the steady-state Jacobian matrix and the position partial derivative matrix, and obtaining the Hermitian Gram matrix of the complex amplitude sensitivity matrix as the spatial light modulator tensor includes: calculating the total differential of the implicit functional representation of the fixed-point condition of the WGS single-step operator with respect to the optical trap position set; obtaining the complex amplitude sensitivity matrix from the total differential representation based on the steady-state Jacobian matrix; and taking the Hermitian Gram matrix of the complex amplitude sensitivity matrix to obtain the spatial light modulator tensor, wherein the spatial light modulator tensor measures the change in the steady-state hologram caused by the optical trap displacement.

[0021] In the above method for generating a spatial light modulator tensor for atomic array rearrangement, after obtaining the spatial light modulator tensor, the method further includes: determining the positive semidefiniteness of the spatial light modulator tensor based on the Hermitian Gram matrix representation of the complex amplitude sensitivity matrix.

[0022] In the above method for generating a spatial light modulator tensor for atomic array rearrangement, after obtaining the spatial light modulator tensor, the method further includes: determining the positive definiteness of the spatial light modulator tensor in response to the full column rank of the complex amplitude sensitivity matrix.

[0023] In the above-described method for generating a spatial light modulator tensor for atomic array rearrangement, after obtaining the spatial light modulator tensor, the method further includes: in response to the spectral radius of the steady-state Jacobian matrix being less than one, determining that the difference tensor between the unit tensor and the steady-state Jacobian matrix is ​​invertible and obtaining the complex amplitude sensitivity matrix; and in response to the complex amplitude sensitivity matrix having full column rank, determining the positive definiteness of the spatial light modulator tensor.

[0024] In the above method for generating spatial light modulator tensors for atomic array rearrangement, the spatial light modulator tensor is used for at least one of the following: Riemannian metric for atomic array rearrangement path planning, Fisher-like metric for hologram generation, and preconditioner for complex amplitude domain gradient flow.

[0025] In the above-described method for generating a spatial light modulator tensor for atomic array rearrangement, after obtaining the spatial light modulator tensor, the method further includes: performing... Sparsification is used to obtain a sparsified spatial light modulator tensor.

[0026] In the above-described method for generating spatial light modulator tensors for atomic array rearrangement, the spatial light modulator tensor is subjected to... The sparsification process to obtain a sparsified spatial light modulator tensor includes: obtaining the block elements of the spatial light modulator tensor represented by the inner product between corresponding columns of the complex amplitude sensitivity matrix and the position partial derivative matrix; simplifying the position partial derivative matrix with an iterative initial state and a uniform rectangular aperture to obtain a simplified complex amplitude sensitivity matrix, and obtaining the simplified block elements of the spatial light modulator tensor in the iterative initial state represented by the aperture integral based on the simplified complex amplitude sensitivity matrix; performing Dirichlet kernel summation and large pixel number continuum on the simplified block elements of the spatial light modulator tensor to obtain the crosstalk intensity between the two optical traps. Coupling rate; and, using the above The far-end integral rate of the coupling rate is used to estimate the truncation bandwidth, and the spatial light modulator tensor is bandwidth-truncated with the truncation bandwidth to obtain the sparsified spatial light modulator tensor.

[0027] According to another aspect of this application, an electronic device is provided, including a processor coupled to a memory, the processor being configured to execute a computer program stored in the memory, such that the electronic device performs the method described above for generating a spatial light modulator tensor for atomic array rearrangement.

[0028] According to another aspect of this application, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program that, when the computer program is run, implements the method described above for generating spatial light modulator tensors for atomic array rearrangement.

[0029] The method for generating spatial light modulator tensors for atomic array rearrangement provided in this application can optimize the path planning of atomic rearrangement by generating spatial light modulator tensors that measure the steady-state hologram changes caused by optical trap displacement, thereby improving the accuracy and generation speed of the generated hologram and achieving better atomic rearrangement results. Attached Figure Description

[0030] Various other advantages and benefits of this application will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0031] Figure 1 The illustration shows a schematic flowchart of a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application.

[0032] Figure 2 The illustration shows a schematic flowchart of the WGS single-step iterative process in the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application.

[0033] Figure 3 The illustration shows a schematic flowchart of the process of obtaining a steady-state Jacobian matrix using Wirtinger calculus in a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application.

[0034] Figure 4 The illustration shows a schematic flowchart of the process of calculating the position partial derivative matrix in the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application.

[0035] Figure 5 The illustration shows a schematic flowchart of the process of obtaining a spatial light modulator tensor in a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of the present application.

[0036] Figure 6 The illustration shows a spatial light modulator tensor in a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application. A schematic flowchart of the sparsification process.

[0037] Figure 7 A schematic block diagram of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0038] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0039] Figure 1 The illustration shows a schematic flowchart of a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application. Figure 1 As shown, the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application includes the following steps.

[0040] S110, construct an initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters, and perform WGS single-step iteration using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round.

[0041] As described above, optical tweezers capture individual cold atoms by forming a bright spot with a laser beam highly focused by a lens, thereby locking the cold atom at the focal point through a dipole force generated by the gradient direction towards the focal point due to uneven light intensity. The cold atom can then move with the laser beam. Meanwhile, spatial light modulators utilize their liquid crystal panels (e.g., 1 pixel, of which Each liquid crystal pixel modulates the phase of light passing through it by changing the phase of the hologram. For example, the coordinates of each pixel are represented as... The hologram composed of the applied phase delay is then represented as: , In other words, the hologram is essentially a phase diagram.

[0042] Thus, the input coherent laser beam, after being phase-modulated by the spatial light modulator, passes through a focal length of... Focusing lenses, such as Fourier lenses, are superimposed on the focal plane to form an array of optical tweezers consisting of independent optical tweezers. This array holds atoms within the optical traps of a corresponding optical trap array, allowing the tweezers to move them between the traps. Therefore, for coordinates in the optical trap array on the focal plane... There is a complex amplitude distribution That is, the complex amplitude field of the focal plane, is expressed as:

[0043] in It is the laser wavelength, for example, 399nm. Thus, the first [missing information] in the optical trap target array... The location of the optical trap, for example, denoted as The strength at that point is Therefore, in order to achieve the target amplitude for each optical trap, for example denoted as Holograms are needed. Make In this embodiment, the WGS (Weighted Gerchberg-Saxton) algorithm is used to solve for the hologram. This is a phase recovery problem, and the WGS algorithm is essentially a steady-state (fixed-point) iteration, which will be explained in detail below.

[0044] In a dense array of atoms, each atom is held in an optical trap by its own optical tweezers. However, since all the optical tweezers share the same diffraction field generated by the spatial light modulator based on the hologram, moving one of the optical tweezers requires the spatial light modulator to recalculate the entire light field, thus shifting the positions and intensities of all the other optical tweezers. In other words, changes in the atom's position affect the equilibrium state of the entire hologram. Therefore, it is desirable to accurately represent how much the movement of a particular atom will disturb the other atoms, thereby determining the new equilibrium state of the hologram.

[0045] Based on this, the target illumination parameters are first obtained. Here, the target illumination parameters include the set of target amplitudes of each optical trap in the pre-configured target array. (including the first) The target amplitude of each optical trap ), the set of positions of each optical trap (including the first) The position of each optical trap Initial hologram Uniformity convergence accuracy threshold The weights of the initial states of each optical trap (including the first one). (weight of each optical trap), and laser wavelength Focal length of the front Fourier lens .

[0046] Here, the weights of the initial states of each optical trap are denoted as... And the first The weights of the optical traps are denoted as follows: .

[0047] Based on the initial hologram The normalized initial pixel plane complex amplitude field (i.e., the pure phase field with a constant modulus of 1) required for constructing a single-step WGS iteration is expressed as:

[0048] in This represents the complex amplitude field of the SLM pixel plane during the 0th (initial) iteration. ( ,here (This refers to the side length of an SLM LCD panel, expressed in pixels.) Two-dimensional pixel coordinates of an SLM LCD panel ( , The initial phase distribution is the input. The imaginary unit, The natural index. In the following text, the complex amplitude field of the SLM pixel plane is referred to as the pixel plane complex amplitude field.

[0049] Mapping the physical positions of each optical trap in the target array on the focal plane to the spatial frequency coordinates required for diffraction calculations is expressed as:

[0050] in For the first The spatial frequency coordinates (or simply frequencies) corresponding to each optical trap. For the target array on the focal plane, the first The spatial coordinates of each optical trap (or simply, position). For a specific light wave (such as a laser), The focal length of the front Fourier lens. It is a phase period constant.

