Method and device for generating ultra-cold atom defect-free array

Abstract

The invention relates to the technical field of quantum physics and quantum, in particular to a super-cold atom defect-free array generation method, which comprises the following steps: S1, capturing cold atoms by using a light potential well generated by a spatial light modulator to form an initial n * 2m array; s2, shooting an image of the initial array, preprocessing the image of the initial array, transmitting the preprocessed data to a neural network for identification, and outputting an atomic position matrix; s3, calculating a moving path from the n * 2m array to the target n * m defect-free array by using a moving algorithm according to the atomic position matrix; and S4, according to the moving path, the atomic position of each column or each row in the array is adjusted, and a final defect-free target array is obtained. According to the invention, the defect-free atom array can be efficiently generated. According to the invention, through combination of neural network identification, loading of the initial array by the spatial light modulator and optimization of atom movement, efficient conversion from the initial n * 2m atom array to the target n * m defect-free array is realized.

Description

Technical Field

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

[0002] In recent years, ultracold atom technology has been widely applied in the fields of quantum information, quantum computing, precision measurement, and basic physical research. Among them, generating a regular array of ultracold atoms is a key technology that enables high-precision manipulation of the positions of atoms and provides a basis for constructing quantum bit arrays and other quantum systems. However, current technical means still face many challenges in generating large-scale, defect-free ultracold atom arrays.

[0003] Traditional methods such as the atomic array generation technology based on optical lattices, although they can theoretically achieve a regular array, are often limited by the instability of the optical interference pattern, external noise, and spontaneous loss of atoms in practical applications. Specifically, it is difficult to avoid vacancies or defects in the array, which directly affects the controllability and reliability of the quantum system.

[0004] In recent years, the array generation technology combined with a spatial light modulator has gradually attracted attention. The spatial light modulator can generate an arbitrary light field distribution through phase modulation and achieve efficient capture of the initial atomic array. However, due to the limitations of the resolution and fill factor of the spatial light modulator, there are often a certain proportion of defective atoms in the generated array, especially when the scale of the target array is enlarged, the problem becomes more prominent.

[0005] To further improve the defect-freeness of the array, the acousto-optic modulator technology is introduced to dynamically adjust the positions of atoms. Through the acousto-optic modulator, high-precision deflection of the laser beam can be achieved, so as to move the captured atoms one by one to fill the vacancies in the array.

[0006] Although the existing technology has made important progress in the generation of ultracold atom arrays, for the combined method based on SLM and AOD, especially the defect-free generation technology for rectangular arrays, there are still the following main disadvantages: Insufficient recognition accuracy for array loading: The existing technology usually relies on traditional image processing algorithms or simple threshold judgment methods to identify the positions of atoms in the array. Due to optical noise, system errors, and the enlargement of the array scale, the accuracy of traditional recognition methods will significantly decrease, easily leading to false detection or omission of atomic positions, thus affecting the subsequent movement optimization process.

[0007] The moving algorithm lacks specialization for rectangular arrays: Existing moving algorithms based on acousto-optic deflectors usually adopt general strategies, mainly focusing on the optimization of arbitrarily regular or randomly distributed atomic arrangements, lacking specially optimized path planning and moving rules. Such general algorithms not only have low efficiency but may also lead to unnecessary atomic movements, thereby increasing operation time and error accumulation. Summary of the Invention

[0008] To solve the problems raised in the background art, the present invention proposes a method for generating a defect-free array of ultracold atoms. By introducing neural network recognition technology and a moving algorithm, a technical solution capable of efficiently generating a defect-free ultracold atom array is developed. Specifically, the present invention focuses on the specialized optimization of rectangular array generation to achieve an efficient conversion from an n×2m initial loading to an n×m defect-free target array, meeting the actual needs of large-scale quantum arrays, and significantly improving the operating efficiency of the system and the quality of array generation.

[0009] The technical solution adopted by the present invention to solve its technical problems is: to provide a method for generating a defect-free array of ultracold atoms, including: S1. Use a spatial light modulator to generate an optical potential well array and capture ultracold atoms to form an initial n×2m atomic array; S2. Take an image of the initial atomic array, preprocess the image and input it into a neural network module to identify the atomic positions and output an n×2m atomic existence matrix, where the 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, plan the atomic movement path from the n×2m initial array to the target n×m defect-free array through a moving algorithm including in-column atomic balance, removal of redundant atoms, and vertical alignment; S4. According to the atomic movement path, use an acousto-optic deflector module to generate a dynamic optical tweezer array, adjust the atoms to the target positions, and obtain the final defect-free n×m array.

[0010] The present invention can efficiently generate a defect-free atomic array, providing a basis for constructing a qubit array and other quantum systems. By combining neural network recognition and a spatial light modulator to load the atomic existence matrix, and on this basis optimizing the movement of atoms, the present invention realizes an efficient conversion from the initial n×2m atomic array to the target n×m defect-free array. The present invention adopts a customized UNet neural network structure to accurately classify individual optical potential wells, significantly improving the accuracy of atomic position recognition. Through a single-column atomic movement strategy, redundant operations are reduced and the movement efficiency is improved.

