A method and device for generating defect-free arrays of ultracold atoms

Abstract

The present invention relates to the fields of quantum physics and quantum technology, and in particular to a method for generating a defect-free array of ultracold atoms, comprising: S1, using a light potential well generated by a spatial light modulator to capture cold atoms to form an initial n×2m array; S2, capturing an image of the initial array, preprocessing the initial array image, transmitting the preprocessed data to a neural network for recognition, and outputting an atomic position matrix; S3, using a movement algorithm to calculate a movement path from the n×2m array to a target n×m defect-free array based on the atomic position matrix; S4, adjusting the atomic positions of each column or row in the array based on the movement path to obtain a final defect-free target array. The present invention is capable of efficiently generating defect-free atomic arrays. By combining neural network recognition, loading the initial array with a spatial light modulator, and optimizing atomic movement, the present invention achieves efficient conversion from an initial n×2m atomic array to a target n×m defect-free array.

Description

Technical Field

[0001] The present invention relates to the fields of quantum physics and quantum technology, and in particular to a method and device for generating a defect-free array of ultracold atoms. Background Art

[0002] In recent years, ultracold atom technology has been widely applied in fields such as quantum information, quantum computing, precision measurement, and fundamental physics research. Generating regular arrays of ultracold atoms is a key technology, enabling high-precision manipulation of atomic positions and providing a foundation for constructing quantum bit arrays and other quantum systems. However, current technologies still face numerous challenges in generating large-scale, defect-free ultracold atom arrays.

[0003] While conventional methods, such as those based on optical lattices, can theoretically produce regular arrays, their practical applications are often limited by the instability of optical interference patterns, external noise, and spontaneous atomic losses. Specifically, these methods struggle to avoid the presence of vacancies or defects in the array, which directly impacts the controllability and reliability of quantum systems.

[0004] In recent years, array generation techniques using spatial light modulators (SLMs) have gained increasing attention. SLMs can generate arbitrary light field distributions through phase manipulation, enabling efficient capture of initial atomic arrays. However, due to the limitations of SLMs' resolution and fill rate, the generated arrays often contain a certain proportion of defective atoms, a problem that becomes more pronounced as the target array size increases.

[0005] To further improve the array's defect-free nature, an acousto-optic modulator (AOM) technique was introduced to dynamically adjust the atomic positions. The AOM allows for high-precision deflection of the laser beam, moving the trapped atoms one by one to fill the vacancies in the array.

[0006] Although existing technologies have made significant progress in the generation of ultracold atomic arrays, the combined SLM and AOD-based approach, especially the defect-free generation technology for rectangular arrays, still has the following major shortcomings:

[0007] Insufficient array loading recognition accuracy: Existing technologies typically rely on traditional image processing algorithms or simple thresholding methods to identify atomic positions within an array. Due to optical noise, systematic errors, and increased array size, the accuracy of these traditional recognition methods decreases significantly, leading to false detection or missed atomic positions, which in turn affects subsequent movement optimization.

[0008] Movement algorithms lack specialized designs for rectangular arrays: Existing movement algorithms based on acousto-optic deflectors typically employ general strategies, focusing on optimizing arbitrary or randomly distributed atomic arrangements. These strategies lack specialized path planning and movement rules. These general algorithms are not only inefficient but can also result in unnecessary atom movement, increasing operation time and accumulating errors. Summary of the Invention

[0009] To address the issues raised in the background technology, this paper proposes a method for generating defect-free arrays of ultracold atoms. By incorporating neural network recognition technology and a mobile algorithm, this paper develops a technical solution capable of efficiently generating defect-free arrays of ultracold atoms. Specifically, this paper focuses on specialized optimization for rectangular array generation to achieve efficient conversion from an initial n×2m array to an n×m defect-free target array, meeting the practical needs of large-scale quantum arrays while significantly improving the system's operational efficiency and array generation quality.

[0010] The technical solution adopted by the present invention to solve the technical problem is to provide a method for generating a defect-free array of ultracold atoms, comprising:

[0011] S1. Use a spatial light modulator to generate an optical potential well array and trap ultracold atoms to form an initial n×2m atomic array;

[0012] S2, taking an image of the initial atomic array, pre-processing the image and inputting it into the neural network module, identifying the atomic positions and outputting an n×2m atomic presence matrix, where a matrix element 0 indicates that there is no atom in the corresponding optical potential well, and 1 indicates that there is an atom;

[0013] S3, based on the atomic existence matrix, with each matrix column as the adjustment target, plans the atomic movement path from the n×2m initial array to the target n×m defect-free array through a movement algorithm including intra-column atom balancing, redundant atom removal, and vertical alignment;

[0014] S4. Based on the atomic movement path, a dynamic optical tweezers array is generated using the acousto-optic deflector module to adjust the atoms to the target position to obtain the final defect-free n×m array.