[0051] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, constructing an initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on target illumination parameters includes: obtaining target illumination parameters, wherein the target illumination parameters include: a set of target amplitudes of each optical trap in a pre-configured target array; a set of positions of each optical trap; a set of weights for an initial hologram, a uniformity convergence accuracy threshold, and the iterative initial state of each optical trap; and the laser wavelength and the focal length of the pre-Fourier lens.

[0052] In the above method for generating the tensor of a spatial light modulator for atomic array rearrangement, constructing the initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters includes: multiplying the initial hologram based on the liquid crystal pixel coordinates of the liquid crystal panel of the spatial light modulator with an imaginary unit and using the result as the exponent of the natural constant to obtain the initial pixel plane complex amplitude field.

[0053] In the above method for generating the tensor of a spatial light modulator for atomic array rearrangement, constructing the initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters includes: multiplying the position of each optical trap in the target array on the focal plane of the spatial light modulator by a phase period constant and then dividing by the laser wavelength and the focal length of the pre-Fourier lens to obtain the frequency of each optical trap.

[0054] Figure 2 The illustration shows a schematic flowchart of the WGS single-step iterative process in the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application. Figure 2 As shown, the WGS single-step iterative process in the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application includes the following steps.

[0055] Step S111: Divide the pixel plane complex amplitude field of the current round by its magnitude to obtain the phase-processed pixel plane complex amplitude field. That is, after obtaining the initial pixel plane complex amplitude field, perform WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field. During the WGS single-step iteration, for example in the... In the nth iteration, first for the current iteration, i.e., the nth iteration... The pixel plane complex amplitude field at the next iteration Performing phase conversion decouples non-physical amplitude fluctuations (corresponding to the hardware properties of pure phase SLM), represented as:

[0056] in For the first The phase-modulated complex amplitude field of the pixel plane in the next iteration (the modulus is always 1). For the first The pixel plane complex amplitude field on the pixel plane of the next iteration of SLM. Let be the modulus of the complex amplitude field in the pixel plane. This essentially expresses the hardware phase modulation property of a pure phase spatial light modulator, since the actual SLM only changes the spatial phase delay of the incident laser. This does not change the amplitude of the laser. Since the calculated result of the complex amplitude field of the pixel plane obtained in each step of the WGS single-step iteration during the forward-inverse Fourier iteration of the wave field is a complex number containing both amplitude and phase, it can be obtained by dividing by its own modulus. This decouples non-physical amplitude oscillations and fluctuations, retaining only pure phase information to achieve holographic phase recovery.

[0057] Step S112: Perform a forward Fourier transform on the phased pixel plane complex amplitude field to obtain the focal plane complex amplitude field on the focal plane. Here, the phased pixel plane complex amplitude field... Performing a forward Fourier transform to simulate lens diffraction projection onto the focal plane is represented as:

[0058] That For the first The complex amplitude field of the focal plane on the focal plane in the next iteration. For the positive Fourier transform operator, The position on the focal plane (represented as spatial coordinates). For the position on the corresponding focal plane The frequency (represented as spatial frequency coordinates), for Summation represents the position of all pixels traversed on the SLM plane. They came to seek peace.

[0059] Step S113: At each optical trap position in the target array, the complex amplitude field of the focal plane on the focal plane is divided by its modulus and multiplied by the target amplitude and the weight of the current round to obtain the amplitude-constrained complex amplitude field of the focal plane. That is, at each optical trap position in the target array... An amplitude constraint is applied at this point, and the actual diffraction phase is recombined with the target weighted amplitude, which is expressed as: For the first The complex amplitude field of the focal plane after amplitude constraint in the next iteration For the first The iteration of the ... Weights of the optical trap For the first The target amplitude of the optical trap For the first Position of the next iteration Complex amplitude (including amplitude and phase) at the focal plane. Its modulus length.

[0060] Step S114: Perform an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field to obtain the pixel plane complex amplitude field for the next iteration. Here, performing an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field yields the next iteration, i.e., the [number missing]th iteration. The pixel plane complex amplitude field on the SLM pixel plane in the next iteration is expressed as:

[0061] in It is the total number of optical traps in the target array.

[0062] In summary, the complete WGS single-step operator is represented as:

[0063] Those skilled in the art will understand that the pixel plane complex amplitude field and the focal plane complex amplitude field are actually tensors composed of complex numbers containing amplitude and phase at each position. That is, the pixel plane complex amplitude field is composed of the pixel plane complex amplitude corresponding to each position of the pixel plane, while the focal plane complex amplitude field is composed of the focal plane complex amplitude corresponding to each position of the focal plane, i.e., each optical trap position.

[0064] In the method for generating spatial light modulator tensors for atomic array rearrangement according to embodiments of this application, performing WGS single-step iteration using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round includes: dividing the pixel plane complex amplitude field of the current round by its magnitude to obtain a phased pixel plane complex amplitude field; performing a forward Fourier transform on the phased pixel plane complex amplitude field to obtain a focal plane complex amplitude field on the focal plane; at the position of each optical trap in the target array, dividing the focal plane complex amplitude field by its magnitude and multiplying it by the target amplitude and the weight of the current round to obtain an amplitude-constrained focal plane complex amplitude field; and performing an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field to obtain the pixel plane complex amplitude field of the next round.

[0065] Alternatively, it can be done in the current round, i.e., the [number]th round. In the next iteration, the optical trap position is extracted. The actual diffraction amplitude of each optical trap in the complex amplitude of the focal plane at that location And based on the gain negative feedback law, adaptive weight updates are performed (if the actual weight is too weak, compensation is amplified; if the weight is too strong, suppression is performed), as follows:

[0066] in and The first , No. During the first iteration The weights of each optical trap.

[0067] In other words, due to the inherent long-range spatial interference crosstalk of the Fourier diffraction integral, the photon energy at each point in the optical tweezers array is difficult to be uniform (resulting in uneven brightness and causing random photothermal escape of the central atom). This can be addressed by monitoring the ideal value. (i.e., the first) (ideal target amplitude of each optical trap) and current actual value The ratio (which is the first) After the first simulation iteration of forward injection, at the specified position The complex amplitude field of diffracted light intensity generated by actual interference (amplitude value), if the actual light intensity at a certain optical trap is too weak (ratio) If the calculation weight of that point is increased, it will be compensated for and amplified; if it is too strong, it will be suppressed, so that the actual amplitude of each optical trap tends to its target amplitude. This ensures that all neutral atoms on the array are in a deep potential well with highly uniform energy, meaning the light intensity uniformity meets the convergence criterion. .

[0068] In the method for generating spatial light modulator tensors for atomic array rearrangement according to embodiments of this application, performing WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round further includes: dividing the target amplitude of each optical well by the modulus of the focal plane complex amplitude at the position of each optical well and multiplying by the weight of each optical well in the current round to obtain the weight of each optical well in the next round.

[0069] Step S120: Based on the single-step iteration of WGS converging to the fixed point, the pixel plane complex amplitude field of the corresponding iteration round is obtained as the pixel plane steady-state complex amplitude field.

[0070] Here, the convergence of the WGS single-step iteration to the fixed point can be determined by the light intensity uniformity index, the difference in complex amplitude between adjacent iterations, the phase map difference, the weight change, the fixed-point residual, the maximum number of iterations, or a combination thereof. For example, the light intensity uniformity index is used as an example below.

[0071] Here, the discrete distribution of the actual light intensity of all optical traps in the target array is statistically analyzed, and a scalar index of light intensity uniformity is calculated. ,in, Let be the standard deviation of the mode length (i.e., amplitude) of the complex amplitude at the focal plane of each optical trap. The average amplitude of each optical trap is expressed as follows:

[0072] The scalar index of light intensity uniformity With the preset uniformity convergence accuracy threshold In comparison, the preset uniformity convergence accuracy threshold is used here. In practice, it is usually taken as 0.1%.

[0073] If the scalar index of light intensity uniformity Greater than the preset uniformity convergence accuracy threshold Then continue to update the pixel plane complex amplitude field of the SLM. and the weights of each optical trap Otherwise, the weight of the optical trap is determined. Full convergence, i.e., the weights at this point It has stabilized and can be considered a parameter rather than a dynamic variable. In practice, approximately 100 iterations are typically sufficient to achieve the desired scalar index of light intensity uniformity. Less than the preset uniformity convergence accuracy threshold .