[0011] Further, the preprocessing of the initial array image in S2 includes: Obtain the original array image containing n×2m optical potential wells; According to the pre-set optical potential well coordinates, crop the initial array image into n×2m sub-images of size 9×9, and each sub-image corresponds to a separate optical potential well region; Normalize the pixel values of the cropped sub-images so that their pixel value ranges are mapped to [0, 1].

[0012] Furthermore, the S2 neural network module includes: An encoder, consisting of three fully connected layers, which respectively reduce the input 81-dimensional data to 64 dimensions, 32 dimensions, and 16 dimensions, and each layer is followed by a ReLU activation function; A decoder, which gradually expands the 16-dimensional data output by the encoder to 32 dimensions, 64 dimensions, and 81 dimensions, retains the encoded features and restores them to the input dimension; An output layer, which maps the decoded output to a scalar through a linear layer, converts it to a probability value through a Sigmoid function, and determines the atomic existence with a threshold of 0.5.

[0013] Furthermore, the vertical alignment of the S3 moving algorithm includes: A1. Take the first k rows of the array after removing redundant atoms as the candidate starting rows of the target defect-free array, and traverse the candidate starting rows 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 atomic position and the target position, and calculate the number of moving steps of the atom 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 to obtain the total number of moving steps corresponding to each k; Construct an nm×nm cost matrix, and the matrix elements are the number of moving steps of each atom from the original array position (i, r) to the target position (j, t); Solve the minimum total cost through the linear sum assignment algorithm; A4. Select the candidate starting row k with the minimum total cost as the starting row of the target defect-free array, map the k to k + m - 1 rows of the original array to the 1 to m rows of the target defect-free array, and generate an n×m defect-free atomic array.

[0014] Furthermore, step A2 includes: Construct a bipartite graph model: Left nodes: The positions (i, r) of all atoms in the original array, a total of n columns × m rows = nm nodes; Right nodes: The n columns × m rows = nm positions (j, t) of the target array; Number of moving steps = ((i, r), (j, t)) = |i - j| + |r - (k + t - 1)| Among them, i is the atomic column index of the array after redundant atom removal, where 1 ≤ i ≤ n; r is the atomic row number of the array after redundant atom removal, where 1 ≤ r ≤ 2m; j is the atomic column index of the target array, where 1 ≤ j ≤ n; t is the atomic row number of the target array, where 1 ≤ t ≤ m; The bipartite graph of the atomic positions and the target positions satisfies the conditions that each atom is only allowed to be assigned to one target position, and each column and each row of the target array contain only one atom.

[0015] Furthermore, the S4 acousto-optic deflector module includes two acousto-optic deflectors, which respectively control the horizontal and vertical movement of the optical tweezers. Their coordinated control includes: The first acousto-optic deflector applies a horizontal acoustic wave to control the X-axis deflection angle θx of the light beam; The second acousto-optic deflector applies a vertical acoustic wave to control the Y-axis deflection angle θy of the light beam; By synchronously adjusting f x and f y , a dynamic optical tweezers array is generated to realize the position movement of atoms in the two-dimensional plane; Among them, the two acousto-optic deflectors avoid beam interference through time-division multiplexing or spatial beam splitting technology, and convert to the corresponding acoustic wave frequencies according to the target position coordinates ( x i , y i ) f x and f y .

[0016] Furthermore, step S4 includes: Applying a high-frequency acoustic wave to the optical medium through the acousto-optic deflector to form a periodic refractive index change structure. When the incident light beam passes through this structure, it deflects according to the frequency change of the acoustic wave to generate a deflected light beam; Focusing the deflected light beam through a focusing optical system to form an optical tweezers beam, and using the optical tweezers beam to capture and manipulate ultracold atoms to form an optical tweezers array; Capturing ultracold atoms through the optical tweezers array; placing the ultracold atoms in the light field of the optical tweezers beam, and using the gradient force of the optical tweezers beam to pull the atoms towards the region with the highest light intensity to achieve capture; According to the preset movement path, by changing the frequency of the acoustic wave, adjusting the direction of the deflected light beam, and driving the captured atoms to move together with the optical tweezers beam to achieve the movement and positioning of the atoms.

[0017] The present invention also provides a device for generating a defect-free array of ultracold atoms, including: A spatial light modulator for generating an optical potential well to capture cold atoms and form an initial array; A photographing device, used for photographing an image of an initial array; A processing unit for image preprocessing, neural network recognition, calculation of movement paths, and adjustment of atomic positions; The acousto-optic deflector unit includes two acousto-optic deflectors, which generate a dynamic optical tweezers array according to the moving path and adjust the atoms to the target position.

