Phase-Stable Hologram Updates for Large-Scale Neutral-Atom Array Reconfiguration

Abstract

Assembling large-scale, defect-free Rydberg atom arrays is a key technology for neutral-atom quantum computation. Dynamic holographic optical tweezers enable the assembly and reconfiguration of such arrays, but phase mismatches between successive holograms can induce destructive interference and transient trap loss during spatial-light-modulator refresh. In this work, we introduce the weighted-projective Gerchberg--Saxton (WPGS) algorithm, a phase-stable approach to dynamic hologram updates for large-scale Rydberg atom-array reconfiguration. By enforcing inter-frame trap-phase continuity while retaining weighted intensity equalization, WPGS suppresses refresh-induced transient degradation. The phase-difference distribution between consecutive holograms further provides a simple diagnostic of transient robustness. Moreover, enforcing the phase constraint reduces the number of iterations required at each update step, thereby accelerating hologram generation. Numerical simulations of 2D and 3D reconfiguration with more than $10^3$ traps, including multilayer assembly and interlayer transport, show robust transient intensities and significantly faster updates than conventional methods. These results establish inter-frame phase continuity as a practical design principle for dynamic holographic control and scalable neutral-atom array reconfiguration.

Figures (4)

• Figure 1: Overview of large-scale neutral-atom-array reconfiguration with the WPGS algorithm. Starting from a stochastically loaded source array, an upstream assignment-and-path-planning stage first maps the occupied traps to target sites and generates a discretized transport sequence toward the target configuration. WPGS then acts on this planned sequence at the hologram-update level. The central pair of frames highlights a representative update from step $l$ to $l+1$, corresponding to the SLM refresh that generates the transient optical response between consecutive holograms. For this update, two design goals are imposed: intensity continuity and inter-frame phase continuity. To realize these goals for the trap field $E_n(\boldsymbol{\phi})$, WPGS alternates updates of the trap weights $W$, global scale $s$, and SLM phase pattern $\boldsymbol{\phi}$ to generate the next hologram $\boldsymbol{\phi}^{(l+1)}$ and thereby promoting smooth refresh transitions as described by Eq. \ref{['eq:transient_tweezers']}.
• Figure 2: Refresh-induced transient degradation in a minimal transport sequence. (a) Minimal $3\times 3$ transport configuration and schematic of the refresh process between two consecutive holograms. (b) Schematic transient-intensity landscape during refresh, evaluated from the normalized two-frame interpolation model $I(\tau,\Delta\varphi)=|a(\tau)+[1-a(\tau)]e^{i\Delta\varphi}|^2$. (c) Representative inter-frame phase changes for one stationary trap and one moving trap, shown for WGS and WPGS. (d) Transient intensity of the representative moving trap across the discrete frame sequence; markers denote the algorithm-generated frames, and the curves between adjacent markers show the continuous refresh interpolation.
• Figure 3: Phase-stable reconfiguration under WPGS in 2D and 3D configurations. (a)--(d) 2D case: (a) Transport trajectories for a $1024$-trap reconfiguration task from a $36\times36$ source array ($79\%$ filling) to a $32\times32$ target array with spacing $5~\mu$m, with mean displacement $\overline{\Delta r}=8.83~\mu$m and maximum displacement $\Delta r_{\mathrm{max}}=18.03~\mu$m. (b) Intensity uniformity $\nu$ versus transport step for WGS and WPGS, with $\nu = 1 - (\max I - \min I)/(\max I + \min I)$. (c) Histogram of frame-to-frame phase difference $\Delta\varphi$, aggregated over all traps and all transport steps, shown as percentages; the standard deviation is $0.2381$ for WGS and $0.0291$ for WPGS. (d) Transition-inclusive relative-intensity distribution $I/I_0$, aggregated over all traps, all transport steps, and all transient samples during SLM refresh according to Eq. \ref{['eq:transient_tweezers']}, where $I_0$ denotes the corresponding initial intensity for each sample; the distribution is shown as percentages, and the inset highlights the low-intensity tail on a logarithmic scale. For WPGS, all samples remain above $I/I_0=0.86$ throughout the full transport sequence, including all transient samples during SLM refresh, whereas for WGS, $2.83\%$ of the corresponding samples fall below the same threshold. (e)--(h) 3D case: (e) Three-layer reconfiguration task with $N_{\mathrm{tot}}=3072$ target traps distributed over $z=-30,0,+30~\mu$m, with $1024$ target traps per layer. The initial layers are nonuniform, given by a $33\times33$ array with spacing $6~\mu$m ($94\%$ filling), a $34\times34$ array with spacing $5~\mu$m ($89\%$ filling), and a $35\times35$ array with spacing $4~\mu$m ($84\%$ filling), respectively; all three layers are reconfigured to identical $32\times32$ target arrays with spacing $5~\mu$m. (f) Layer-resolved intensity uniformity $\nu$ versus transport step. (g) Layer-resolved histograms of frame-to-frame phase difference $\Delta\varphi$; the standard deviations for the bottom, middle, and top layers are $0.0390$, $0.0389$, and $0.0388$, respectively. (h) Layer-resolved transition-inclusive relative-intensity distributions $I/I_0$. In all three layers, every trap remains above $I/I_0=0.91$ throughout the full transport sequence, including all transient samples during SLM refresh.
• Figure 4: Offset-bilayer transport with smooth optical transitions. (a) Task geometry for offset-bilayer transport. Two $10\times10$ tweezer arrays with in-plane spacing $5~\mu\mathrm{m}$ and axial separation $20~\mu\mathrm{m}$ are laterally offset by $2.5~\mu\mathrm{m}$, so that each site in one layer lies at the center of four nearest-neighbor sites in the adjacent layer. A representative subset of trajectories exchanges sites between layers, and some trajectories further include in-plane motion to fill vacant target sites. (b) Representative $I/I_0$ traces for two moving trajectories and two stationary trajectories during the transport sequence. (c) Histogram of frame-to-frame phase difference $\Delta\varphi$ for the non-uniform-target WPGS run; the standard deviation is $0.0214$. (d) Transition-inclusive relative-intensity distribution $I/I_0$ for the same run. Every trap remains above $I/I_0=0.96$ throughout the full transport sequence, including all transient samples during SLM refresh.