[0015] The present invention can efficiently generate defect-free atomic arrays, providing a foundation for constructing quantum bit arrays and other quantum systems. By combining neural network recognition and loading an atomic existence matrix with a spatial light modulator, the present invention optimizes atomic movement on this basis, achieving an efficient conversion from an initial n×2m atomic array to a target n×m defect-free array. The present invention uses a customized UNet neural network structure to accurately classify individual optical potential wells, significantly improving the accuracy of atomic position identification. The single-column atomic movement strategy reduces redundant operations and improves movement efficiency.

[0016] Furthermore, S2 preprocesses the initial array image including:

[0017] Acquire the original array image containing n×2m optical potential wells;

[0018] According to the preset light potential well coordinates, the initial array image is cut into n×2m sub-images of size 9×9, each sub-image corresponds to a separate light potential well area;

[0019] Normalize the pixel values ​​of the cropped sub-image so that its pixel value range is mapped to [0,1].

[0020] Furthermore, the S2 neural network module includes:

[0021] The encoder consists of three fully connected layers, which reduce the dimensionality of the input 81-dimensional data to 64, 32, and 16 dimensions respectively. Each layer is followed by a ReLU activation function.

[0022] The decoder gradually upgrades the 16-dimensional data output by the encoder to 32, 64, and 81 dimensions, retaining the encoded features and restoring them to the input dimension;

[0023] The output layer maps the decoded output to a scalar through a linear layer, converts it into a probability value through a Sigmoid function, and uses a threshold of 0.5 to determine the existence of atoms.

[0024] Furthermore, the vertical alignment of the S3 movement algorithm includes:

[0025] A1. Take the first k rows of the array after redundant atoms are removed as candidate starting rows of the target defect-free array, and traverse the candidate starting row k of the target array; where k is an integer from 1 to m+1;

[0026] A2. For each candidate starting row k, construct a bipartite graph model of the atom position and the target position, and calculate the number of steps the atom moves from the original array position (i, r) to the target position (j, t):

[0027] A3. Use the Hungarian algorithm to solve the minimum weight matching of the bipartite graph and obtain the total number of moves corresponding to each k;

[0028] Construct an nm×nm cost matrix, where the matrix elements are the number of steps required to move each atom from the original array position (i, r) to the target position (j, t);

[0029] Solve the minimum total cost using the linear sum allocation algorithm;

[0030] A4. Select the candidate starting row k with the minimum total cost as the starting row of the target defect-free array, map rows k to k+m-1 of the original array to rows 1 to m of the target defect-free array, and generate an n×m defect-free atomic array.

[0031] Furthermore, step A2 includes:

[0032] Construct a bipartite graph model:

[0033] Left node: the positions (i, r) of all atoms in the original array, a total of n columns × m rows = nm nodes;

[0034] Right node: n columns × m rows = nm positions (j, t) of the target array;

[0035] Number of moving steps = ((i,r), (j,t)) = |ij| + |r-(k+t-1)|

[0036] Where i is the atomic column index of the array after redundant atoms are removed, 1≤i≤n; r is the atomic row number of the array after redundant atoms are removed, 1≤r≤2m; j is the atomic column index of the target array, 1≤j≤n; t is the atomic row number of the target array, 1≤t≤m;

[0037] The bipartite graph of atom positions and target positions satisfies the following conditions: each atom is allowed to be assigned to only one target position; each column and each row of the target array contains only one atom.

[0038] Furthermore, the S4 acousto-optic deflector module includes two acousto-optic deflectors, which control the horizontal and vertical movement of the optical tweezers respectively. The coordinated control includes:

[0039] The first acousto-optic deflector applies horizontal sound waves to control the X-axis deflection angle θx of the light beam;

[0040] The second acousto-optic deflector applies vertical sound waves to control the Y-axis deflection angle θy of the light beam;

[0041] Through synchronous regulation f x and f y , generating a dynamic optical tweezers array to achieve the position movement of atoms in a two-dimensional plane;

[0042] Among them, the two acousto-optic deflectors avoid beam interference through time-division multiplexing or spatial beam splitting technology, and according to the target position coordinates ( x i , y i ) is converted to the corresponding sound wave frequency f x and f y .

[0043] Furthermore, step S4 includes:

[0044] Applying high-frequency sound waves to the optical medium through an acousto-optic deflector to form a periodic refractive index variation structure. When the incident light beam passes through the structure, it is deflected according to the frequency variation of the sound wave, generating a deflected light beam.

[0045] The deflected light beam is focused by a focusing optical system to form an optical tweezers beam, which is used to capture and manipulate ultracold atoms to form an optical tweezers array;

[0046] Ultracold atoms are captured using an optical tweezers array. The ultracold atoms are placed in the light field of the optical tweezers beam, and the gradient force of the optical tweezers beam is used to pull the atoms toward the area with the highest light intensity, achieving capture.

[0047] According to the preset moving path, by changing the frequency of the sound wave and adjusting the direction of the deflected light beam, the trapped atoms are driven to move along with the optical tweezers beam, thereby achieving the movement and positioning of the atoms.