[0018] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention can efficiently generate defect-free atomic arrays for the construction of quantum bit arrays and other quantum systems. The present invention combines neural network recognition and spatial light modulator loading of atomic existence matrix, and optimizes the movement of atoms on this basis, thereby achieving efficient conversion from the initial n×2m atomic array to the target n×m defect-free array. The present invention adopts a customized UNet neural network structure to accurately classify a single optical potential well, significantly improving the accuracy of atomic position identification. Through the single-column atomic movement strategy, redundant operations are reduced and the movement efficiency is improved.

[0019] (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.

[0020] (3) The present invention can adapt to large-scale rectangular arrays. The optimization algorithm designed for rectangular arrays in the present invention can be easily expanded to meet the needs of larger-scale array generation.

[0021] (4) The present invention can achieve low complexity of the 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 the traditional global optimization algorithm, the strategy of the present invention significantly reduces the calculation time. By reducing the complexity of the algorithm, 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

[0022] Figure 1 is an initial array diagram of a method for generating an ultracold atomic defect-free array according to an embodiment of the present invention; Figure 2 It is a pre-sorting schematic diagram of a method for generating an ultracold atom defect-free array according to an embodiment of the present invention; Figure 3 A defect-free target array diagram of a method for generating an ultracold atom defect-free array according to an embodiment of the present invention; Figure 4 It is a schematic structural diagram of a device for generating an ultracold atom defect-free array according to an embodiment of the present invention; Figure 5It is another structural schematic diagram of an apparatus for generating a defect-free array of ultracold atoms according to an embodiment of the present invention. Detailed implementation manners

[0023] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0024] Embodiment 1:

[0025] This embodiment provides a method for generating a defect-free array of ultracold atoms, including: S1. Use a spatial light modulator to generate an optical potential well array and capture ultracold atoms to form an initial n×2m atomic array; S2. Take a picture of the initial atomic array, preprocess the image and input it into a neural network module to identify the atomic positions and output an n×2m atomic existence matrix, where the 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, plan the atomic movement path from the n×2m initial array to the target n×m defect-free array through a movement algorithm including in-column atomic balance, redundant atom removal, and vertical alignment; S4. According to the atomic movement path, use an acousto-optic deflector module to generate a dynamic optical tweezer array, adjust the atoms to the target positions, and obtain the final defect-free n×m array.

[0026] As an implementation manner, the preprocessing of the initial array image in S2 includes: Obtain the original array image containing n×2m optical potential wells; According to the pre-set optical potential well coordinates, crop the initial array image into n×2m sub-images with a size of 9×9, and each sub-image corresponds to a separate optical potential well area; Normalize the pixel values of the cropped sub-images so that their pixel value ranges are mapped to [0,1].

[0027] As an implementation manner, the neural network module in S2 includes: An encoder, composed of three fully connected layers, which respectively reduce the input 81-dimensional data to 64 dimensions, 32 dimensions, and 16 dimensions, and each layer is followed by a ReLU activation function; A decoder, gradually increasing the dimension of the 16-dimensional data output by the encoder to 32 dimensions, 64 dimensions, and 81 dimensions, retaining the encoded features and restoring them to the input dimension; The output layer maps the decoded output to a scalar through a linear layer, converts it into a probability value through the Sigmoid function, and determines the existence of atoms with a threshold of 0.5.

[0028] As an implementation, the in-column atom balance of the S3 movement algorithm includes: A1. Count the number of atoms in each column and label it as a "missing column", "redundant column", or "balanced column"; A2. First, search for redundant columns in the left or right adjacent column of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the total number of redundant atoms in the left and right adjacent columns is less than the number of missing atoms in the missing column, regenerate the initial atom array; A3. Select the bottommost atom in the redundant column and move it to fill the missing column; the movement path is optimized based on the Manhattan distance, and the movement quantity Δ is the minimum of the excess atoms in the adjacent column and the deficit atoms in the missing column.

[0029] As an implementation, the removal of redundant atoms in the S3 movement algorithm includes: Traverse upward from the bottom row of each column, mark and remove redundant atoms exceeding the target quantity m; The removal path is planned to move downward along the column to the outside of the array, and the removal cost formula is:

[0030] Where r l is the row index of the k-th redundant atom, and the row index is numbered from top to bottom, E c is the total number of redundant atoms.

[0031] As an implementation, the vertical alignment of the S3 movement algorithm includes: Define the target row range as 1 to m, and calculate the Manhattan distance between the current atom position and the target row; Allocate movement priorities according to the principle of the minimum distance. If the multi-atom target rows are the same, allocate from bottom to top; The total movement distance optimization formula is: ;

[0032] As an implementation, as Figure 4 shown, the S4 acousto-optic deflector module includes two acousto-optic deflectors, which respectively control the horizontal and vertical direction movements of the optical tweezers, and its collaborative control includes: The first acousto-optic deflector applies a horizontal acoustic wave to control the X-axis deflection angle of the light beam θ x , satisfying the formula: ; Where λis the incident laser wavelength, f x is the horizontal acoustic wave frequency, and v is the propagation speed of the acoustic wave in the medium; The second acousto-optic deflector applies an acoustic wave in the vertical direction to control the Y-axis deflection angle of the light beam θ y , satisfying the formula: ; Among them, f y is the vertical acoustic wave frequency; By synchronously adjusting f x and f y , a dynamic optical tweezer array is generated to realize the position movement of atoms in a two-dimensional plane.

