Accelerating the Assembly of Defect-Free Atomic Arrays with Maximum Parallelisms

Defect-free atomic arrays have been demonstrated as a scalable and fully controllable platform for quantum simulations and quantum computations. To push the qubit size limit of this platform further, we design an integrated measurement and feedback system, based on field-programmable gate array (FPGA), to quickly assemble two-dimensional defect-free atomic array using maximum parallelisms. The total time cost of the rearrangement is first reduced by processing atom detection, atomic occupation analysis, rearrangement strategy formulation, and acousto-optic deflectors driving signal generation in parallel in time. Then, by simultaneously moving multiple atoms in the same row (column), we save rearrangement time by parallelism in space. To best utilize these parallelisms, we propose an alternative algorithm named the Tetris algorithm to reassemble atoms to arbitrary target array geometry from two-dimensional stochastically loaded atomic arrays. For an $L\times L$ target array geometry, the number of moves scales as $L$, and the total rearrangement time scales at most as $L^2$. Although in this work we do not test on actual atoms, we simulate the performance of our FPGA system experimentally with all components integrated except for the atoms. We present the overall performance for different target geometries, and demonstrate a dramatic boost in rearrangement time cost and the potential to scale up defect-free atomic array to 1000 atoms in room-temperature platform and 10 000 atoms in cryogenic environment.

Figure 1

(a) The rearrangement control flow. (b) A typical time sequence of our system. Each row shows the operation periods for one module or device, where a high-level signal indicates that the module is in operation. The blue, green, yellow, and red blocks indicate the periods of processing the first, second, third, and the last row of atoms, respectively. By organizing these modules to work in parallel, the total time cost $\tau$ is significantly reduced. (c) The spectra of the AOD driving signals to simultaneous rearrange atoms in a row. The $Y\mathrm{AOD}$, which controls the tweezer position in vertical direction, requires only a monochromatic driving signal, while the $X\mathrm{AOD}$ requires a multitone waveform. (d) Improving the quality of mobile tweezer controls to avoid atom loss or heating during the rearrangement. When a tweezer begins to move, its trap depth is ramped up to smoothly transfer the atom to the mobile tweezers from static traps. Then the tweezer accelerates to the maximum velocity with a fixed acceleration. This process is reversed when approaching the final destination.

Figure 2

Illustration of the Tetris algorithm. (a) The rearrangement strategy of a $4\times 4$ target square lattice. Moves 1–6 are row-by-row rearrangements. In each move, we first horizontally align atoms with the defects in the previous move (marked blue). Then the atoms left are assigned to the leftmost sites in the target geometry. This does not require knowledge of the next rows of atoms (marked transparent). The row rearrangement ensures that each column has enough atoms required by the target array. Moves 7–10 are column-by-column compression where atoms are moved to the final target positions. (b) The rearrangement of a larger array. The row-by-row rearrangements organize the atoms into blocks (Tetriminoes). The column-by-column compression arrange atoms into target geometry (Tetrimino eliminations). (c) Examples of arbitrary target geometries achieved with Tetris algorithm, by rotating the AODs or pixelating the desired pattern: staggered (c1), kagome (c2), honeycomb (c3) lattices, and the pixelated “THU” symbol (c4).

Figure 3

Monte Carlo simulation of the rearrangement complexity: the number of parallel displacements as a function of total atom number $N$ for different algorithms and target geometries. Blue and red dots represent compact and staggered geometries based on the Tetris algorithm, while black dots represent compact geometry based on the Hungarian algorithm for comparison. Each point is averaged over 10 000 simulations with the error bar showing the standard deviations. The dashed lines show the power-law fitting with scaling factor of $N^{1.6(1)}$ for compact geometry with the Hungarian algorithm, $N^{1.03(7)}$ for compact geometry with the Tetris algorithm, and $N^{0.736(6)}$ for staggered geometry with the Tetris algorithm when the initial loading efficiency is 50%.

Figure 4

Design of the hardware structure. The hardware modules and the peripherals are drawn in brown and gray boxes, respectively. The photon-counting data for each pixel accumulated by the EMCCD is directly transferred to the on-FPGA decoder through raw logical-level signals on a row-by-row basis. The decoder determines the atom occupation and sends such information to the PS as digital signals. The PS makes the strategy based on the Tetris algorithm and informs the DWG, which then uses a set of DDSs and an addition tree to generate a multitone waveform. The DAC outputs rf signals to control the AODs.

Figure 5

Experimental snapshots of the mobile tweezer generation. (a) The frequency spectra of the $X\mathrm{AOD}$ driving signal for generating the mobile tweezers for the first two moves of the example rearrangement in the main text. The resolution bandwidth is set to $50\mathrm{kHz}$ and the moving speed is slowed down by 30 times for better visual effect. (b) Snapshot of 32 AOD tweezers. The lower panel shows the integration of the intensity along the vertical direction. (c) Snapshot of a $32\times 8$ array of AOD tweezers. The intensity inhomogeneity in both (b) and (c) is suppressed to within 4%.

Figure 6

Experimental demonstration of the overall scalability of the rearrangement system. The total time costs $\tau$ as a function of $N$ to assemble a compact (blue) or staggered (red) target array are shown. Each point is averaged over 500 realizations with the error bars showing the standard deviation. The dashed lines are fittings to power functions with scaling factor of $N^{0.88(6)}$ for compact geometry, and $N^{0.65(1)}$ for staggered geometry. Note that the total time cost depends on the moving speed of atoms, but the scaling is independent on this choice. The green lines show the collective lifetime of $N$ atoms with individual vacuum-limited lifetime $30\mathrm{s}$ (dark green) and $20\mathrm{s}$ (light green). The intersecting points of the collective lifetime curves and the rearrangement time curves mark the lifetime-limited array size. Inset: the scalability of the rearrangement system in a broader range. The green lines correspond to individual vacuum-limited atomic lifetime $6000\mathrm{s}$ (darkest) and $30\mathrm{s}$.