[0048] The present invention also provides a device for generating a defect-free array of ultracold atoms, comprising:

[0049] A spatial light modulator, used to generate optical potential to trap cold atoms and form an initial array;

[0050] a photographing device, for photographing an image of the initial array;

[0051] A processing unit for image preprocessing, neural network recognition, movement path calculation, and atomic position adjustment;

[0052] The acousto-optic deflector unit includes two acousto-optic deflectors, which generate a dynamic optical tweezers array according to the movement path and adjust the atoms to the target position.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The present invention can efficiently generate defect-free atomic arrays, providing a foundation for constructing quantum bit arrays and other quantum systems. By combining neural network recognition and loading the atomic existence matrix with a spatial light modulator, the present invention optimizes the movement of atoms on this basis, achieving an efficient conversion from an initial n×2m atomic array to a target n×m defect-free array. The present invention uses a customized UNet neural network structure to accurately classify individual optical potential wells, significantly improving the accuracy of atomic position identification. The single-column atomic movement strategy reduces redundant operations and improves movement efficiency.

[0055] (2) The present invention can reduce error accumulation. Since the impact range of each movement operation is limited to a single row or column, the accumulation of global errors is avoided, thereby ensuring the stability of the final array quality.

[0056] (3) The present invention is adaptable to large-scale rectangular arrays. The optimization algorithm designed for rectangular arrays can be easily extended to meet the needs of larger-scale array generation.

[0057] (4) The present invention enables a low-complexity mobile path algorithm. The mobile path algorithm is decomposed into three steps, each of which focuses on the current local problem, avoiding the complex calculations required for global path planning. Compared with traditional global optimization algorithms, the strategy of the present invention significantly reduces the calculation time. By reducing the algorithm complexity, the present invention can efficiently generate defect-free atomic arrays while taking into account the calculation speed, execution efficiency, and hardware adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is an initial array diagram of a method for generating an ultracold atomic defect-free array according to an embodiment of the present invention;

[0059] Figure 2 1 is a schematic diagram of a pre-sorting method for generating an ultracold atom defect-free array according to an embodiment of the present invention;

[0060] Figure 3 This is a defect-free target array diagram of a method for generating a defect-free ultracold atom array according to an embodiment of the present invention;

[0061] Figure 4 This is a schematic structural diagram of a device for generating a defect-free array of ultracold atoms according to an embodiment of the present invention;

[0062] Figure 5 This is another structural schematic diagram of a device for generating a defect-free array of ultracold atoms according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0064] Example 1:

[0065] This embodiment provides a method for generating a defect-free array of ultracold atoms, comprising:

[0066] S1. Use a spatial light modulator to generate an optical potential well array and trap ultracold atoms to form an initial n×2m atomic array;

[0067] S2, taking an image of the initial atomic array, pre-processing the image and inputting it into the neural network module, identifying the atomic positions and outputting an n×2m atomic presence matrix, where a matrix element 0 indicates that there is no atom in the corresponding optical potential well, and 1 indicates that there is an atom;

[0068] S3, based on the atomic existence matrix, with each matrix column as the adjustment target, plans the atomic movement path from the n×2m initial array to the target n×m defect-free array through a movement algorithm including intra-column atom balancing, redundant atom removal, and vertical alignment;

[0069] S4. Based on the atomic movement path, a dynamic optical tweezers array is generated using the acousto-optic deflector module to adjust the atoms to the target position to obtain the final defect-free n×m array.

[0070] As an embodiment, S2 preprocesses the initial array image including:

[0071] Acquire the original array image containing n×2m optical potential wells;

[0072] According to the preset light potential well coordinates, the initial array image is cut into n×2m sub-images of size 9×9, each sub-image corresponds to a separate light potential well area;

[0073] Normalize the pixel values ​​of the cropped sub-image so that its pixel value range is mapped to [0,1].

[0074] As an embodiment, the S2 neural network module includes:

[0075] The encoder consists of three fully connected layers, which reduce the dimensionality of the input 81-dimensional data to 64, 32, and 16 dimensions respectively. Each layer is followed by a ReLU activation function.

[0076] The decoder gradually upgrades the 16-dimensional data output by the encoder to 32, 64, and 81 dimensions, retaining the encoded features and restoring them to the input dimension;

[0077] The output layer maps the decoded output to a scalar through a linear layer, converts it into a probability value through a Sigmoid function, and uses a threshold of 0.5 to determine the existence of atoms.

[0078] As an implementation, the intra-column atomic balancing of the S3 movement algorithm includes:

[0079] A1. Count the number of atoms in each column and mark it as "missing column", "redundant column" or "balanced column";

[0080] A2. Preferentially search for redundant columns from the left or right adjacent columns of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the sum of the redundant atoms in the left and right adjacent columns is less than the missing atoms in the missing column, regenerate the initial atomic array;

[0081] A3. Select the bottom atom in the redundant column and move it to fill the missing column. The moving path is optimized based on the Manhattan distance, and the number of moves Δ is the minimum value of the number of excess atoms in the adjacent column and the number of missing atoms in the missing column.