[0074] In this embodiment of the application, the complete state of WGS consists of two types of variables, represented as follows:

[0075] in A hologram of SLM. The weight set consists of the weights of each optical trap, for example, represented as a weight vector. When treated as parameters rather than dynamic variables, the state simplifies to And converges to the steady-state complex amplitude field of the pixel plane. , can be represented as:

[0076] here, This is a complete WGS single-step operator (including phase transformation, forward transformation, amplitude forcing, and inverse transformation). It is the set of locations of all optical traps in the target array.

[0077] At this point, the complete state of WGS after convergence. That is, the fully convergent state variables of WGS Approximately equal to a stable hologram after convergence The state approximately degenerates to contain only phase, which indicates that after repeated oscillations along the optical path, the entire optical diffraction coherent network reaches an energy-phase equilibrium. In other words, if the hologram at this point... The input is given to the SLM, and after being diffracted by a lens through Fourier transform of parallel light, it is transmitted to the focal plane, achieving the preset... The required complex amplitude distribution of the focal plane is accurately generated. Then, the WGS single-step operator is executed again in this state. Since the input and output are identical, no further drift in the complex amplitude field occurs. Therefore, the steady-state complex amplitude field of the pixel plane... That is, WGS single-step operator The fixed point. This is also the basis for subsequent treatment of atomic position shifts ( The premise that the measurement of crosstalk in the optical field caused by changes is valid is based on the following assumptions.

[0078] Here, those skilled in the art will understand that weights Sufficient convergence can be viewed as an assumption of parameter simplification, if the weights... If convergence is not achieved, a complete block Jacobian matrix is ​​required. That is, the derivation of the steady-state Jacobian matrix described below assumes that the weights have fully converged, as illustrated above. Otherwise, it is necessary to compute the complete block Jacobian matrix corresponding to the non-converged weights as an optional extension that can be derived from this application.

[0079] Step S130: Calculate the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane to obtain the steady-state Jacobian matrix.

[0080] In this embodiment of the application, the WGS single-step operator Including pixel plane complex amplitude field Length of the module Since the calculation involves both complex conjugate and non-holomorphic mappings, its derivative can be processed using Wirtinger calculus to calculate the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane. Of course, those skilled in the art will understand that other methods can also be used to calculate the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane, such as converting the differentiation of complex functions into a method of differentiating the mapping over a two-dimensional real space.

[0081] Figure 3 The illustration shows a schematic flowchart of the process of obtaining the steady-state Jacobian matrix using Wirtinger calculus in a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application. Figure 3 As shown, the process of obtaining the steady-state Jacobian matrix using Wirtinger calculus in the method for generating the spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application includes the following steps.

[0082] Step S131: Construct a phased pixel plane steady-state complex amplitude field based on the phased operation in the WGS single-step operator, and obtain the Jacobian coefficients of each optical trap corresponding to the phased pixel plane steady-state complex amplitude field. Here, for the pixel plane steady-state complex amplitude field... Phase conversion is performed to decouple the amplitude, and only the phase is retained to obtain the phase-converted pixel plane steady-state complex amplitude field. :

[0083] Then, the phased pixel plane steady-state complex amplitude field is... Perform Fourier transform and then apply it to the spatial frequency coordinates of each optical trap. Take the modulus at point 1 to obtain the first... Focal plane amplitude of each optical trap :

[0084] Based on the Weight of each optical trap Target amplitude Amplitude of focal plane The first rank required to obtain the subsequent rank-k expansion Jacobian coefficient of each optical trap (Eliminating the (Explicit dependence of amplitude)

[0085] Step S132: Construct a focal plane tangent space projection operator based on the complex perturbation vector acting on the phased pixel plane steady-state complex amplitude field, used to project the complex perturbation vector onto the imaginary part direction of the focal plane. Here, for the pixel plane steady-state complex amplitude field... Wirtinger calculus respectively for and The partial derivative is expressed as:

[0086] in Represents phase mapping Here, the phase mapping pairs and It is simultaneously dependent and not holomorphic, therefore the standard complex derivative does not exist. The two Wirtinger partial derivatives can give its complete first-order linear response, avoiding the omission of the antiholomorphic term.

[0087] Then, the two partial derivatives are applied to the first-order complex perturbation vector. The combined effects of these operators can be simplified to a projection operator that retains only the tangential (imaginary) phase component while filtering out the radial amplitude component, expressed as:

[0088] in This represents the operation of taking the imaginary part of a complex number. Represents the pixel coordinates applied to the SLM. The complex perturbation vector at that point. Here, for the complex perturbation vector... Its function is to have That is, only the imaginary components perpendicular to the local phase of a small perturbation on the SLM will change the pure phase field, while the radial amplitude component is filtered out by the pure phase constraint. Thus, the focal plane tangent space projection operator is obtained. , it put along The direction is projected using the imaginary part, where It is the first The phase of each optical trap.

[0089] That is, in the steady-state complex amplitude field of the pixel plane fixed point (Right now ) at, to Applying a perturbation, denoted as the first-order complex perturbation vector. ,Depend on Phased pixel plane steady-state complex amplitude field exist The disturbance at that point is:

[0090] in This indicates the operation of extracting the real part of a complex number.

[0091] Define the pixel plane tangent space projection operator (It projects the complex perturbation vector onto a pure virtual direction orthogonal to the existing phase on the pixel plane), resulting in:

[0092] in It is a normalized perturbation field that retains only the pure phase variation component after projection is applied. Position on the SLM pixel plane The applied complex perturbation vector, It is the steady-state complex amplitude field of the pixel plane (as a reference field). It is the operator for extracting the imaginary part of a complex number, and It is the imaginary unit.

[0093] Then perform a forward Fourier transform, that is:

[0094] Amplitude-forced linearization is used for steady-state complex amplitude fields at the focal plane. At this point, the phase-normalized perturbation is calculated as follows:

[0095] in This indicates that the perturbation at the focal plane is also projected onto a phase perpendicular to its convergence. The imaginary (tangential) direction.

[0096] Therefore, the above pixel plane tangent space projection operator With the projection of the imaginary part of the focal plane here Combined, and due to the setting of the perturbation by the position of the SLM pixel plane The injection and projection operators are defined according to the phase distribution at the starting point, thus obtaining the focal plane tangent space projection operator. This indicates that the complex perturbation vector can only propagate backward in the component along the phase tangent direction, thus filtering out the radial component.

[0097] Step S133: Multiply the Jacobian coefficients of each optical trap, the tangent space projection operator, and the plane wave factor for plane wave modulation to obtain the steady-state Jacobian matrix. That is, based on the forward Fourier transform. perturbation When propagated to the focal plane, it will appear at the target frequency point in the Fourier integral. Introduce a base factor at [location]. The updated complex amplitude field of the focal plane is reflected back to the pixel plane of the SLM through an inverse Fourier transform, i.e. This allows the inverse transform to be calculated from the focal plane. Each optical trap returns to the pixel of the SLM. At this point, the inverse phase factor is introduced. This forms the plane wave factor used for plane wave modulation. In other words, plane wave modulation configures each optical trap with its frequency. Determined plane wave factor , used to indicate the first Coordinates of each optical trap in the SLM plane and Phase transfer between them.

[0098] Then, the Jacobian coefficient of each optical trap is... The tangent space projection operator and the plane wave factor Multiplying them together yields the matrix elements of the steady-state Jacobian matrix:

[0099] in, These are the matrix elements of the steady-state Jacobian matrix, representing coordinates. When a disturbance occurs at a location, it causes the coordinates to... The differential rate of change of the complex amplitude, It is the total number of optical traps in the target array. Indicates the first Each optical trap in spatial frequency coordinates The interference plane wave factor under the coordinate difference is used to... Spatial phase transfer is performed on top. Used to locate the source point Disturbance at the location Projected towards the The characteristic imaginary part direction of each optical trap It is a one-dimensional composite dimension-reduced projection operator. Therefore, the steady-state Jacobian matrix is ​​the sum of several low-rank terms composed of the plane wave factor and the one-dimensional phase tangent space projection, and the rank does not exceed the total number of optical traps.

[0100] This is equivalent to applying the linearity of the forward and inverse Fourier transforms, along with the linearization of amplitude constraints, to each optical trap position. The local perturbation at a single point is represented by the Jacobian-Vector Product (JVP) backpropagation, and the interference plane wave factor terms of all optical traps are combined to obtain the explicit elements of the expansion of the Jacobian matrix describing the crosstalk differential rate of the perturbation at any pixel on the SLM plane to other coordinate nodes on the entire SLM plane, i.e., the above. .