[0033] As an implementation manner, step S4 includes: Applying a high-frequency acoustic wave to the optical medium through an acousto-optic deflector to form a periodic refractive index change structure. When the incident light beam passes through this structure, it deflects according to the frequency change of the acoustic wave to generate a deflected light beam; Focusing the deflected light beam through a focusing optical system to form an optical tweezer beam, and using the optical tweezer beam to capture and manipulate ultracold atoms to form an optical tweezer array; Capturing ultracold atoms through the optical tweezer array; placing the ultracold atoms in the optical field of the optical tweezer beam, and using the gradient force of the optical tweezer beam to pull the atoms towards the region with the highest light intensity to achieve capture; According to the preset movement path, by changing the frequency of the acoustic wave, adjusting the direction of the deflected light beam, and driving the captured atoms to move together with the optical tweezer beam to achieve the movement and positioning of the atoms.

[0034] As an implementation manner, the dynamic capture process jointly controlled by the double acousto-optic deflectors includes: The two acousto-optic deflectors avoid beam interference through time-division multiplexing or spatial beam splitting technology, and convert to the corresponding acoustic wave frequencies according to the target position coordinates ( x i , y i ) f x and f y .

[0035] There is also provided a device for generating a defect-free array of ultracold atoms, as shown in Figure 4 and Figure 5 , including: A spatial light modulator for generating an optical potential well to capture cold atoms and form an initial array; An ultrasensitive camera for taking images of the initial array; A processing unit for image preprocessing, neural network recognition, calculation of movement paths, and adjustment of atomic positions; The acousto-optic deflector unit generates a dynamic optical tweezers array according to the moving path and adjusts the atoms to the target position.

[0036] Embodiment 2: A method for generating an ultracold atomic defect-free array, comprising: 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.

[0037] S2, using an ultra-sensitive EMCCD camera (frame rate 1kHz) to capture the initial array image; 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 determination: The sub-image was input into a pre-trained autoencoder network (encoder: 81→64→32→16 dimensions; decoder: 16→32→64→81 dimensions), and the probability of atomic existence was output. The threshold of 0.5 was used to determine the existence of atoms, and an 8×16 atomic existence matrix was generated.

[0038] S3, balance within the column: count the number of atoms in each column, if the number of atoms in a column is greater than 8, it is marked as a redundant column, and if it is less than 8, it is a missing column. Prioritize moving atoms from the redundant column to the missing column, the number of moves Δ=min(redundant number, missing number), and the path is optimized based on Manhattan distance; Redundancy removal: Traverse upward from the bottom of the redundant column and remove atoms beyond m=8. The removal cost is calculated according to the formula calculate; Vertical alignment: Calculate the Manhattan distance between the current position of the atom and the target row (rows 1-8), give priority to moving the atom with the shortest distance, and optimize the total distance to the minimum value; .

[0039] 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 adjusting f x and f y , generate a dynamic optical tweezers array; atomic movement: according to the path planning results, the dual acousto-optic deflectors are used in time-division multiplexing to control the beam deflection, gradually pulling the atoms to the target site, and finally forming a defect-free 8×8 array.

[0040] Embodiment 3: Step A1: Count the number of atoms in each column and label it as "missing column", "redundant column", or "balanced column". Suppose a 6×12 initial array is generated, as Figure 1 shown. The number and distribution of atoms in each column are shown in Table 1 (the row index is numbered from the top as 1 to 12, and the top 6 rows are to be retained): Table 1 shows the initial distribution state of the atoms.

[0041]

[0042] Classification rules: Redundant column: Number of atoms > 6; Missing column: Number of atoms < 6; Balanced column: Number of atoms = 6.

[0043] Step A2: As Figure 2 shown, first look for a redundant column in the left adjacent column or the right adjacent column of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the total number of redundant atoms in the left and right adjacent columns is less than the number of missing atoms in the missing column, regenerate the initial atom array; Step A3: Select the bottommost atom in the redundant column and move it to fill the missing column; Operation example (column 5 is the missing column): Right adjacent column 6 (redundant +3): Number of moves: Δ = min(3,1) = 1.

[0044] Select atom: The bottommost atom (row 12) in redundant column 6.

[0045] Moving path: Column 6 row 12 → Column 5 target row 12.

[0046] Manhattan distance: Horizontal distance = |6 - 5| = 1 → Total distance = 1.