[0082] As an implementation method, the redundant atom removal of the S3 move algorithm includes:

[0083] Traverse upward from the bottom row of each column, marking and removing redundant atoms that exceed the target number m;

[0084] The removal path is planned to move down the column to the outside of the array. The removal cost formula is:

[0085]

[0086] in, r l is the row index of the kth redundant atom, and the row indexes are numbered from top to bottom. E c is the total number of redundant atoms.

[0087] As an implementation, the vertical alignment of the S3 movement algorithm includes:

[0088] Define the target row range as 1 to m and calculate the Manhattan distance between the current atom position and the target row;

[0089] Assign movement priorities based on the principle of minimum distance. If multiple atom target rows are the same, assign them from bottom to top.

[0090] The total moving distance optimization formula is:

[0091] ;

[0092] As an implementation method, Figure 4 As shown, the S4 acousto-optic deflector module includes two acousto-optic deflectors, which control the horizontal and vertical movement of the optical tweezers respectively. Its coordinated control includes:

[0093] The first acousto-optic deflector applies horizontal sound waves to control the X-axis deflection angle of the light beam. θ x , satisfying the formula:

[0094] ;

[0095] in, λ is the incident laser wavelength, f x is the horizontal sound wave frequency, v is the propagation speed of the sound wave in the medium;

[0096] The second acousto-optic deflector applies vertical sound waves to control the Y-axis deflection angle of the light beam. θ y , satisfying the formula:

[0097] ;

[0098] in, f y is the vertical sound wave frequency;

[0099] Through synchronous regulation f x and f y , generating a dynamic optical tweezers array to achieve the position movement of atoms in a two-dimensional plane.

[0100] As an implementation method, step S4 includes:

[0101] Applying high-frequency sound waves to the optical medium through an acousto-optic deflector to form a periodic refractive index variation structure. When the incident light beam passes through the structure, it is deflected according to the frequency variation of the sound wave, generating a deflected light beam.

[0102] The deflected light beam is focused by a focusing optical system to form an optical tweezers beam, which is used to capture and manipulate ultracold atoms to form an optical tweezers array;

[0103] Ultracold atoms are captured using an optical tweezers array. The ultracold atoms are placed in the light field of the optical tweezers beam, and the gradient force of the optical tweezers beam is used to pull the atoms toward the area with the highest light intensity, achieving capture.

[0104] According to the preset moving path, by changing the frequency of the sound wave and adjusting the direction of the deflected light beam, the trapped atoms are driven to move along with the optical tweezers beam, thereby achieving the movement and positioning of the atoms.

[0105] As an implementation method, the dynamic capture process of the coordinated control of dual acousto-optic deflectors includes:

[0106] The two acousto-optic deflectors avoid beam interference by time-division multiplexing or spatial beam splitting technology, and x i , y i ) is converted to the corresponding sound wave frequency f x and f y .

[0107] Also provided is a device for generating defect-free arrays of ultracold atoms, such as Figure 4 and Figure 5 Shown, including:

[0108] A spatial light modulator, used to generate a light potential well to trap cold atoms and form an initial array;

[0109] an ultra-sensitive camera to capture images of the initial array;

[0110] A processing unit for image preprocessing, neural network recognition, calculation of movement paths, and adjustment of atomic positions;

[0111] The acousto-optic deflector unit generates a dynamic optical tweezers array according to the movement path and adjusts the atoms to the target position.

[0112] Example 2:

[0113] A method for generating a defect-free array of ultracold atoms, comprising:

[0114] S1. Use a spatial light modulator to generate a two-dimensional optical potential well array with a well spacing of 3μm and a well depth of 1mK to capture ultracold rubidium-87 atoms (temperature <10μK) to form an initial 8×16 (n=8, m=8) atomic array.

[0115] S2, using an ultra-sensitive EMCCD camera (frame rate 1kHz) to capture the initial array image;

[0116] Image preprocessing: The original image (resolution 1024×1024) was cropped into 8×16 9×9 pixel sub-images according to preset coordinates, and the pixel values ​​were normalized to [0, 1]. Neural network judgment: The sub-images were input into a pre-trained autoencoder network (encoder: 81→64→32→16 dimensions; decoder: 16→32→64→81 dimensions), and the probability of atom existence was output. A threshold of 0.5 was used to determine the existence of atoms, generating an 8×16 atom existence matrix.

[0117] S3, intra-column balance: Count the number of atoms in each column. If the number of atoms in a column is greater than 8, it is marked as redundant, and if it is less than 8, it is marked as missing. Prioritize moving atoms from redundant columns to missing columns, with the number of moves Δ=min(redundant number, missing number). The path is optimized based on Manhattan distance.

[0118] Redundancy removal: Traverse upward from the bottom of the redundant column and remove atoms exceeding m=8. The removal cost is calculated according to the formula calculate;

[0119] Vertical alignment: Calculate the Manhattan distance between the current position of the atom and the target row (rows 1-8), prioritize moving the atom with the shortest distance, and optimize the total distance to the minimum; .