[0101] Therefore, the obtained steady-state Jacobian matrix accurately represents WGS at the microscopic level, where the steady-state Jacobian matrix is ​​essentially a matrix with a rank of maximum value. The coupling response of the optical system is not only modulated by the ratio of weight to amplitude, but its energy is also dependent on the plane wave substrate across the entire plane, as part of the operator superposition of (i.e., the total number of optical traps in the target array). Interference occurs, thus accurately presenting the complex superposition and leakage entanglement of each optical trap field at the holographic spatial frequency.

[0102] Therefore, those skilled in the art will understand that calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a small perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus is essentially based on the WGS single-step operator, through the steady-state complex amplitude field of the pixel plane... fixed point (Right now ) at, to Apply micro-perturbation The matrix elements of the steady-state Jacobian matrix are obtained through the phase transformation, forward Fourier transform, amplitude forcing, and inverse Fourier transform process of the WGS single-step operator.

[0103] That is, by Phased pixel plane steady-state complex amplitude field exist The disturbance at that point is:

[0104] Based on linear forward Fourier transform:

[0105] Based on linear amplitude forcing, in At this point, the phase-normalized perturbation is:

[0106] Finally, based on the linear inverse Fourier transform and by combining the results of the four steps, we obtain:

[0107] That is, the focal plane tangent space projection operator corresponds to the inverse part of the phase transformation and amplitude forcing steps, while the Jacobian coefficient and plane wave factor correspond to the forward Fourier transform, the amplitude part of the amplitude forcing step, and the inverse Fourier transform.

[0108] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane to obtain the steady-state Jacobian matrix includes: calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a small perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to obtain the steady-state Jacobian matrix.

[0109] Furthermore, in the above-described method for generating the spatial light modulator tensor for atomic array rearrangement, calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a micro-perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to obtain the steady-state Jacobian matrix includes: constructing a phased steady-state complex amplitude field of the pixel plane based on the phased operation in the WGS single-step operator and obtaining the Jacobian coefficients of each optical well corresponding to the phased steady-state complex amplitude field of the pixel plane; constructing a focal plane tangent space projection operator for projecting the complex perturbation vector onto the imaginary part direction of the focal plane based on the complex perturbation vector acting on the phased steady-state complex amplitude field of the pixel plane; and multiplying the Jacobian coefficients of each optical well, the focal plane tangent space projection operator, and the plane wave factor for plane wave modulation to obtain the steady-state Jacobian matrix.

[0110] In this embodiment of the application, since the total pixel size of the SLM is extremely large (e.g. The storage of the steady-state Jacobian matrix may require a large amount of storage space, therefore sparsification is desired. Here, the physical oscillation characteristics of the steady-state Jacobian matrix are considered because of the plane wave factor. Interference with distance exhibits antiphase cancellation (i.e., when...) Time oscillations superimpose and cancel each other out. The crosstalk characteristic width (characterized by the aperture diffraction limit of the SLM) is an optical property. When the physical lattice point extends beyond a specific nearest-neighbor diffraction range boundary, the crosstalk value rapidly decays and degrades. Therefore, it is possible to construct a probe vector that is non-zero only within the neighborhood of the optical trap. Thus, utilizing the rank... Structure, only needs to be detected sparse elements, of which It is half the side length of the neighborhood, meaning the neighborhood is the target optical trap. Grid points. Among them, the crosstalk feature width. Represented as:

[0111] in It is the laser wavelength. It is the focal length of the Fourier lens, and This is the effective illumination aperture size of the spatial light modulator (e.g., the product of the number of pixels and the pixel pitch, on the order of millimeters), which determines the angular resolution limit of the spatial light modulator's diffraction. It is important to note that here... This is not the minimum center-to-center distance (minimum optical trap spacing) between adjacent optical traps in the target optical trap array; the order of magnitude of the minimum optical trap spacing is approximately... For example, in With a crosstalk characteristic width of approximately 8.19 mm, the crosstalk characteristic width is calculated. Approximately 9.74 .

[0112] Specifically, nearest neighbor detection can be performed per light trap using torch.autograd.functional.jvp ( Sparse elements (grid-based) are stored in cuSPARSE CSR format (e.g., approximately 24MB) to avoid explicit storage. A dense matrix, in which Here, torch.autograd.functional.jvp computes the Jacobian-vector product to probe the vector. (in the neighborhood) Grid processing 1) Column-by-column detection The non-zero element is represented as:

[0113] in It is the amplitude of an infinitesimal perturbation (take the limit after differentiation). It is obtained directly using the directional derivative. With probe vector The product does not require explicit construction. For dense matrices, by probing each local basis vector, the nearest non-zero columns of the Jacobian can be extracted, reducing the computational cost from... It drops to a level proportional to bandwidth.

[0114] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, after obtaining the steady-state Jacobian matrix, it further includes: probing the non-zero elements of the steady-state Jacobian matrix column by column with a probe vector that is non-zero only in the neighborhood of the light trap to extract the non-zero elements of the steady-state Jacobian matrix to obtain a sparsified steady-state Jacobian matrix.

[0115] Step S140: Calculate the partial derivatives of the WGS single-step operator with respect to the positions of all optical traps to obtain the position partial derivative matrix.

[0116] Figure 4 The illustration shows a schematic flowchart of the process for calculating the position partial derivative matrix in a method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application. Figure 4 As shown, the process of calculating the position partial derivative matrix in the method for generating the spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application includes the following steps.

[0117] Step S141: The phased steady-state complex amplitude field of the pixel plane is modulated pixel by pixel using the horizontal and vertical coordinates of the pixel plane of the SLM to obtain the horizontal coordinate modulation field and the vertical coordinate modulation field.

[0118] That is, for the phased pixel plane steady-state complex amplitude field The positional partial derivative originates from the plane wave factor. For the position of the optical trap Factors lost during differentiation ,in Since the SLM's pixel coordinates are constants, the pixel coordinates of the SLM need to be used as the multiplicative operator. and It acts on the phased field. Therefore, using the horizontal coordinate... with vertical coordinate Pixel-by-pixel modulation of phase-shifted pixel plane steady-state complex amplitude field The transverse coordinate modulation field is obtained. and longitudinal coordinate modulation field :

[0119] In other words, the differential theorem of the Fourier transform states that differentiating the frequency domain with respect to frequency is equivalent to multiplying the spatial domain by the coordinates. (Optical trap position) By frequency Entering the phase of a plane wave, taking its derivative yields the coordinate factor, therefore using coordinates... and Modulated pixel plane steady-state complex amplitude field This transforms position sensitivity into an object that can be directly calculated using Fourier transform.

[0120] Step S142: Perform Fourier transform on the transverse coordinate modulation field and the longitudinal coordinate modulation field, and sample at the frequency of each optical trap to obtain the transverse component modulation spectrum sample value and the longitudinal component modulation spectrum sample value of each optical trap.

[0121] That is, the frequency of each optical trap on the focal plane. It is achieved by using the phased pixel plane steady-state complex amplitude field The frequency of each optical trap, obtained by Fourier transform after performing Fourier transforms on the transverse and longitudinal coordinate modulation fields respectively. The above transformation results are sampled to obtain the transverse and longitudinal component modulation spectrum sample values ​​for each optical trap:

[0122] in It is a two-dimensional continuous (or discrete) forward Fourier transform integral operator, which can transform the coordinate modulation field to the focal plane and sample it at the frequency of the target optical trap. The resulting complex value is proportional to the direction and amplitude of the first-order change of the complex amplitude field of the focal plane when the optical trap is moved, and is the frequency domain carrier of position sensitivity.

[0123] Step S143: Multiply the transverse component modulation spectrum sample value and the longitudinal component modulation spectrum sample value of each optical trap by the frequency-coordinate mapping constant to combine the positional partial derivative components of each optical trap along the transverse and longitudinal directions.

