Astigmatism-free 3D Optical Tweezer Control for Rapid Atom Rearrangement

TL;DR

This work tackles the fundamental bottleneck of fast 3D atom transport in optical tweezer arrays by eliminating chirp-induced astigmatism with a four-AOD, 4f-configured 3D-AODL. It introduces fading-Shepard waveforms to enable sustained axial motion without flicker, decoupling lateral steering from vertical focusing. Time-resolved 3D tomography and Monte Carlo simulations show aberration-free, omnidirectional tweezer control and up to ~70% faster long-range transport with preserved trap integrity. The approach promises faster, scalable rearrangement in neutral-atom quantum processors and broader utility in high-speed 3D optical manipulation for quantum information, metrology, and microscopy.

Abstract

Reconfigurable arrays of neutral atoms are a leading platform for quantum computing, quantum simulation, and quantum metrology. The most common method for atom reconfiguration using optical tweezers relies on frequency chirping of acousto-optic deflectors (AODs). However, chirp-induced acoustic lensing limits the speed of atom transport by deformation of the tweezer profile and warping of the tweezer trajectory. We use a three-dimensional acousto-optic deflector lens (3D-AODL) to mitigate both effects, a design predicted to halve current state-of-the-art long-range transport times. Additionally, we introduce fading-Shepard waveforms that bypass the finite AOD bandwidth and thus enable sustained axial displacement. We demonstrate unrestricted 3D motion within a cuboid volume of at least 200 $μ$m $\times$ 200 $μ$m $\times$ 136 $μ$m, with tweezer velocities exceeding 4.2 m/s. The ability to move optical tweezers along arbitrary trajectories in 3D should enable rapid in-plane and out-of-plane rearrangement of atoms in 2D or 3D tweezer arrays and optical lattices, as well as omnidirectional trajectories and dynamical engineering of optical potentials. This technology has the potential to advance quantum control and atom manipulation in current atom-array quantum computers, boosting clock rates and enabling rapid sorting in geometries scalable to millions of qubits.

Figures (5)

• Figure 1: 3D-AODL setup for time-resolved 3D light field tomography. (a) Experimental schematic. Chirped rf drives applied to the first 2D-AODs (Ax, Ay) create cylindrical lensing; the left inset shows acoustic (solid) and optical (dashed) wavefronts, resulting in astigmatism in the intermediate plane (middle inset); This aberration is compensated by the second 2D-AODs (Bx, $By$), which are configured in a $4f$ arrangement relative to the first. The output is Fourier-imaged onto a camera with a $F=100$ mm objective. Scanning the camera position and light-pulse delay renders time-resolved tomography of the tweezer light field. The right inset shows a reconstructed light field, with color indicating the flow of time (red to blue). (b) Beam steering without lensing, when parallel AODs are driven with counter-chirped frequencies whose sum is constant. (c) Lensing without steering, when parallel AODs are driven with co-chirped frequencies whose difference is constant. Note: "4f inversion" refers to propagation through the 4f system in (a), omitted for brevity.
• Figure 2: Comparison of conventional VS 3D-AODL tweezer trajectories. (a) 3D reconstruction of minimum-jerk trajectories. Each trajectory is a stroboscopic overlay of frames spaced 2$\,\mu$s apart, with scatterer brightness encoding the tweezer intensity. Red/Purple: Conventional 2D-AOD transports along the +X and diagonal +(X+Y) directions, exhibiting out-of-plane focal shifts. Blue/Green: AODL transports along the same directions, which remain in-plane. (b1, b2) Lateral displacement (top) and focal shift (bottom) versus time for +X (b1) and diagonal (b2) transport. In conventional cases, focal shifts are proportional to the time derivative of the corresponding lateral displacement. (c1, c2) Simulated atom survival probability and final temperature. Horizontal dashed lines denote initial atom energy, shaded regions denote $1\sigma$ variation across Monte Carlo trajectories. Note: image space coordinates $(X,\,Y,\,Z)$ follow the mirrored camera view (right-handed), opposite to the left-handed lab frame coordinates in Fig. \ref{['fig: M1']}; this does not affect the conclusions.
• Figure 3: Constrained vs unconstrained axial transport. (a) Single-tone minimum-jerk waveforms with transport times of 20, 40, and 80 µs. Top: drive frequency vs time. Middle: focal shifts $Z_x$ and $Z_y$ remain nearly equal, indicating axial motion with minimal astigmatism. Bottom: tweezer intensity vs time, showing increasing losses for longer transports due to AOD diffraction-efficiency roll-off. (b) fading-Shepard waveform for an 80 µs transport. Top two: AODs $Ax$ and $Bx$. Bottom two: AODs $Ay$ and $By$. In each pair of plots, the top plot is a spectrogram of chirped rf tones (green) with single frequency extensions for reference (gray dashdotted). The lower plot shows the power spectral density (PSD) of each tone. Blue (red) spectrogram regions indicate rf tones fading in (fading out), where PSD increases (decreases).
• Figure 4: Out-of-plane "L" shaped trajectory of a 4$\times$4 tweezer array. (a) Reconstructed 3D tweezer trajectories, color-coded by time, showing an “L”-shaped path of an uniformly spaced array. (b) Spectrogram of fading-Shepard waveforms. The waveform is divided into three segments: linear motion in Z (0–160 $\mu$s), static with constant Z offset (160–320 $\mu$s), and linear motion in X with fixed Z offset (320–480 $\mu$s). (c) Position stability. Top: X, Y, and Z trajectories; Bottom: Deviation from the ideal path, showing axial jitter$<$0.4 $\mu$m and lateral jitter$<$0.08 $\mu$m. Array spacing of $4$ MHz corresponds to $32.5\,\mu\text{m}^*$. (d) Shape stability: waists, intensity, and aberration metrics remain stable, with intensity fluctuating by $\sim\pm$9% and astigmatism by $\sim\pm$0.1.
• Figure 5: Programmable 3D trajectories. (a1) Elevated lateral transport. Each trajectory is designed to lift an atom out-of-plane by 68 $\mu$m, followed by a 130 $\mu$m lateral translation before returning to the original plane. (a2) Drive spectrograms (top) and tweezer positions (bottom) for representative cases: trajectory 1 is constructed from three stitched minimum-jerk segments, and trajectory 4 is a single smooth path that minimizes overall jerk. (b--c) Programmable trajectory shaping in a 5$\times$5 array with 32.5$\,\mu$m$^*$ spacing. Shown here are helical and heart-shaped paths, illustrating flexible waveform programmability. (d) 3D potential modulation in a 25$\times$25 array with 8.125$\,\mu$m$^*$ spacing. Omnidirectional motion enables complex periodic modulation of trap potentials per site, such as the Trefoil-knots as shown. No fading-Shepard waveforms are required in this case due to the small modulation amplitude.