[0120] S4, using dual acousto-optic deflectors, horizontal and vertical sound wave frequency range 80-120MHz, laser wavelength 780nm, sound speed v=4200m / s; optical tweezers generation: by adjustingf x and f y , generating a dynamic optical tweezers array; Atom movement: According to the path planning results, the dual acousto-optic deflectors are time-division multiplexed to control the beam deflection, gradually pulling the atoms to the target site, and finally forming a defect-free 8×8 array.

[0121] Example 3:

[0122] Step A1: Count the number of atoms in each column and mark it as "missing column", "redundant column" or "balanced column";

[0123] Assume that a 6×12 initial array is generated, such as Figure 1 The number and distribution of atoms in each column are shown in Table 1 (row indexes are numbered 1 to 12 from the top, and the goal is to retain the top 6 rows):

[0124] Table 1 shows the initial distribution state of atoms.

[0125]

[0126] Classification rules:

[0127] Redundant column: number of atoms > 6;

[0128] Missing column: number of atoms < 6;

[0129] Balanced column: number of atoms = 6.

[0130] Step A2: Figure 2 As shown, redundant columns are preferentially searched from the left or right adjacent columns of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the sum of the redundant atoms in the left and right adjacent columns is less than the atoms missing in the missing column, the initial atomic array is regenerated;

[0131] Step A3: Select the bottom atom in the redundant column and move it to fill the missing column;

[0132] Operation example (column 5 is missing):

[0133] Right adjacent column 6 (redundant +3):

[0134] Number of moves: Δ=min(3,1)=1.

[0135] Select Atom: The bottommost atom in Redundant column 6 (row 12).

[0136] Movement path: Column 6, Row 12 → Column 5, Target Row 12.

[0137] Manhattan distance: lateral distance = |6-5| = 1 → total distance = 1.

[0138] The updated status is shown in Table 2.

[0139] Table 2 shows the state after missing atoms are filled.

[0140]

[0141] The redundant atom removal of the S3 moving algorithm includes: traversing upward from the bottom row of each column, marking and removing redundant atoms that exceed the target number m; the removal path is planned to move down along the column to the outside of the array.

[0142] The atom with the largest row index in the redundant column (i.e., the bottommost) is removed or moved first.

[0143] Example: The redundant atom in column 1 (redundant +1) is in row 12 (bottom), and the cost of removing it is:

[0144] C eject =(12-12+1)=1;

[0145] The redundant atoms in column 2 (redundancy +2) are rows 10 and 11 (bottom), and the cost of removing them is:

[0146] C eject =(12-7+1)+(12-11+1)=8.

[0147] The redundant atoms in column 6 (redundancy +2) are rows 8 and 10 (bottom), and the cost of removing them is:

[0148] C eject =(12-8+1)+(12-10+1)=8.

[0149] The updated status is shown in Table 3.

[0150] Table 3 shows the status after redundant atoms are removed.

[0151]

[0152] The vertical alignment of the S3 movement algorithm includes: defining the target row range as 1 to m, calculating the Manhattan distance between the current atom position and the target row; allocating movement priorities according to the minimum distance principle, and if multiple atoms have the same target row, they are allocated from bottom to top.

[0153] ;

[0154] First column: C n1 =(6-3)+(7-4)+(8-5)+(9-6)=12;

[0155] Second column: C n2=(5-2)+(6-3)+(7-4)+(8-5)+(9-6)=15;

[0156] Third column: C n3 =(3-1)+(4-2)+(6-3)+(9-4)+(10-5)+(12-6)=23;

[0157] Fourth column: C n4 =(6-1)+(7-2)+(8-3)+(9-4)+(10-5)+(11-6)=25;

[0158] Fifth column: C n5 =(3-2)+(6-3)+(9-4)+(10-5)+(12-6)=20;

[0159] Sixth column: C n6 =(4-3)+(5-4)+(6-5)+(7-6)=4.

[0160] C total =C n1 +C n2 +C n3 +C n4 +C n5 +C n6 =12+15+23+25+20+4=99.

[0161] The updated status is shown in Table 4 and Figure 3 shown.

[0162] Table 4 shows the state of atoms after vertical alignment.