[0047] The updated state is shown in Table 2.

[0048] Table 2 shows the state after filling the missing atoms.

[0049]

[0050] The removal of redundant atoms in the S3 moving algorithm includes: traversing upward from the bottom row of each column, marking and removing redundant atoms exceeding the target number m; the removal path is planned to move downward along the column outside the array.

[0051] The atom with the largest row index (i.e., the bottommost) in the redundant column is preferentially removed or moved.

[0052] Example: The redundant atom in column 1 (redundant +1) is row 12 (bottom), removal cost: C eject =(12 - 12 + 1)=1; The redundant atoms in column 2 (redundancy + 2) are rows 10 and 11 (bottom), removal cost: C eject =(12 - 7 + 1)+(12 - 11 + 1)=8.

[0053] The redundant atoms in column 6 (redundancy + 2) are rows 8 and 10 (bottom), removal cost: C eject =(12 - 8 + 1)+(12 - 10 + 1)=8.

[0054] The updated state is shown in Table 3.

[0055] Table 3 is the state after redundant atom removal.

[0056]

[0057] 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; assigning movement priorities according to the principle of the smallest distance, and if the target rows of multiple atoms are the same, assign from bottom to top.

[0058] ;

[0059] First column: C n1 =(6 - 3)+(7 - 4)+(8 - 5)+(9 - 6)=12; Second column: C n2 =(5 - 2)+(6 - 3)+(7 - 4)+(8 - 5)+(9 - 6)=15; Third column: C n3 =(3 - 1)+(4 - 2)+(6 - 3)+(9 - 4)+(10 - 5)+(12 - 6)=23; Fourth column: C n4 =(6 - 1)+(7 - 2)+(8 - 3)+(9 - 4)+(10 - 5)+(11 - 6)=25; Fifth column: C n5 =(3 - 2)+(6 - 3)+(9 - 4)+(10 - 5)+(12 - 6)=20; Sixth column: C n6 =(4 - 3)+(5 - 4)+(6 - 5)+(7 - 6)=4.

[0060] C total =C n1 +C n2 +Cn3 +C n4 +C n5 +C n6 = 12 + 15 + 23 + 25 + 20 + 4 = 99。

[0061] The updated status is shown in Table 4 and Figure 3 as follows.

[0062] Table 4 shows the status after atomic vertical alignment.

[0063]