[0124] That is, the sampled values ​​of the transverse component modulation spectrum of each optical trap. and longitudinal component modulation spectrum sampling value Multiply by the frequency-coordinate mapping constant (This is a physical conversion of coordinate modulation equivalent to frequency domain differentiation), and the position partial derivatives of each optical trap along the transverse and longitudinal directions are obtained by combining them:

[0125] The position of each optical trap Represented as This is to deconstruct the local spatial degrees of freedom in the horizontal and vertical directions. Here, in order to correct for the dependency simplification assumption (the ordinary multiplication factor)... Algorithm errors, such as those caused by replacing the integral weighting term, lead to a systematic overestimation of crosstalk strength. Expanding along the Fourier kernel phase angle of the true wavefront, when the... When an optical trap attempts to physically offset itself, a chained partial derivative operation is performed within the originally smooth integral transform network. Furthermore, the spatial matrix scale dimension coordinates (i.e., the horizontal coordinates) of the SLM plane of the liquid crystal panel are... with vertical coordinate The direct weighted operator is injected into the integral kernel to calculate the flux distortion partial derivatives of each optical trap caused by the shift drive, which is expressed as follows:

[0126] here, It is the WGS single-step operator with respect to the first step in the focal plane. The horizontal coordinates of each optical trap The lateral partial derivative component represents the rate of change of the entire projection field induced by a very small lateral physical movement of the optical trap. As described above, the global optical coupling constant multiplier derived from the derivative of the exponentially transferred phase factor of the far-field Fourier diffraction integral can be represented.

[0127] In other words, when performing partial derivative calculations on the target optical trap, if the frequency domain spatial constant components (such as spatial frequency coordinates) are simply used... While directly extracting the common multiplier simplifies computation, it neglects the practical realities of large-aperture planar light emission in SLMs. The calculation of the partial derivative of the WGS single-step operator with respect to the light trap position considers the core factors causing changes in the reconstruction domain due to focus movement, which depends on the solid plane coordinate distribution of the liquid crystal pixels in the source-end holographic liquid crystal panel. and For steady-state phase field After non-uniform aperture-scale weighted modulation, the spatial spectrum abrupt change that occurs at a specific wave vector accurately reproduces the spatial differential law followed by the light path when the optical trap undergoes forced motion.

[0128] Step S144: Flatten the position partial derivative components of each optical trap along the lateral and longitudinal directions into column vectors of the complex amplitude field and splice them according to the lateral and longitudinal coordinate order of the optical trap to obtain the position partial derivative matrix.

[0129] In other words, after traversing all the optical traps, the partial derivatives of the positions along the lateral and longitudinal axes corresponding to each individual optical trap are summarized to generate a set of components for the discrete sites. Here, since the motion of each optical trap includes lateral and longitudinal axes (usually denoted as second-order degrees of freedom, i.e., each optical trap has...), the partial derivatives of the positions along the lateral and longitudinal axes are summarized to generate a set of components for the discrete sites. shaft and The vector behavior of the axis translation state space is thus normalized and configured into a high-dimensional coherent tensor. For example, setting the shape mapping boundary of the macroscopic array (e.g., the total number of optical traps is...) The total number of degrees of freedom for overall displacement is The positional partial derivative components of each optical trap along the lateral and longitudinal directions are flattened into column vectors of the complex amplitude field of the pixel plane, and then... By sequentially concatenating the horizontal and vertical coordinates, we obtain the position partial derivative matrix representing how the minute movements of all optical trap positions are linearly mapped to the changes in the complex amplitude field of the pixel plane on the SLM plane.

[0130] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, calculating the partial derivatives of the WGS single-step operator with respect to the positions of all optical traps to obtain the position partial derivative matrix includes: modulating the phased pixel plane steady-state complex amplitude field pixel by pixel with the lateral and longitudinal coordinates of the pixel plane of the SLM to obtain a lateral coordinate modulation field and a longitudinal coordinate modulation field; performing a Fourier transform on the lateral coordinate modulation field and the longitudinal coordinate modulation field and sampling at the frequency of each optical trap to obtain a lateral component modulation spectrum sample value and a longitudinal component modulation spectrum sample value for each optical trap; multiplying the lateral component modulation spectrum sample value and the longitudinal component modulation spectrum sample value of each optical trap by a frequency-coordinate mapping constant to combine the position partial derivative components of each optical trap along the lateral and longitudinal directions; and flattening the position partial derivative components of each optical trap along the lateral and longitudinal directions into column vectors of the pixel plane complex amplitude field and concatenating them according to the lateral and longitudinal coordinate order of the optical traps to obtain the position partial derivative matrix.

[0131] Step S150: Based on the steady-state Jacobian matrix and the position partial derivative matrix, the complex amplitude sensitivity matrix is ​​obtained by the total differential of the fixed-point condition of the WGS single-step operator, and the Hermitian Gram matrix of the complex amplitude sensitivity matrix is ​​obtained as the spatial light modulator tensor.

[0132] Figure 5 The illustration shows a schematic flowchart of the process of obtaining the spatial light modulator tensor in the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application. Figure 5 As shown, the process of obtaining the spatial light modulator tensor in the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application includes the following steps.

[0133] Step S151: Calculate the total differential of the implicit functional representation of the fixed-point condition of the WGS single-step operator with respect to the set of optical trap positions.

[0134] As mentioned above, in atomic rearrangement, the set of optical trap positions As time progresses, the spatial light modulator tensor expectation metric... tiny changes At that time, the steady-state complex amplitude field of the pixel plane How it changes, including the set of optical trap locations. Abbreviated as:

[0135] When the WGS iteration converges, the steady-state complex amplitude field of the pixel plane is obtained. Therefore, when the WGS single-step operator is at a fixed point, it is in the steady-state complex amplitude field of the pixel plane. This state can be described as the WGS single-step operator at a fixed point. Then the fixed-point condition of the WGS single-step operator can be written as an implicit function:

[0136] Set of optical trap locations The total differential is obtained by the implicit function theorem:

[0137] Step S152: Obtain the complex amplitude sensitivity matrix from the total differential representation based on the steady-state Jacobian matrix. That is, the steady-state Jacobian matrix is ​​expressed as:

[0138] From the above total differential expression, we obtain:

[0139] in It is a multidimensional diagonal reference identity matrix, obtained by subtracting the inverse of the steady-state Jacobian matrix in the WGS convergence region. As a crosstalk amplifier, it acts on the position partial derivative matrix That is, the positional partial derivative matrix. This only describes the direct effect of the moving optical trap on the hologram. However, since WGS iterates to a fixed point, this initial perturbation will be repeatedly propagated and superimposed through the WGS single-step operator, forming an infinite series. The geometric series converges when the spectral radius is less than 1. This is called a crosstalk amplifier. The essence of optical crosstalk is amplifying a single direct effect into a convergent total effect; moving one optical trap will cause leakage through the diffraction field, affecting all optical traps. Therefore, As a complex amplitude sensitivity matrix, it can be denoted, for example, as... .

[0140] Furthermore, the above equation holds true if WGS converges, and the necessary and sufficient condition for WGS convergence is that the WGS single-step operator... At steady state (i.e., at a fixed point), the Jacobian satisfies the spectral radius. In other words, can WGS converge to a fixed point in a single iteration? It depends on the WGS single-step operator. The first derivative at this fixed point is the aforementioned steady-state Jacobian matrix. Therefore, spectral radius This means that when the hologram is subjected to a small external perturbation, the error will decrease geometrically in subsequent iterations of WGS (with the spectral radius as the attenuation factor), and the WGS iterative algorithm will spontaneously reconverge to the fixed point. Conversely, if... If the perturbation diverges, the iteration will fail to converge.

[0141] In the embodiments of this application, alternatively, the steady-state Jacobian matrix, the positional partial derivative matrix, or the complex amplitude sensitivity matrix can be obtained by at least one of analytical differentiation, automatic differentiation, finite difference, complex step size differentiation, adjoint sensitivity analysis, experimental calibration, statistical Fisher information estimation, and Gauss-Newton approximation.

[0142] Alternatively, the complex amplitude sensitivity matrix can be obtained by at least one of explicit matrix inversion, Neumann series expansion, fixed-point iteration, conjugate gradient, GMRES, BiCGSTAB, preconditioned Krylov subspace method, low-rank approximation, Sherman-Morrison-Woodbury formula, or Tikhonov regularized linear solution.

[0143] Step S153: Obtain the Hermitian Gram matrix of the complex amplitude sensitivity matrix to obtain the spatial light modulator tensor. The spatial light modulator tensor measures the change in the steady-state hologram caused by the optical trap displacement.