[0163]

[0164] Define the target row range as 2 to m+1,

[0165] First column: |1-2|+|2-3|+|6-4|+|7-5|+|8-6|+|9-7|=1+1+2+2+3+2=11

[0166] Second column: |1-2|+|5-3|+|6-4|+|7-5|+|8-6|+|9-7|=1+2+2+2+2+2=11

[0167] Third column: |3-2|+|4-3|+|6-4|+|9-5|+|10-6|+|12-7|=1+1+2+4+4+5=17

[0168] Fourth column: |6-2|+|7-3|+|8-4|+|9-5|+|10-6|+|11-7|=4+4+4+4+4+4=24

[0169] Fifth column: |1-2|+|3-3|+|6-4|+|9-5|+|10-6|+|12-7|=1+2+4+4+5=16

[0170] Sixth column: |1-2|+|2-3|+|4-4|+|5-5|+|6-6|+|7-7|=2

[0171] C total =81

[0172] Define the target row range as 3 to m+2,

[0173] First column: |1-3|+|2-4|+|6-5|+|7-6|+|8-7|+|9-8|=2+2+1+1+1+1=8

[0174] Second column: |1-3|+|5-4|+|6-5|+|7-6|+|8-7|+|9-8|=2+1+1+1+1+1=7

[0175] Third column: |3-3|+|4-4|+|6-5|+|9-6|+|10-7|+|12-8|=1+3+3+4=11

[0176] Fourth column: |6-3|+|7-4|+|8-5|+|9-6|+|10-7|+|11-8|=3+3+3+3+3+3=18

[0177] Fifth column: |1-3|+|3-4|+|6-5|+|9-6|+|10-7|+|12-8|=2+1+1+3+3+4=13

[0178] Sixth column: |1-3|+|2-4|+|4-5|+|5-6|+|6-7|+|7-8|=2+2+1+1+1+1=8

[0179] C total =65

[0180] Define the target row range as 4 to m+3,

[0181] First column: |1-4|+|2-5|+|6-6|+|7-7|+|8-8|+|9-9|=6

[0182] Second column: |1-4|+|5-5|+|6-6|+|7-7|+|8-8|+|9-9|=3

[0183] Third column: |3-4|+|4-5|+|6-6|+|9-7|+|10-8|+|12-9|=9

[0184] Fourth column: |6-4|+|7-5|+|8-6|+|9-7|+|10-8|+|11-9|=12

[0185] Fifth column: |1-4|+|3-5|+|6-6|+|9-7|+|10-8|+|12-9|=12

[0186] Sixth column: |1-4|+|2-5|+|4-6|+|5-7|+|6-8|+|7-9|=14

[0187] C total =56

[0188] Define the target row range as 5 to m+4,

[0189] First column: |1-5|+|2-6|+|6-7|+|7-8|+|8-9|+|9-10|=12

[0190] Second column: |1-5|+|5-6|+|6-7|+|7-8|+|8-9|+|9-10|=4+1+1+1+1+1=9

[0191] Third column: |3-5|+|4-6|+|6-7|+|9-8|+|10-9|+|12-10|=2+2+1+1+1+2=9

[0192] Fourth column: |6-5|+|7-6|+|8-7|+|9-8|+|10-9|+|11-10|=1+1+1+1+1+1=6

[0193] Fifth column: |1-5|+|3-6|+|6-7|+|9-8|+|10-9|+|12-10|=4+3+1+1+1+2=12

[0194] Sixth column: |1-5|+|2-6|+|4-7|+|5-8|+|6-9|+|7-10|=4+4+3+3+3+3=20

[0195] C total =68

[0196] Define the target row range as 6 to m+5,

[0197] First column: |1-6|+|2-7|+|6-8|+|7-9|+|8-10|+|9-11|=5+5+2+2+2+2=18

[0198] Second column: |1-6|+|5-7|+|6-8|+|7-9|+|8-10|+|9-11|=5+2+2+2+2+2=20

[0199] Third column: |3-6|+|4-7|+|6-8|+|9-9|+|10-10|+|12-11|=3+3+2+0+0+1=9

[0200] Fourth column: |6-6|+|7-7|+|8-8|+|9-9|+|10-10|+|11-11|=0

[0201] Fifth column: |1-6|+|3-7|+|6-8|+|9-9|+|10-10|+|12-11|=5+4+2+0+0+1=12

[0202] Sixth column: |1-6|+|2-7|+|4-8|+|5-9|+|6-10|+|7-11|=5+5+4+4+4+4=26

[0203] C total =85

[0204] First column: |1-7|+|2-8|+|6-9|+|7-10|+|8-11|+|9-12|=6+6+3+3+3+3=24

[0205] Second column: |1-7|+|5-8|+|6-9|+|7-10|+|8-11|+|9-12|=6+3+3+3+3+3=21

[0206] Third column: |3-7|+|4-8|+|6-9|+|9-10|+|10-11|+|12-12|=4+4+3+1+1+0=13

[0207] Fourth column: |6-7|+|7-8|+|8-9|+|9-10|+|10-11|+|11-12|=1+1+1+1+1+1=6

[0208] Fifth column: |1-7|+|3-8|+|6-9|+|9-10|+|10-11|+|12-12|=6+5+3+1+1+0=16

[0209] Sixth column: |1-7|+|2-8|+|4-9|+|5-10|+|6-11|+|7-12|=6+6+5+5+5+5=32

[0210] C total =112

[0211] In summary, when the fourth row is used as the first row of the target array, the total vertical alignment cost is minimized.