[0064] Define the target row range as 2 to m + 1. First column: |1 - 2| + |2 - 3| + |6 - 4| + |7 - 5| + |8 - 6| + |9 - 7| = 1 + 1 + 2 + 2 + 3 + 2 = 11 Second column: |1 - 2| + |5 - 3| + |6 - 4| + |7 - 5| + |8 - 6| + |9 - 7| = 1 + 2 + 2 + 2 + 2 + 2 = 11 Third column: |3 - 2| + |4 - 3| + |6 - 4| + |9 - 5| + |10 - 6| + |12 - 7| = 1 + 1 + 2 + 4 + 4 + 5 = 17 Fourth column: |6 - 2| + |7 - 3| + |8 - 4| + |9 - 5| + |10 - 6| + |11 - 7| = 4 + 4 + 4 + 4 + 4 + 4 = 24 Fifth column: |1 - 2| + |3 - 3| + |6 - 4| + |9 - 5| + |10 - 6| + |12 - 7| = 1 + 2 + 4 + 4 + 5 = 16 Sixth column: |1 - 2| + |2 - 3| + |4 - 4| + |5 - 5| + |6 - 6| + |7 - 7| = 2 C total = 81 Define the target row range as 3 to m + 2. First column: |1 - 3| + |2 - 4| + |6 - 5| + |7 - 6| + |8 - 7| + |9 - 8| = 2 + 2 + 1 + 1 + 1 + 1 = 8 Second column: |1 - 3| + |5 - 4| + |6 - 5| + |7 - 6| + |8 - 7| + |9 - 8| = 2 + 1 + 1 + 1 + 1 + 1 = 7 Third column: |3 - 3| + |4 - 4| + |6 - 5| + |9 - 6| + |10 - 7| + |12 - 8| = 1 + 3 + 3 + 4 = 11 Fourth column: |6 - 3| + |7 - 4| + |8 - 5| + |9 - 6| + |10 - 7| + |11 - 8| = 3 + 3 + 3 + 3 + 3 + 3 = 18 Column 5: |1 - 3| + |3 - 4| + |6 - 5| + |9 - 6| + |10 - 7| + |12 - 8| = 2 + 1 + 1 + 3 + 3 + 4 = 13 Column 6: |1 - 3| + |2 - 4| + |4 - 5| + |5 - 6| + |6 - 7| + |7 - 8| = 2 + 2 + 1 + 1 + 1 + 1 = 8 C total = 65 Define the target row range as 4 to m + 3, Column 1: |1 - 4| + |2 - 5| + |6 - 6| + |7 - 7| + |8 - 8| + |9 - 9| = 6 Column 2: |1 - 4| + |5 - 5| + |6 - 6| + |7 - 7| + |8 - 8| + |9 - 9| = 3 Column 3: |3 - 4| + |4 - 5| + |6 - 6| + |9 - 7| + |10 - 8| + |12 - 9| = 9 Column 4: |6 - 4| + |7 - 5| + |8 - 6| + |9 - 7| + |10 - 8| + |11 - 9| = 12 Column 5: |1 - 4| + |3 - 5| + |6 - 6| + |9 - 7| + |10 - 8| + |12 - 9| = 12 Column 6: |1 - 4| + |2 - 5| + |4 - 6| + |5 - 7| + |6 - 8| + |7 - 9| = 14 C total = 56 Define the target row range as 5 to m + 4, Column 1: |1 - 5| + |2 - 6| + |6 - 7| + |7 - 8| + |8 - 9| + |9 - 10| = 12 Column 2: |1 - 5| + |5 - 6| + |6 - 7| + |7 - 8| + |8 - 9| + |9 - 10| = 4 + 1 + 1 + 1 + 1 + 1 = 9 Column 3: |3 - 5| + |4 - 6| + |6 - 7| + |9 - 8| + |10 - 9| + |12 - 10| = 2 + 2 + 1 + 1 + 1 + 2 = 9 Column 4: |6 - 5| + |7 - 6| + |8 - 7| + |9 - 8| + |10 - 9| + |11 - 10| = 1 + 1 + 1 + 1 + 1 + 1 = 6 Column 5: |1 - 5| + |3 - 6| + |6 - 7| + |9 - 8| + |10 - 9| + |12 - 10| = 4 + 3 + 1 + 1 + 1 + 2 = 12 Column 6: |1 - 5| + |2 - 6| + |4 - 7| + |5 - 8| + |6 - 9| + |7 - 10| = 4 + 4 + 3 + 3 + 3 + 3 = 20 C total = 68 Define the target row range as 6 to m + 5, First column: |1 - 6| + |2 - 7| + |6 - 8| + |7 - 9| + |8 - 10| + |9 - 11| = 5 + 5 + 2 + 2 + 2 + 2 = 18 Second column: |1 - 6| + |5 - 7| + |6 - 8| + |7 - 9| + |8 - 10| + |9 - 11| = 5 + 2 + 2 + 2 + 2 + 2 = 20 Third column: |3 - 6| + |4 - 7| + |6 - 8| + |9 - 9| + |10 - 10| + |12 - 11| = 3 + 3 + 2 + 0 + 0 + 1 = 9 Fourth column: |6 - 6| + |7 - 7| + |8 - 8| + |9 - 9| + |10 - 10| + |11 - 11| = 0 Fifth column: |1 - 6| + |3 - 7| + |6 - 8| + |9 - 9| + |10 - 10| + |12 - 11| = 5 + 4 + 2 + 0 + 0 + 1 = 12 Sixth column: |1 - 6| + |2 - 7| + |4 - 8| + |5 - 9| + |6 - 10| + |7 - 11| = 5 + 5 + 4 + 4 + 4 + 4 = 26 C total = 85 First column: |1 - 7| + |2 - 8| + |6 - 9| + |7 - 10| + |8 - 11| + |9 - 12| = 6 + 6 + 3 + 3 + 3 + 3 = 24 Second column: |1 - 7| + |5 - 8| + |6 - 9| + |7 - 10| + |8 - 11| + |9 - 12| = 6 + 3 + 3 + 3 + 3 + 3 = 21 Third column: |3 - 7| + |4 - 8| + |6 - 9| + |9 - 10| + |10 - 11| + |12 - 12| = 4 + 4 + 3 + 1 + 1 + 0 = 13 Fourth column: |6 - 7| + |7 - 8| + |8 - 9| + |9 - 10| + |10 - 11| + |11 - 12| = 1 + 1 + 1 + 1 + 1 + 1 = 6 Fifth column: |1 - 7| + |3 - 8| + |6 - 9| + |9 - 10| + |10 - 11| + |12 - 12| = 6 + 5 + 3 + 1 + 1 + 0 = 16 Sixth column: |1 - 7| + |2 - 8| + |4 - 9| + |5 - 10| + |6 - 11| + |7 - 12| = 6 + 6 + 5 + 5 + 5 + 5 = 32 C total = 112 In summary, when the fourth row is used as the first row of the target array, the total vertical alignment cost is minimized.

[0065] Example 4: Step A1: Count the number of atoms in each column and label them as "missing column", "redundant column", or "balanced column". Suppose a 6×12 initial array is generated, and the number and distribution of atoms in each column are shown in Table 5 (the row indices are numbered from the top as 1 to 12, and the top 6 rows are to be retained): Table 5 is the distribution status table of another initial atomic array.