[0144] Based on the complex amplitude sensitivity matrix Construct the spatial light modulator tensor , is represented as:

[0145] in This represents the Hermitian conjugate transpose, which is obtained by transposing the matrix and then finding its conjugate over the complex domain. In other words, it involves taking the complex amplitude sensitivity matrix. Hermitian Gram matrix This yields the spatial light modulator tensor, which measures the change in the hologram caused by the displacement of the optical trap. Its matrix size is (Each optical trap has) and (Two degrees of freedom). Block element Indicates the move of the first The and the first The inner product (i.e., coupling) between the holographic changes caused by each coordinate component. Here, the complex amplitude sensitivity matrix... The column vectors represent the changes in the complex amplitude field of the steady-state pixel plane caused by perturbations at the position of the optical trap, and their Hermitian Gram matrix measures the changes in the steady-state hologram.

[0146] The spatial light modulator tensor is divided into blocks according to the optical trap number. Can be written as indivual sub-block The scalar coupling matrix used for visualization can be defined as:

[0147] That is, because each optical trap has and Two degrees of freedom, therefore The Middle , The coupling of the optical trap is Sub-blocks. By taking their Frobenius norm and compressing the directional degrees of freedom into a single scalar, we obtain the scalar coupling matrix between optical traps. This is used to visualize crosstalk distribution.

[0148] according to It can be seen The change in the steady-state hologram caused by the optical trap displacement (i.e., the change in the hologram when WGS iteration converges to a fixed point) was accurately measured, and its block elements... Quantization of the moving optical trap After a small step, and through infinite iterations of WGS, the optical trap finally converges. The perturbation intensity generated by the amplitude, i.e. the WGS optical crosstalk coupling intensity between the two optical traps.

[0149] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, obtaining a complex amplitude sensitivity matrix from the total differential of the fixed-point condition of the WGS single-step operator based on the steady-state Jacobian matrix and the position partial derivative matrix, and obtaining the Hermitian Gram matrix of the complex amplitude sensitivity matrix as the spatial light modulator tensor includes: calculating the total differential of the implicit functional representation of the fixed-point condition of the WGS single-step operator with respect to the optical trap position set; obtaining the complex amplitude sensitivity matrix from the total differential representation based on the steady-state Jacobian matrix; and taking the Hermitian Gram matrix of the complex amplitude sensitivity matrix to obtain the spatial light modulator tensor, wherein the spatial light modulator tensor measures the change in the steady-state hologram caused by the optical trap displacement.

[0150] Due to the spatial light modulator tensor It is a Hermitian Gram matrix, which is naturally positive semi-definite and can be directly used as a Riemannian metric. Here, the spatial light modulator tensor can be verified. The positive semidefiniteness and positive definiteness of the property. Let... , , It is a Hermitian Gram matrix, and ,but (Hermitian) and (This holds true for all semi-positive definite values).

[0151] and, , When the column is full Therefore, it is positively determined. That is to say, (Strict positive definiteness if and only if) When the column rank is full, that is, the optical trap configuration is non-degenerate and In typical parameters ( The positive definiteness holds under the condition that the optical traps are non-overlapping. Here, the necessary and sufficient condition for WGS convergence is that the steady-state Jacobian matrix of the WGS single-step operator satisfies the spectral radius. This can be used to satisfy the convergence of WGS iterations, and also ensures the spectral radius condition. Reversible, with the complex amplitude sensitivity matrix Full-rank guaranteed spatial light modulator tensor The positive definiteness of .

[0152] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, after obtaining the spatial light modulator tensor, the method further includes: determining the positive semidefiniteness of the spatial light modulator tensor based on the Hermitian Gram matrix representation of the complex amplitude sensitivity matrix.

[0153] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, after obtaining the spatial light modulator tensor, the method further includes: determining the positive definiteness of the spatial light modulator tensor in response to the full column rank of the complex amplitude sensitivity matrix.

[0154] In the method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application, after obtaining the spatial light modulator tensor, the method further includes: in response to the spectral radius of the steady-state Jacobian matrix being less than one, determining that the difference tensor between the unit tensor and the steady-state Jacobian matrix is ​​invertible and obtaining the complex amplitude sensitivity matrix; and in response to the complex amplitude sensitivity matrix being full column rank, determining the positive definiteness of the spatial light modulator tensor.

[0155] Furthermore, in order to enhance the density Spatial light modulator tensor Storage efficiency, for the spatial light modulator tensor Perform sparsification, for example Sparsification is performed to convert it into a CSR sparse matrix that can be stored and computed in real time on the GPU.

[0156] Figure 6 The illustration shows the spatial light modulator tensor in the method for generating the spatial light modulator tensor according to an embodiment of this application. A schematic flowchart of the sparsification process. (e.g.) Figure 6 As shown, the spatial light modulator tensor in the spatial light modulator tensor generation method according to an embodiment of this application... The sparsification process includes the following steps.

[0157] Step S161: Obtain the block elements of the spatial light modulator tensor represented by the inner product between the corresponding columns of the complex amplitude sensitivity matrix and the position partial derivative matrix.

[0158] For complex amplitude sensitivity matrix The spatial light modulator tensor block elements Defined as the complex amplitude sensitivity matrix The inner product between the corresponding columns:

[0159] in For the spatial light modulator tensor The Block elements and These are the complex amplitude sensitivity matrices. The and the List, These are the spatial coordinates of the optical trap. For complex conjugate, This is the inner product. As mentioned above, block elements... It is the first move and the The inner product of the steady-state hologram changes caused by each optical trap is used to quantify the optical crosstalk coupling strength between the two optical traps after complete convergence by WGS.

[0160] Furthermore, the positional partial derivative matrix is ​​obtained to obtain the WGS single-step operator with respect to the first... The position of each optical trap The partial derivatives, here, are obtained by using the differential theorem of the Fourier transform to convert the differentiation with respect to position into a function of pixel coordinates. and Weighted values ​​are then subjected to a Fourier transform, for example, for pixel coordinates. Represented as:

[0161] here, It is a WGS single-step operator. It is the first The position (i.e., spatial coordinates) of each optical trap. For phased pixel plane complex amplitude field, These are the horizontal and vertical coordinates of the SLM pixel (in units of length). The wavelength of the laser. Let be the focal length of the Fourier lens. For Fourier transform, The spatial frequency coordinates of the optical trap. The unit is the imaginary unit. That is, moving the optical trap position is equivalent to shifting the sampling point in the frequency domain. According to the Fourier differential theorem, its sensitivity is determined by the pixel coordinates. The spectrum of the weighted, phase-modulated complex amplitude field of the pixel plane is given. It should be noted that the weighting factor is the pixel coordinate. (Length dimension), not spatial frequency The two have different dimensions and cannot be used interchangeably.

[0162] Step S162: Simplify the position partial derivative matrix with the iterative initial state and uniform rectangular aperture to obtain the simplified complex amplitude sensitivity matrix, and obtain the simplified block elements of the spatial light modulator tensor of the iterative initial state in aperture integral based on the simplified complex amplitude sensitivity matrix.

[0163] In the initial state of the iteration Approximation to neglect the steady-state Jacobian matrix ,Right now And assuming a uniform rectangular aperture The position partial derivative is simplified to a single plane wave multiplied by the first-order moment of the aperture, for example, for pixel coordinates. Represented as: The first of the complex amplitude sensitivity matrix List in the initial state of the iteration Approximation, For the first Complex weights of each optical trap ( As weight, For the target amplitude, For the first (phase of each optical trap) For rectangular aperture at frequency The first moment at the point (approximately constant under uniform illumination). This is the SLM aperture characteristic function. That is, under conditions of weak crosstalk and uniform illumination, the sensitivity of the optical trap displacement can degenerate to a plane wave multiplied by the first-order aperture moment. For pixel coordinates... The quantities are the same.

[0164] Then, substituting the approximate amplitude column into the inner product representation of the block elements of the spatial light modulator tensor, the corresponding columns of the complex amplitude sensitivity matrix are combined in two components to obtain the iterative initial state represented by the aperture integral. Block elements: Initial state of the iteration Approximate block elements The complex weighted conjugate product of the two optical traps. The pixel coordinates are squared and weighted (from two coordinate weightings). The frequency difference between the two optical traps is summed and iterated over all pixels of the SLM. Here, the approximate block element is determined by the sum of phase differences weighted by the squares of the aperture coordinates, which is a weighted sum of the squares of the pixel coordinates. This can accurately reflect the modulation of crosstalk by the spatial distribution of the SLM aperture.

[0165] Step S163: Perform Dirichlet kernel summation and large pixel number continuum on the simplified block elements of the spatial light modulator tensor to obtain the crosstalk intensity between the two optical traps. Coupling rate.