[0212] Example 4:

[0213] Step A1: Count the number of atoms in each column and mark it as "missing column", "redundant column" or "balanced column";

[0214] Assume that a 6×12 initial array is generated, and the number and distribution of atoms in each column are shown in Table 5 (row indices are numbered 1 to 12 from the top, and the goal is to retain the top 6 rows):

[0215] Table 5 is a distribution table of another initial atomic array.

[0216]

[0217] Classification rules:

[0218] Redundant column: number of atoms > 6;

[0219] Missing column: number of atoms < 6;

[0220] Balanced column: number of atoms = 6.

[0221] Step A2: preferentially search for redundant columns from the left or right adjacent columns of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the sum of the redundant atoms in the left and right adjacent columns is less than the atoms missing in the missing column, then regenerate the initial atomic array;

[0222] Step A3: Select the bottom atom in the redundant column and move it to fill the missing column;

[0223] Operation example (column 2 is missing):

[0224] Left adjacent column 1 (redundant +1):

[0225] Number of moves: Δ=min(1,1)=1.

[0226] Select Atom: The bottom-most atom in Redundant Column 1 (row 12).

[0227] Movement path: Column 1 Row 12 → Column 2 Target Row 12.

[0228] Manhattan distance: lateral distance = |1-2| = 1 → total distance = 1.

[0229] Operation example (column 6 is missing):

[0230] Right adjacent column 5 (redundant +3):

[0231] Number of moves: Δ=min(3,2)=2.

[0232] Select atoms: the bottommost atom of redundant column 5 (rows 9, 11).

[0233] Movement path:

[0234] Column 5 → Column 6 (distance = |5-6| = 1).

[0235] Column 5 → Column 6 (distance = |5-6| = 1).

[0236] Total movement cost: 1+1=2.

[0237] The updated status is shown in Table 6.

[0238] Table 6 is a distribution table of atoms of another initial atomic array after filling.

[0239]

[0240] The redundant atom removal of the S3 moving algorithm includes: traversing upward from the bottom row of each column, marking and removing redundant atoms that exceed the target number m; the removal path is planned to move down along the column to the outside of the array.

[0241] The atom with the largest row index in the redundant column (i.e., the bottommost) is removed or moved first.

[0242] Example: The redundant atoms in column 3 (redundancy +2) are rows 9 and 11 (bottom). The cost of removing them is:

[0243] C eject =(12-9+1)+(12-11+1)=4+2=6;

[0244] The redundant atom in column 5 (redundancy +1) is row 7 (bottom), and the cost of removing it is:

[0245] C eject =12-7+1=6.

[0246] The updated status is shown in Table 7.

[0247] Table 7 is a distribution table of another initial atomic array after redundant atoms are removed.

[0248]

[0249] The vertical alignment of the S3 movement algorithm includes: defining the target row range as 1 to m, calculating the Manhattan distance between the current atom position and the target row; allocating movement priorities according to the minimum distance principle, and if multiple atoms have the same target row, they are allocated from bottom to top.

[0250] ;

[0251] First column: Cn1 =(3-2)+(5-3)+(7-4)+(9-5)+(11-6)=15;

[0252] Second column: C n2 =(2-1)+(4-2)+(6-3)+(8-4)+(10-5)+(12-6)=15;

[0253] Third column: C n3 =7-6=1;

[0254] Fourth column: C n4 =(2-1)+(4-2)+(6-3)+(8-4)+(10-5)+(12-6)=15;

[0255] Fifth column: C n5 =0;

[0256] Sixth column: C n6 =(2-1)+(4-2)+(6-3)+(8-4)+(9-5)+(11-6)=19.

[0257] C total =C n1 +C n2 +C n3 +C n4 +C n5 +C n6 =15+15+1+15+0+19=65.

[0258] The updated status is shown in Table 8.

[0259] Table 8 is a distribution table of another atomic initial array after the atoms are vertically aligned.

[0260]

