AOL4FOLTR: 3D Atom Trap Rearrangement

• AOL4FOLTR is an acousto-optic lens system that enables rapid 3D trap rearrangement with sub-10 μs axial and sub-1 μs lateral control for neutral atom quantum computing.
• It integrates a double-pass dynamic-focus module with independent lateral steering via AODs to decouple axial and transverse beam control.
• Experimental results demonstrate high throughput and precision in atom positioning, paving the way for scalable, defect-free quantum registers.

AOL4FOLTR refers to an acousto-optic lens system designed for fast, three-dimensional trap rearrangement of neutral atoms in quantum computing architectures. It enables rapid and precise 3D shuttling of atoms in optical tweezer arrays by combining a dynamically tunable focal stage based on double-pass acousto-optic deflectors (AODs) with high-speed, independent lateral steering. This system is a technical advance over previous approaches limited to two-dimensional motion or slow axial (focus) control, directly addressing the core requirements of scalable neutral atom quantum computers for defect-free array assembly, connectivity, and rapid mid-circuit operations (Guo et al., 10 Oct 2025).

1. Overview and Motivation

AOL4FOLTR is motivated by the need for fast on-line trap rearrangement (FOLTR) in neutral atom quantum computing platforms. In these architectures, atoms are trapped in tightly focused optical tweezers and must be rearranged dynamically to produce defect-free arrays and to allow all-to-all qubit operations or mid-circuit measurements. Conventional approaches, such as mechanical (piezo) focus shifting, offer only millisecond-scale update rates and are inherently restricted by inertia. Earlier solutions using AODs as cylindrical lenses allowed only 2D rearrangement and suffered from asymmetrical aberrations. AOL4FOLTR overcomes these constraints by providing inertia-free, sub-10 μs axial (z) control and simultaneous sub-1 μs lateral (x, y) steering, thus enabling true three-dimensional, high-throughput atomic motion (Guo et al., 10 Oct 2025).

2. Acousto-Optic Lens Architecture

The AOL4FOLTR architecture comprises two primary stages: a double-pass dynamic-focal module and a transverse steering module.

• Dynamic-Focus Stage: The input optical tweezer beam, after polarization conditioning, passes through two crossed TeO₂ AODs. The beam is reflected back via a cat-eye retroreflector (lens + mirror), producing a double-pass of the AODs. The RF drive frequency of these AODs is linearly chirped to induce a spatial frequency gradient, generating a variable cylindrical lens. The cat-eye arrangement ensures that chirping only modifies the focus, not the beam propagation direction.
• Transverse Steering Stage: After focus control, the beam passes through an orthogonally oriented pair of AODs operating as deflectors (one for x, one for y), each driven by independent RF sources. These AODs steer the focal spot position transversely in the object plane, fully decoupling the axial and lateral control channels.

The system is completed with a microscope objective, which brings the beam to focus at the atomic plane. This modular separation of axial and lateral steering is critical for generating arbitrary 3D trajectories for atomic transport (Guo et al., 10 Oct 2025).

3. Analytical Models and Key Formulas

AOL4FOLTR operation is analytically characterized by the following relations:

• Single/Double-Pass Effective Focal Length: For a chirp rate $\dot f$,

$$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$

where $v_A$ is acoustic velocity, $\lambda$ the wavelength. In double-pass, the focal shift is doubled.

• Axial Displacement (Focus Shift):

$\Delta z = -\frac{2\lambda F_M^2}{v_A^2} \dot f$

where $F_M$ is the focal length of the final microscope objective.

• Transverse Deflection:

$$\theta_{x,y}(f_{x,y}) = \frac{\lambda}{v_A}(f_{x,y} - f_{0})$$

$$\Delta x = F_M \theta_x, \quad \Delta y = F_M \theta_y$$

where $f_{x,y}$ are the AOD RF frequencies.

• Multiplexed Trajectories: Multiple RF tones allow simultaneous control of many tweezers, where the overall field is a linear superposition of deflections corresponding to each atom.

Higher-order corrections for finite-aperture, bandwidth, and non-ideal response are discussed and can introduce small deviations at high chirp rates. These effects are mitigated by appropriate optical design (Guo et al., 10 Oct 2025).

4. Performance Metrics and Experimental Results

Bench measurements and system characterization yield the following data-driven operational parameters:

Metric	Value/Range
Focal-shift sensitivity	27.8 mm per (MHz/μs) chirp (measured) vs 33 mm theoretical
Max continuous chirp rate	~4.8 MHz/μs (set by $\tau = D/v_A$, $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$0)
Static-focus range	±300 mm (maps to ±50 μm in atom plane)
Transverse steering range	±50 μm per 10 MHz RF deviation
Optical throughput	Dynamic-focus: ~70%; Steering: ~80%; Total: ≃56%
Response time	Focus: ≃8 μs; Lateral: ≃1 μs
End-to-end atom move time	Typical 3D move: 110 μs; 100 defects: ~11 ms
Position precision	<100 nm (target)
Minimal heating	$$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$1 motional quanta per move

Axial and lateral steering rates are orders of magnitude faster than mechanical or earlier acousto-optic methods. Double-pass AOD configuration eliminates dominant astigmatism relative to single-pass cylindrical arrangements (Guo et al., 10 Oct 2025).

5. Algorithmic Implementation for 3D Rearrangement

AOL4FOLTR enables the following FOLTR procedure:

• For each atom with initial position $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$2 and desired final $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$3:
  • Compute minimum-jerk trajectories $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$4, $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$5 (steering AODs), $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$6 (focus chirp).
  • At each $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$7, program the dynamic-focus RF for $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$8 and steering RFs for $$F_{\rm AOL}^{(1)} = \frac{v_A^2}{\lambda} (\dot f)^{-1}$$9, $v_A$0, using:

  $v_A$1 - Multiplexed moves are supported via adding RF tones for each atom.

Total 3D rearrangement of arrays of size $v_A$2 can thus be accomplished within a few milliseconds (Guo et al., 10 Oct 2025).

6. Technical Challenges and Scalability

Remaining obstacles include:

• RF Drive Cross-Talk: Multiplexed frequency spectra can cause intermodulation and require pre-compensation.
• Thermal Lensing: High acoustic powers in AODs (TeO₂) induce thermal gradients, shifting $v_A$3.
• AWG/FPGA Control: Scaling to $v_A$4 tweezers demands wideband, real-time, high-fidelity arbitrary waveform generation.
• Optical Aberrations: Nonlinearities and defocus at bandwidth edges, corrected by careful relay optics.

Potential technical improvements outlined include higher-aperture AOD crystals, ASIC/FPGA for real-time RF control, and integrated microscope objectives for concurrent imaging and focusing (Guo et al., 10 Oct 2025).

7. Applications and Outlook

AOL4FOLTR, by providing inertia-free, robust, and rapid 3D atomic control, supports advanced neutral atom quantum information processing:

• Defect-Free Quantum Registers: Deterministic assembly of $v_A$5-atom arrays in arbitrary geometries.
• All-to-All Coupling: Realization of fully connected entangling gates facilitated by 3D rearrangement.
• Mid-Circuit Measurement: Fast shuttling of atoms for error correction and readout within circuit lifetimes.
• Scalability: Direct applicability to large-scale (>100-qubit) neutral atom platforms.
• Future developments: Integration of high-fidelity control electronics, further reduction of residual motional heating, and hybrid arrangements for simultaneous imaging and rearrangement.

AOL4FOLTR constitutes a key component for scalable, fault-tolerant quantum computation architectures based on neutral atoms (Guo et al., 10 Oct 2025).