[0166] The iterative initial state The approximate block elements are summed along a finite number of pixels in one dimension (geometric series) in a closed form as the Dirichlet kernel, i.e., a finite DFT summation:

[0167] in For the number of pixels in one dimension, For pixel index. for Directional frequency difference, The pixel pitch is given, and the exponential factor is the linear phase. That is, the sum of the phase differences under a finite aperture is exactly equal to the Dirichlet (periodic) phase difference. The core is the intrinsic structure of finite pixel diffraction.

[0168] when Sometimes, Then the Dirichlet nucleus is approximately equal to function:

[0169] in For normalization Function, denominator This is the linearized result of the denominator for a small-angle approximation. That is, when the number of pixels is sufficiently large and the diffraction angle is sufficiently small, the Dirichlet kernel and the continuous aperture... The diffraction point diffusion functions are consistent.

[0170] Therefore, substituting the relationship between frequency difference and optical trap spacing, for the transverse... and longitudinal Multiplying the squares of the two dimensions by taking their modulo, we obtain the principal order of the scalar coupling matrix. Decay law:

[0171] in: Scalar coupling matrix element ( (Frobenius norm of sub-blocks) It is the aperture integral constant. , The distance between the two optical traps, For crosstalk feature width, This refers to the effective illumination aperture size of the spatial light modulator (determined by the number of pixels and pixel pitch of the spatial light modulator), rather than the minimum spacing between the optical traps. This indicates that the crosstalk strength between the two optical traps follows a two-dimensional... Attenuation law, crosstalk characteristic width It is determined by the diffraction limit (effective aperture of the SLM, not the optical trap spacing). Specifically, the condition for its validity is: a uniform rectangular aperture ( (constant), weight convergence ( It is a constant. ), Approximation (ignoring the steady-state Jacobian matrix), Furthermore, while simultaneously containing , and In the case of component light, non-uniform illumination or large-angle diffraction does not degenerate into However, under uniform illumination and small-angle diffraction conditions, The approximate accuracy is better than 1%.

[0172] Step S164, using the The far-end integral rate of the coupling rate is used to estimate the truncation bandwidth, and the spatial light modulator tensor is bandwidth-truncated with the truncation bandwidth to obtain the sparsified spatial light modulator tensor.

[0173] use Far-end integral law estimation of truncated bandwidth The remaining Frobenius energy is used to select a bandwidth that meets the required accuracy:

[0174] Here, bandwidth is truncated. It is based on the crosstalk characteristic width The number of grid points in units can be seen Tail energy varies with bandwidth by The rate decay ensures that only a small number of nearest neighbors are needed to capture the vast majority of crosstalk energy.

[0175] Therefore, the bandwidth of the spatial light modulator tensor can be truncated to retain only the bandwidth required for the modulator. Non-zero elements in the neighborhood of the integer are set to zero, and the rest are set to zero (e.g., ...). (Capturing 99.98% of the energy), thereby compressing and storing the sparsed spatial light modulator tensor in cuSPARSE CSR format (e.g., approximately 24 MB).

[0176] Table 1 below shows the numerical comparison of sparsification of the spatial light modulator tensor (where atoms are...). 171 Yb, , optical trap spacing ).

[0177] Table 1

[0178] Here, in terms of bandwidth Under the level-1 approximation, the error is, for example, And energy capture %.

[0179] In this embodiment of the application, the sparsity may include at least one of level-0, level-1, and level-2 approximations, wherein the level-1 approximation preserves a preset bandwidth. The nearest neighbor block element is set to zero, and the remaining elements are set to zero. The bandwidth is based on The tail integration energy or the target Frobenius error threshold is determined, and the sparse matrix can be stored in CSR, CSC, COO, block sparse or low-rank plus sparse form.

[0180] The method for generating a spatial light modulator tensor for atomic array rearrangement according to an embodiment of this application further includes: performing... Sparsification is used to obtain a sparsified spatial light modulator tensor.

[0181] Furthermore, in the above-described method for generating spatial light modulator tensors for atomic array rearrangement, the spatial light modulator tensor is subjected to... The sparsification process to obtain a sparsified spatial light modulator tensor includes: obtaining the block elements of the spatial light modulator tensor represented by the inner product between corresponding columns of the complex amplitude sensitivity matrix and the position partial derivative matrix; simplifying the position partial derivative matrix with an iterative initial state and a uniform rectangular aperture to obtain a simplified complex amplitude sensitivity matrix, and obtaining the simplified block elements of the spatial light modulator tensor in the iterative initial state represented by the aperture integral based on the simplified complex amplitude sensitivity matrix; performing Dirichlet kernel summation and large pixel number continuum on the simplified block elements of the spatial light modulator tensor to obtain the crosstalk intensity between the two optical traps. Coupling rate; and, using the above The far-end integral rate of the coupling rate is used to estimate the truncation bandwidth, and the spatial light modulator tensor is bandwidth-truncated with the truncation bandwidth to obtain the sparsified spatial light modulator tensor.

[0182] The spatial light modulator tensor generated by the method for generating spatial light modulator tensors for atomic array rearrangement according to the embodiments of this application can be used as a Riemann metric for atomic array rearrangement path planning. That is, the generalized kinetic energy of the optical trap moving at a predetermined speed can be represented based on the spatial light modulator tensor, and the optimal transmission path under SLM crosstalk constraints is given along the geodesic of this metric.

[0183] Furthermore, the spatial light modulator tensor generated by the method for generating spatial light modulator tensors for atomic array rearrangement according to the embodiments of this application can be used as a Fisher-like metric during hologram generation. That is, under the Poisson photon noise model, the block elements of the spatial light modulator tensor can be interpreted as Fisher-like information of the focal plane intensity distribution with respect to the optical trap position. It should be noted that this Fisher-like metric is an approximate correspondence of the leading-order in the sense of complete noise and observation model, rather than a strict Fisher information equivalence relationship.

[0184] Furthermore, the spatial light modulator tensor generated by the method for generating spatial light modulator tensors for atomic array rearrangement according to embodiments of this application can be used as a complex amplitude domain gradient flow (CDGF) preconditioner, and the tensor inverse matrix of the spatial light modulator tensor can be used as a preconditioner. As the natural precondition matrix for the complex amplitude domain gradient flow, it can guarantee that each correction is made along the optimal descent direction (natural gradient).

[0185] Therefore, the method for generating spatial light modulator tensors for atomic array rearrangement according to the embodiments of this application can optimize the path planning of atomic rearrangement by generating spatial light modulator tensors that measure the steady-state hologram changes caused by optical trap displacement, thereby improving the accuracy and generation speed of the generated hologram and achieving better atomic rearrangement results.

[0186] According to an embodiment of this application, an electronic device is further provided, the electronic device including a processor coupled to a memory, the processor being configured to execute a computer program stored in the memory, such that the electronic device performs the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application as described above.

[0187] According to an embodiment of this application, an electronic device is further provided, the electronic device including a processor and a memory, the processor being coupled to the memory, the processor being configured to execute a computer program stored in the memory, such that the electronic device performs the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application as described above.

[0188] Figure 7 A schematic block diagram of an electronic device according to an embodiment of this application is shown. Figure 7 As shown, an electronic device 200 according to an embodiment of this application includes a coupled processor 210 and a memory 220.

[0189] According to an embodiment of this application, a computer program product is further provided, the computer program product comprising: computer program code, which, when run on a computer, causes the computer to execute the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application as described above.

[0190] According to an embodiment of this application, a computer-readable storage medium is further provided, the computer-readable medium storing program code, which, when run on a computer, causes the computer to perform the method for generating spatial light modulator tensors for atomic array rearrangement according to an embodiment of this application as described above.

[0191] The terms “component,” “module,” “system,” etc., used in this specification are used to refer to computer-related entities, hardware, firmware, combinations of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable file, an execution thread, a program, and / or a computer. As illustrated, applications running on computing devices and computing devices can both be components. One or more components may reside in a process and / or an execution thread, and components may be located on a single computer and / or distributed among two or more computers. Furthermore, these components can be executed from various computer-readable media on which various data structures are stored. Components can communicate, for example, via local and / or remote processes based on signals having one or more data packets (e.g., data from two components interacting with another component between a local system, a distributed system, and / or a network, such as the Internet interacting with other systems via signals).

[0192] Those skilled in the art will recognize that the various illustrative logical blocks and steps described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this application.