[0261] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for generating a defect-free array of ultracold atoms, characterized in that: include: S1. Use a spatial light modulator to generate an optical potential well array and trap ultracold atoms to form an initial n×2m atomic array; S2, taking an image of the initial atomic array, pre-processing the image and inputting it into the neural network module, identifying the atomic positions and outputting an n×2m atomic presence matrix, where a matrix element 0 indicates that there is no atom in the corresponding optical potential well, and 1 indicates that there is an atom; S3, based on the atomic existence matrix, with each matrix column as the adjustment target, plans the atomic movement path from the n×2m initial array to the target n×m defect-free array through a movement algorithm including intra-column atom balancing, redundant atom removal, and vertical alignment; S4. Based on the atomic movement path, a dynamic optical tweezers array is generated using the acousto-optic deflector module to adjust the atoms to the target position to obtain the final defect-free n×m array; The intra-column atomic balance of the S3 movement algorithm includes: A1. Count the number of atoms in each column and mark it as "missing column", "redundant column" or "balanced column"; A2. Preferentially search for redundant columns from the left or right adjacent columns of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the sum of the redundant atoms in the left and right adjacent columns is less than the missing atoms in the missing column, regenerate the initial atomic array; A3. Select the bottommost atom in the redundant column and move it to fill the missing column to obtain a balanced atomic array; the movement path is optimized based on the Manhattan distance, and the number of moves Δ is the minimum value of the number of excess atoms in the adjacent column and the number of missing atoms in the missing column; The S3 move algorithm removes redundant atoms including: Traverse upward from the bottom row of each column, mark and remove redundant atoms that exceed the target number m, and obtain the array after redundant atoms are removed; The removal path is planned to move down the column to the outside of the array; The vertical alignment of the S3 mobile algorithm includes: A1. Take the first k rows of the array after redundant atoms are removed as candidate starting rows of the target defect-free array, and traverse the candidate starting row k of the target array; where k is an integer from 1 to m+1; A2. For each candidate starting row k, construct a bipartite graph model of the atom position and the target position, and calculate the number of steps the atom moves from the original array position (i, r) to the target position (j, t): A3. Use the Hungarian algorithm to solve the minimum weight matching of the bipartite graph and obtain the total number of moves corresponding to each k; Construct an nm×nm cost matrix, where the matrix elements are the number of steps required to move each atom from its original array position (i, r) to its target position (j, t). Use the linear sum-and-distribution algorithm to find the minimum total cost. A4. Select the candidate starting row k with the minimum total cost as the starting row of the target defect-free array, map rows k to k+m-1 of the original array to rows 1 to m of the target defect-free array, and generate an n×m defect-free atomic array.

2. The method for generating a defect-free array of ultracold atoms according to claim 1, characterized in that: S2 preprocesses the initial array image including: Acquire an original array image containing an n×2m light potential well; according to the pre-set light potential well coordinates, crop the initial array image into n×2m 9×9 sub-images, each corresponding to a separate light potential well area; normalize the pixel values ​​of the cropped sub-images so that their pixel value range is mapped to [0,1].

3. The method for generating a defect-free array of ultracold atoms according to claim 2, characterized in that: The S2 neural network module includes: an encoder, which consists of three fully connected layers, reducing the dimensionality of the input 81-dimensional data to 64, 32, and 16 dimensions respectively, and each layer is followed by a ReLU activation function; a decoder, which gradually increases the dimensionality of the 16-dimensional data output by the encoder to 32, 64, and 81 dimensions, retaining the encoding features and restoring it to the input dimension; an output layer, which maps the decoded output to a scalar through a linear layer, converts it into a probability value through a Sigmoid function, and determines the existence of atoms with a threshold of 0.

5.

4. The method for generating a defect-free array of ultracold atoms according to claim 1, characterized in that: Step A2 includes: Construct a bipartite graph model: Left node: the positions (i, r) of all atoms in the original array, a total of n columns × m rows = nm nodes; Right node: n columns × m rows = nm positions (j, t) of the target array; Number of moves = ((i,r), (j,t)) = |i−j| + |r−(k+t−1)|; Where i is the atomic column index of the array after redundant atoms are removed, 1≤i≤n; r is the atomic row number of the array after redundant atoms are removed, 1≤r≤2m; j is the atomic column index of the target array, 1≤j≤n; t is the atomic row number of the target array, 1≤t≤m; the bipartite graph of atomic positions and target positions satisfies the following conditions: each atom is only allowed to be assigned to one target position; each column and each row of the target array contains only one atom.

5. The method for generating a defect-free ultracold atom array according to claim 1, wherein: The S4 acousto-optic deflector module includes two acousto-optic deflectors, which control the horizontal and vertical movement of the optical tweezers respectively. Its coordinated control includes: The first acousto-optic deflector applies horizontal sound waves to control the X-axis deflection angle θ of the light beam. x ; The second acousto-optic deflector applies vertical sound waves to control the Y-axis deflection angle θ of the light beam. y ; By synchronously adjusting f x With f y , generating a dynamic optical tweezers array to achieve the position movement of atoms in a two-dimensional plane; Among them, the two acousto-optic deflectors avoid beam interference through time-division multiplexing or spatial beam splitting technology, and according to the target position coordinates (x i ,y i ) is converted to the corresponding sound wave frequency f x and f y .

6. The method for generating a defect-free array of ultracold atoms according to claim 5, characterized in that: Step S4 includes: Applying high-frequency sound waves to the optical medium through an acousto-optic deflector to form a periodic refractive index variation structure. When the incident light beam passes through the structure, it is deflected according to the frequency variation of the sound wave, generating a deflected light beam. The deflected light beam is focused by a focusing optical system to form an optical tweezers beam, which is used to capture and manipulate ultracold atoms to form an optical tweezers array; Ultracold atoms are captured using an optical tweezers array. The ultracold atoms are placed in the light field of the optical tweezers beam, and the gradient force of the optical tweezers beam is used to pull the atoms toward the area with the highest light intensity, achieving capture. According to the preset moving path, by changing the frequency of the sound wave and adjusting the direction of the deflected light beam, the trapped atoms are driven to move along with the optical tweezers beam, thereby achieving the movement and positioning of the atoms.

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