[0066]

[0067] Classification rules: Redundant column: The number of atoms > 6; Missing column: The number of atoms < 6; Balanced column: The number of atoms = 6.

[0068] Step A2: First, look for redundant columns in 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 total number of redundant atoms in the left and right adjacent columns is less than the number of missing atoms in the missing column, regenerate the initial atomic array. Step A3: Select the bottommost atom in the redundant column and move it to fill the missing column. Operation example (Column 2 is the missing column): Left adjacent column 1 (redundant +1): Moving quantity: Δ = min(1, 1) = 1.

[0069] Select atom: The bottommost atom (row 12) in redundant column 1.

[0070] Moving path: Column 1, row 12 → Column 2, target row 12.

[0071] Manhattan distance: Horizontal distance = |1 - 2| = 1 → Total distance = 1.

[0072] Operation example (Column 6 is the missing column): Right adjacent column 5 (redundant +3): Moving quantity: Δ = min(3, 2) = 2.

[0073] Select atom: The bottommost atoms (row 9, 11) in redundant column 5.

[0074] Moving path: Column 5 → Column 6 (distance = |5 - 6| = 1).

[0075] Column 5 → Column 6 (distance = |5 - 6| = 1).

[0076] Total moving cost: 1 + 1 = 2.

[0077] The updated status is shown in Table 6.

[0078] Table 6 is the distribution status table after the atoms of another initial atom array are filled.

[0079]

[0080] The removal of redundant atoms in the S3 movement algorithm includes: traversing upward from the bottom row of each column, marking and removing redundant atoms exceeding the target number m; the removal path is planned to move downward along the column to the outside of the array.

[0081] The atom with the largest row index (i.e., the bottom one) in the redundant column is removed or moved first.

[0082] Example: The redundant atoms in column 3 (redundancy +2) are in rows 9 and 11 (bottom), and the removal cost is: C eject =(12 - 9 + 1)+(12 - 11 + 1)=4 + 2 = 6; The redundant atom in column 5 (redundancy +1) is in row 7 (bottom), and the removal cost is: C eject =12 - 7 + 1 = 6.

[0083] The updated status is shown in Table 7.

[0084] Table 7 is the distribution status table after the redundant atoms of another initial atom array are removed.

[0085]

[0086] 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; assigning movement priorities according to the principle of the smallest distance, and if multiple atoms have the same target row, assigning them from bottom to top.

[0087] ;

[0088] The first column: C n1 =(3 - 2)+(5 - 3)+(7 - 4)+(9 - 5)+(11 - 6)=15; The second column: C n2 =(2 - 1)+(4 - 2)+(6 - 3)+(8 - 4)+(10 - 5)+(12 - 6)=15; The third column: C n3 =7 - 6 = 1; The fourth column: C n4 =(2 - 1)+(4 - 2)+(6 - 3)+(8 - 4)+(10 - 5)+(12 - 6)=15; The fifth column: C n5 =0; Sixth column: C n6 =(2 - 1)+(4 - 2)+(6 - 3)+(8 - 4)+(9 - 5)+(11 - 6)=19.

[0089] C total =C n1 +C n2 +C n3 +C n4 +C n5 +C n6 =15 + 15 + 1 + 15 + 0 + 19 = 65.

[0090] The updated status is shown in Table 8.

[0091] Table 8 is the distribution status table after the atomic vertical alignment of the initial array of another atom.

[0092]

[0093] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present 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, Including: S1. Generate an optical potential well array using a spatial light modulator and capture ultracold atoms to form an initial n×2m atomic array; S2. Take an image of the initial atomic array, preprocess the image and input it into a neural network module to identify the atomic positions and output an n×2m atomic existence matrix, where the 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, plan the atomic movement path from the n×2m initial array to the target n×m defect-free array through a movement algorithm including in-column atomic balance, redundant atom removal, and vertical alignment; S4. According to the atomic movement path, use an acousto-optic deflector module to generate a dynamic optical tweezer array, adjust the atoms to the target positions, and obtain the final defect-free n×m array.

2. The method for generating a defect-free array of ultracold atoms according to claim 1, wherein The preprocessing of the initial array image in S2 includes: Obtain the original array image containing n×2m optical potential wells; According to the pre-set optical potential well coordinates, crop the initial array image into n×2m sub-images with a size of 9×9, and each sub-image corresponds to a separate optical potential well region; Normalize the pixel values of the cropped sub-images so that their pixel value ranges are mapped to [0,1].

3. A method for generating a defect-free array of ultracold atoms according to claim 2, characterized in that, The neural network module in S2 includes: An encoder, consisting of three fully connected layers, which respectively reduce the input 81-dimensional data to 64 dimensions, 32 dimensions, and 16 dimensions, and each layer is followed by a ReLU activation function; A decoder, gradually increasing the dimension of the 16-dimensional data output by the encoder to 32 dimensions, 64 dimensions, and 81 dimensions, retaining the encoded features and restoring them to the input dimension; An output layer, mapping the decoded output to a scalar through a linear layer, converting it into a probability value through a Sigmoid function, and determining the atomic existence with a threshold of 0.