[0193] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0194] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0195] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0196] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0197] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0198] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for generating spatial light modulator tensors for atomic array rearrangement, characterized in that, include: An initial pixel plane complex amplitude field is constructed on the pixel plane of the spatial light modulator based on the target illumination parameters, and a WGS single-step iteration using the WGS single-step operator is performed on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round. The pixel plane complex amplitude field of the corresponding iteration round is obtained by the WGS single-step iteration convergence to the fixed point as the pixel plane steady-state complex amplitude field; Calculate the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane to obtain the steady-state Jacobian matrix; Calculate the partial derivatives of the WGS single-step operator with respect to the positions of all optical traps to obtain the position partial derivative matrix; as well as The complex amplitude sensitivity matrix is ​​obtained by taking the total differential of the fixed-point condition of the WGS single-step operator based on the steady-state Jacobian matrix and the position partial derivative matrix, and the Hermitian Gram matrix of the complex amplitude sensitivity matrix is ​​obtained as the spatial light modulator tensor.

2. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, The initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator constructed based on the target illumination parameters includes: The target illumination parameters are obtained, including: the set of target amplitudes of each optical trap in the pre-configured target array, the set of positions of each optical trap, the initial hologram, the uniformity convergence accuracy threshold, the set of weights of the iterative initial states of each optical trap, the laser wavelength, and the focal length of the front Fourier lens.

3. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 2, characterized in that, The initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator constructed based on the target illumination parameters includes: The initial pixel plane complex amplitude field is obtained by multiplying the initial hologram of the liquid crystal pixel coordinates of the liquid crystal panel based on the spatial light modulator with the imaginary unit and using the result as the exponent of the natural constant.

4. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 2, characterized in that, The initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator constructed based on the target illumination parameters includes: The frequency of each optical trap is obtained by multiplying the position of each optical trap in the target array on the focal plane of the spatial light modulator by a phase period constant and then dividing by the laser wavelength and the focal length of the pre-Fourier lens.

5. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, Performing WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field for the corresponding iteration round includes: Divide the pixel plane complex amplitude field of the current round by its modulus to obtain the phased pixel plane complex amplitude field; A forward Fourier transform is performed on the phased pixel plane complex amplitude field to obtain the focal plane complex amplitude field on the focal plane; At the position of each optical trap in the target array, the focal plane complex amplitude field is divided by its modulus and then multiplied by the target amplitude and the weight of the current round to obtain the amplitude-constrained focal plane complex amplitude field; and, Perform an inverse Fourier transform on the focal plane complex amplitude field after amplitude constraint to obtain the pixel plane complex amplitude field for the next round.

6. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 5, characterized in that, Performing WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field for the corresponding iteration round further includes: Divide the target amplitude of each optical well by the modulus of the complex amplitude of the focal plane at the location of each optical well, and multiply by the weight of each optical well in the current round to obtain the weight of each optical well in the next round.

7. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, Calculating the partial derivatives of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane to obtain the steady-state Jacobian matrix includes: The steady-state Jacobian matrix is ​​obtained by calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to apply a small perturbation to the steady-state complex amplitude field of the pixel plane.

8. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 7, characterized in that, The steady-state Jacobian matrix is ​​obtained by calculating the partial derivatives of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to apply a small perturbation to the steady-state complex amplitude field of the pixel plane, including: The phased pixel plane steady-state complex amplitude field is constructed based on the phased operation in the WGS single-step operator, and the Jacobian coefficients of each optical trap corresponding to the phased pixel plane steady-state complex amplitude field are obtained. A focal plane tangent space projection operator is constructed based on the complex perturbation vector acting on the phased pixel plane steady-state complex amplitude field to project the complex perturbation vector onto the imaginary part direction of the focal plane; and... The steady-state Jacobian matrix is ​​obtained by multiplying the Jacobian coefficient of each optical trap, the focal plane tangent space projection operator, and the plane wave factor used for plane wave modulation.

9. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, After obtaining the steady-state Jacobian matrix, the following further steps are included: The non-zero elements of the steady-state Jacobian matrix are extracted by probing column by column with probe vectors that are non-zero only in the neighborhood of the optical trap to obtain a sparsified steady-state Jacobian matrix.

10. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, Calculating the partial derivatives of the WGS single-step operator with respect to the positions of all optical traps to obtain the position partial derivative matrix includes: The phased steady-state complex amplitude field of the pixel plane is modulated pixel by pixel using the horizontal and vertical coordinates of the pixel plane of the spatial light modulator to obtain the horizontal coordinate modulation field and the vertical coordinate modulation field; Fourier transform is performed on the transverse coordinate modulation field and the longitudinal coordinate modulation field, and sampling is performed at the frequency of each optical trap to obtain the transverse component modulation spectrum sampling value and the longitudinal component modulation spectrum sampling value of each optical trap. Multiply the transverse and longitudinal modulation spectrum sample values ​​of each optical trap by a frequency-coordinate mapping constant to combine the positional partial derivatives of each optical trap along the transverse and longitudinal directions; and, The positional partial derivative components of each optical trap along the lateral and longitudinal directions are flattened into column vectors of the complex amplitude field of the pixel plane and spliced ​​according to the lateral and longitudinal coordinates of the optical trap to obtain the positional partial derivative matrix.

11. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, The complex amplitude sensitivity matrix is ​​obtained by taking the total differential of the fixed-point condition of the WGS single-step operator based on the steady-state Jacobian matrix and the position partial derivative matrix, and the Hermitian Gram matrix of the complex amplitude sensitivity matrix is ​​obtained as the tensor of the spatial light modulator, including: Calculate the implicit functional representation of the fixed-point condition of the WGS single-step operator as the total differential with respect to the set of optical trap positions; The complex amplitude sensitivity matrix is ​​obtained from the total differential representation based on the steady-state Jacobian matrix; and... The Hermitian Gram matrix of the complex amplitude sensitivity matrix is ​​taken to obtain the spatial light modulator tensor, which measures the change in the steady-state hologram caused by the optical trap displacement.

12. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 11, characterized in that, After obtaining the spatial light modulator tensor, the process further includes: The positive semidefiniteness of the spatial light modulator tensor is determined based on the Hermitian Gram matrix representation of the complex amplitude sensitivity matrix.

13. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 11, characterized in that, After obtaining the spatial light modulator tensor, the process further includes: The positive definiteness of the spatial light modulator tensor is determined in response to the full column rank of the complex amplitude sensitivity matrix.

14. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 11, characterized in that, After obtaining the spatial light modulator tensor, the process further includes: In response to the spectral radius of the steady-state Jacobian matrix being less than one, the difference tensor between the unit tensor and the steady-state Jacobian matrix is ​​determined to be invertible, and the complex amplitude sensitivity matrix is ​​obtained. The positive definiteness of the spatial light modulator tensor is determined in response to the full column rank of the complex amplitude sensitivity matrix.

15. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 11, characterized in that, The spatial light modulator tensor is used for at least one of the following: a Riemannian metric for atomic array rearrangement path planning, a Fisher-like metric for hologram generation, and a preconditioner for complex amplitude domain gradient flow.

16. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 1, characterized in that, After obtaining the spatial light modulator tensor, the process further includes: Perform the spatial light modulator tensor Sparsification is used to obtain a sparsified spatial light modulator tensor.

17. The method for generating spatial light modulator tensors for atomic array rearrangement as described in claim 16, characterized in that, Perform the spatial light modulator tensor Sparsification to obtain a sparsity spatial light modulator tensor includes: Obtain the block elements of the spatial light modulator tensor as the inner product between corresponding columns of the complex amplitude sensitivity matrix, and the position partial derivative matrix; The position partial derivative matrix is ​​simplified using the iterative initial state and the uniform rectangular aperture to obtain the simplified complex amplitude sensitivity matrix, and the simplified block elements of the spatial light modulator tensor of the iterative initial state, expressed as the aperture integral, are obtained based on the simplified complex amplitude sensitivity matrix. The simplified block elements of the spatial light modulator tensor are summed using Dirichlet kernels and subjected to large pixel number continuum to obtain the crosstalk intensity between the two optical traps. Coupling rate; and, Using the above The far-end integral rate of the coupling rate is used to estimate the truncation bandwidth, and the spatial light modulator tensor is bandwidth-truncated with the truncation bandwidth to obtain the sparsified spatial light modulator tensor.

18. An electronic device, characterized in that, The device includes a processor coupled to a memory, the processor being configured to execute a computer program stored in the memory, such that the electronic device performs a method for generating a spatial light modulator tensor for atomic array rearrangement as described in any one of claims 1 to 17.

19. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, implements the method for generating spatial light modulator tensors for atomic array rearrangement as described in any one of claims 1 to 17.

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