Acousto-optic lens for 3D shuttling of atoms in a neutral atom quantum computer

TL;DR

The paper addresses fast, three-dimensional transport of neutral-atom qubits in optical tweezer arrays despite acousto-optic lensing that confines motion to a plane. It introduces a practical double-pass AOL design that decouples transverse steering from longitudinal focusing, enabling programmable 3D focal trajectories with minimal additional power loss. Optical tests demonstrate controllable focal shifts and a finite RF-to-focus delay (~$8~\mu\mathrm{s}$), validating the method and its alignment with theory. The approach enables off-plane shuttling for atom rearrangement, fully connected two-qubit gates, and separate-plane imaging, offering a path toward scalable, high-fidelity neutral-atom quantum computers and 3D trap painting in cold-atom systems.

Abstract

We present a novel acousto-optic lens (AOL) design for neutral atom quantum computing. This approach enhances atom rearrangement in optical tweezer arrays and addresses the speed limitations imposed by the cylindrical lensing effect of acousto-optic deflectors (AODs). By combining a double-pass AOD configuration for dynamic focal tuning with a standard pair of crossed AODs for transverse beam steering, our design enables the generation of arbitrary focal point trajectories. This configuration enables shuttling of atoms in 3D space, thereby helping to realise fully connected two-qubit gates and mid-circuit measurements. We detail the optical implementation, characterize its performance, and discuss its applications in scalable quantum computing architectures.

Figures (6)

• Figure 1: Design of a variant of an acousto-optical lens (AOL). (a) The laser beam enters from the right side into the PBS and passes through the Faraday rotator and a half-wave plate, which together function as an optical circulator. The use of this configuration is primarily to ensure polarization matching with the AOD. After double-passing through the crossed AOD, the laser beam proceeds through a normal crossed AOD for transverse movement and is finally focused by the microscope. (b) Illustrates both the focal and transverse move of atoms enabled by the AOL. In a conventional crossed-AOD setup, movable tweezers can only shuttle atoms within a single focal plane, restricting the achievable spacing between traps. By contrast, the AOL allows atoms to be moved out of the focal plane, enabling full 3D shuttling.
• Figure 2: Lensing effect of an AOD and double-pass configuration for focus adjustment. (a) Laser beam passing through the AOD crystal is focused by an additional lens $F_M$. The center graph shows injection with a constant RF frequency, which only bends the output beam angle without affecting the focal position. The left (right) graph shows up (down) chirping of the RF frequency, resulting in focus extension (shortening) $\delta_0$. Note that there is always a time-varying transverse movement $\Delta$ due to the ramping of the center RF frequency. (b) Schematic of our novel acousto-optical lens (AOL), based on a double-pass configuration using crossed AODs. The laser beam is first directed to a beam splitter (BS) and then double-passes through the crossed AODs. An optional beam-shrinking telescope with magnification $M_S<1$ is used to match the beam size between the AOD aperture and the final focusing lens (e.g., a microscope objective) with focal length $F_M$. The total focal shift $\delta$ follows the relation given in Eq. \ref{['formula: focal shift double pass']}. This shift can be enhanced by selecting AODs with larger apertures, which require a lower magnification in the beam-shrinker and thereby lead to a larger effective focal shift. (c) The double-pass configuration cancels the transverse movement automatically and ensures phase matching of the AOD. $\textbf{k}_1$, $\textbf{k}_2$ and $\textbf{k}_3$ are the wave numbers of the incident, first-order deflected and retroreflected beam respectively. $\textbf{k}_4$ is the output beam. $\textbf{K}$ is the wave number of the sound wave. (d) Phase matching diagram for the AOD shows how the tangential phase matching automatically works for the retroreflected beam. The transparent red arrow close to $\textbf{k}_2$ ($\textbf{k}_3$) also shows the wide range of phase match angle which allow for large range of radio frequency.
• Figure 3: The AOL is characterized at static focus positions, where each data point corresponds to a fixed focal position during measurement. (a) and (b) illustrate the change in focus when only one AOD is driven with a chirped RF signal, which manifests as astigmatism. Here, $df_{\rm RF}/dt$ denotes the RF frequency ramping rate, which can be positive or negative and thereby induces the corresponding focal shift $\delta$. The slope of the resulting curve yields the parameter $-2\lambda F_M^2/v_A^2$, with $F_M = 100~\text{mm}$ in this test setup. (c) shows that when both AODs are driven with identical linearly chirped RF signals, a focal shift is observed along both $x$- and $y$-directions, effectively making the system a spherical lens.
• Figure 4: The AOL is characterized using arbitrary RF frequency trajectories in a dynamical focus test. Figures (a)–(c) present measurements for three different RF frequency profiles: sinusoidal, exponential decay, and constant-jerk. The bottom panels display the applied RF frequency trajectories (black line) $f_{\rm RF}(t)$, while the top panels show the negative derivatives of RF frequency trajectories (green line) $-df_{\rm RF}/dt$ and the corresponding measured focal-position shifts (red diamond) $\delta(t)$, where the vertical axes of them are linked by the parameter $2\lambda F_m^2 / v_A^2$, whose value (27.8 mm/(MHz/$\mu$s)in this setup) is obtained from average of two directions in the static-focus measurements. The measured focal shifts are fitted with the target trajectory functions (red line). The observed time delay between RF ramping speed and focal position and focal-shift distortions are discussed in Sec. \ref{['sec: characterization']}.
• Figure 5: Simulation of tweezer trap deformation and atomic motional excitation due to the lensing effect of a single AOD during transverse motion. The simulation is based on a 0.5 mW, 828 nm laser focused by a microscope objective with a focal length of 4 mm, producing a tweezer with a waist of 0.9 $\mu$m. The AOD used is the DTSXY-400 from AA Optics, with an acoustic velocity of 650 m/s. (a) Simulated tweezer potentials at various transverse speeds $v_T$, showing trap deformation, reduction in trap depth, and eventual splitting into two potential wells when $v_T > 1~\mu\text{m}/\mu\text{s}$. (b) Trap depth (pink) $U_{\rm trap}$ and trap frequencies (radial $x, y$ and axial $z$) as functions of transverse speed. The axial frequency drops to zero around $v_T = 1.0~\mu\text{m}/\mu\text{s}$, indicating the onset of trap splitting. Note that the top axes shows the astigmatism (focal shift) $\delta_0$ which is proportional to the transverse moving speed of the tweezer by Eq. \ref{['astig vs speed']}. (c) - (e) Simulations of atom transport over 200 $\mu$s using minimum-jerk trajectories for various transport distances. Longer distances result in higher peak velocities, which enhance the lensing effect and increase motional excitation. The bottom panels show the time evolution of the average motional excitation $\Delta N$, both with and without lensing compensation. When $v_T$ exceeds 1.0 $\mu\text{m}/\mu\text{s}$, excitation grows rapidly in the uncompensated case. Note that the ratio of trap depth to trap frequency sets a threshold for atom loss. With our proposed AOL-based compensation scheme, the trap deformation can be dynamically corrected, leading to significantly reduced excitation and enabling faster, high-fidelity atomic transport.