5.

4. A method for generating a defect-free array of ultracold atoms according to claim 1, characterized in that, The in-column atomic balance of the movement algorithm in S3 includes: A1. Count the number of atoms in each column and label them as "missing column", "redundant column", or "balanced column"; A2. First, look for redundant columns in the left adjacent column or right adjacent column of the missing column; if there are no redundant atoms in the left and right adjacent columns of the missing column or the total number of redundant atoms in the left and right adjacent columns is less than the number of 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 an array after atomic balance; the movement path is optimized based on the Manhattan distance, and the movement quantity Δ is the minimum of the excess atoms in the adjacent column and the deficit atoms in the missing column.

5. A method for generating a defect-free array of ultracold atoms according to claim 4, characterized in that, The redundant atom removal of the movement algorithm in S3 includes: Traverse from the bottom row of each column upward, mark and remove redundant atoms exceeding the target quantity m to obtain an array after redundant atom removal; The removal path is planned to move downward along the column outside the array.

6. A method for generating a defect-free array of ultracold atoms according to claim 5, characterized in that, The vertical alignment of the movement algorithm in S3 includes: A1. Use the first k rows of the array after redundant atom removal as the candidate starting rows of the target defect-free array, and traverse the candidate starting rows 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 atomic positions and target positions, and calculate the movement steps of the atoms 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 moving steps corresponding to each k. Construct an nm×nm cost matrix, where the matrix elements are the number of moving steps for each atom to move from the original array position (i, r) to the target position (j, t). Solve the minimum total cost through the linear sum assignment algorithm. A4. Select the candidate starting row k with the minimum total cost as the starting row of the target defect-free array, map the k to k+m-1 rows of the original array to the 1 to m rows of the target defect-free array, and generate an n×m defect-free atom array.

7. A method for generating a defect-free array of ultracold atoms according to claim 6, characterized in that, Step A2 includes: Construct a bipartite graph model: Left nodes: The positions (i, r) of all atoms in the original array, with a total of n columns × m rows = nm nodes. Right nodes: The n columns × m rows = nm positions (j, t) of the target array. The number of moving steps = ((i, r), (j, t)) = |i - j| + |r - (k + t - 1)| where i is the atomic column index of the array after redundant atom removal, 1 ≤ i ≤ n; r is the atomic row number of the array after redundant atom removal, 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 the atomic position and the target position satisfies the conditions: Each atom is only allowed to be assigned to one target position; each column and each row of the target array contain only one atom.

8. A method for generating a defect-free array of ultracold atoms according to claim 1, characterized in that The acousto-optic deflector module S4 includes two acousto-optic deflectors, which respectively control the horizontal and vertical movement of the optical tweezer. Its coordinated control includes: The first acousto-optic deflector applies acoustic waves in the horizontal direction to control the X-axis deflection angle of the light beam θ x ; The second acousto-optic deflector applies acoustic waves in the vertical direction to control the deflection angle of the light beam in the Y-axis direction. θ y ; By synchronous adjustment f x with f y , a dynamic optical tweezer array is generated to achieve the position movement of atoms in a two-dimensional plane; Among them, two acousto-optic deflectors avoid beam interference through time-division multiplexing or spatial beam splitting technology, and are converted into corresponding acoustic wave frequencies according to the target position coordinates ( x i ,y i ) f x and f y .

9. A method for generating a defect-free array of ultracold atoms according to claim 8, characterized in that, Step S4 includes: Apply high-frequency sound waves to the optical medium through the acousto-optic deflector to form a periodic refractive index change structure. When the incident light beam passes through this structure, it deflects according to the frequency change of the sound wave to generate a deflected light beam. Focus the deflected light beam through a focusing optical system to form an optical tweezer beam, and use the optical tweezer beam to capture and manipulate ultracold atoms to form an optical tweezer array. Capture ultracold atoms through the optical tweezer array; place the ultracold atoms in the optical field of the optical tweezer beam, and use the gradient force of the optical tweezer beam to pull the atoms towards the region with the highest light intensity to achieve capture. According to the preset movement path, by changing the frequency of the sound wave, adjust the direction of the deflected light beam, and drive the captured atoms to move together with the optical tweezer beam to achieve the movement and positioning of the atoms.

10. An apparatus for generating a defect-free array of ultracold atoms, characterized in that, It includes: A spatial light modulator for generating an optical potential well to capture cold atoms and form an initial array. A photographing device for photographing the image of the initial array. A processing unit for preprocessing the image, neural network recognition, calculating the movement path, and adjusting the atomic position. An acousto-optic deflector unit, including two acousto-optic deflectors, generating a dynamic optical tweezer array according to the movement path and adjusting the atoms to the target position.

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