Local polarization control of optical tweezer arrays

The gist: This work demonstrates independent, site-resolved linear polarization rotation across an optical tweezer array by exploiting the local birefringence tunability of a spatial light modulator, enabling magic-angle sideband cooling and dynamic transport between distinct polarization zones.

Local Polarization Control

The researchers demonstrate independently programmable polarization rotation at the individual sites of an optical tweezer array using a liquid-crystal spatial light modulator (SLM) at an intermediate image plane The SLM functions as a birefringent phase retarder with high spatial resolution, enabling us to control the polarization of each tweezer individually They program polarization patterns onto the tweezer array in two configurations: (i) a uniform polarization pattern that sets every site to the tensor magic-angle condition for the 1S0 ↔ 3P1 intercombination transition, and (ii) a staggered pattern in which two groups of atoms are spectrally isolated

Experimental Setup and Calibration

The experimental setup involves a global 813-nm laser beam diffracted by an acousto-optic deflector (AOD) to generate a one-dimensional array of optical tweezers An SLM placed at an intermediate image plane, combined with a pair of QWPs, allows for arbitrary linear polarization rotations of each tweezer The rotation is half the phase φ imprinted by the illuminated SLM pixels To calibrate the relationship between experimentally inferred θ and the applied voltage on the liquid crystal pixels, they perform spectroscopy on the narrow intercombination transition (1S0 ↔ 3P1) to observe differential light shifts The fit assumes that the atom experiences linearly polarized light

Sideband Cooling and Uniformization

Local polarization tuning enables sideband cooling by engineering magic-angle conditions with local polarization tuning Under this condition, the state-dependent differential light shifts vanish (ν = 0), decoupling the sensitivity of the cooling resonance from site-to-site tweezer intensity non-uniformity The optimal loading condition collapses to a single cooling laser frequency across all traps when local polarization corrections are applied They find that differential trap light shifts are nulled at θ = θM = 49.2(4)◦

Zone Architecture and Transport

The study proposes a zone-based 2D architecture for a strontium quantum processor leveraging local polarization programmability In the cooling zone, atoms are trapped in AOD-generated tweezers tuned to θ ≈ θM and sideband cooled to the motional ground state Outside of the cooling zone, polarization rotation spectrally detunes the 1S0 ↔ 3P1 transition away from resonance with the cooling laser, isolating those atoms from the cooling light and minimizing crosstalk They demonstrate coherent transport between distinct polarization zones For atom transport across polarization zones, they observe no measurable degradation in survival for polarization changes up to ∆θ = π/8, but atom survival drops markedly when ∆θ increases from π/8 to π/2 A linear phase ramp between two superpixels is introduced to smooth the polarization transition over a finite distance, recovering the ∆θ = 0 baseline for ramp lengths ≳ 2.0w

Polarization Noise and Stabilization

They characterize polarization noise using optical polarimetry and atomic spectroscopy, finding mrad-level polarization noise and drifts that closed-loop atomic feedback further suppresses on long timescales Active stabilization via closed-loop feedback updates the superpixel phases to steer the probed line centers of the 1S0 ↔ 3P1 carrier transition to the free-space value, achieving a standard deviation of 20 kHz with feedback This polarization-angle noise translates to effective frequency noise via the differential light shift slope ∂ν/∂θ, resulting in a standard deviation of 3.0(4) mrad at the nominal trap depth

Conclusion and Outlook

The work establishes local polarization control for tweezer arrays as a new tool for quantum science applications Their findings set the stage for further exploration of quantum metrology and quantum simulation with dynamically reconfigurable strontium arrays in 2D The results establish tweezer polarization as a programmable, per-site degree of freedom, alongside position and intensity This capability is expected to find use where polarization shapes the trapping potential or the strength of atom–light coupling

How it works

The method exploits a liquid-crystal spatial light modulator (SLM) at an intermediate image plane to control the polarization of each tweezer individually The SLM functions as a birefringent phase retarder with high spatial resolution, enabling us to control the polarization of each tweezer individually This is achieved by programming polarization patterns onto the tweezer array in two configurations: (i) a uniform polarization pattern that sets every site to the tensor magic-angle condition for the 1S0 ↔ 3P1 intercombination transition, and (ii) a staggered pattern in which two groups of atoms are spectrally isolated

Sideband Cooling Mechanism

Sideband cooling is achieved by engineering magic-angle conditions with local polarization tuning The researchers employ three independent beams aligned to the tweezers, where the cooling beams possess the appropriate polarization component to drive π-transitions The optimization of the cooling parameters involves iteratively adjusting tweezer polarizations to achieve the best cooling performance for each beam

Atom Transport Strategy

Atom transport between zones is investigated by programming a bipartite profile featuring a sharp polarization change of ∆θ between adjacent zones When the polarization change increases from π/8 to π/2, atom survival drops markedly due to spatial mode deformation at the sharp interface A linear phase ramp is introduced between two superpixels to smooth the polarization transition over a finite distance, which recovers the ∆θ = 0 baseline for ramp lengths ≳ 2.0w

Noise Suppression

Polarization noise is characterized using optical polarimetry and atomic spectroscopy, finding mrad-level polarization noise and drifts that closed-loop atomic feedback further suppresses on long timescales The feedback protocol uses the prior calibration of ν and θ versus SLM pixel voltage for each tweezer site to null any accumulated differential light shift Over a 16-hour duration, the stabilized tweezers show both a smaller site-to-site spread in line center and a two-fold reduction in temporal fluctuation

Zone Architecture Implementation

The proposed zone architecture envisions atoms being trapped in AOD-generated tweezers tuned to θ ≈ θM and sideband cooled to the motional ground state in the cooling zone Atoms are then transported by the same tweezers to a computing zone for quantum information processing Polarization rotation spectrally detunes the 1S0 ↔ 3P1 transition away from resonance with the cooling laser, isolating those atoms from the cooling light and minimizing crosstalk

Polarization Noise Characterization

The polarization-angle noise is measured by probing the carrier peak width, which encodes more information than just the peak center position The model for the peak width shows that it is proportional to the trapping laser intensity (trap depth), allowing them to extract an estimate of the polarization fluctuation of 3.0(4) mrad This corresponds to a polarization angle standard deviation of 3.

1. How to achieve precise quantum state engineering of trapped particles by exploiting the polarization dependence of anisotropic vector and tensor light shifts. This allows for controlling qubit states based on polarization-sensitive atomic properties in 88Sr arrays.

2. Implement sideband cooling under a magic-angle condition by using local polarization tuning to homogenize differential light shifts imparted by the 813-nm tweezers, enabling efficient cooling even in spatially inhomogeneous arrays.

3. Develop a polarization-defined zone architecture for quantum processors where atoms are addressed selectively by laser frequency, as demonstrated by creating patterns that facilitate magic-angle sideband cooling on odd-index tweezers while shifting the resonance of evenindex tweezers 0.4 MHz away.

4. Enable coherent transport between distinct polarization zones for trapped atoms, allowing them to survive transport across boundaries where the polarization changes, as shown by observing survival up to ∆θ = π/8 and recovering baseline survival at ∆θ = π.

5. Implement closed-loop stabilization referenced to the atomic transition frequency, reaching mrad-level stability for tweezer polarization noise, by using site-resolved, in-situ spectroscopy of the 1S0 ↔ 3P1 transition to provide feedback.

6. Create a system capable of characterizing and mitigating polarization noise by modeling the peak width dependence on trap depth using the equation FWHM = aW + p(1 − a)2W squared + cσ squared, allowing for estimation of the polarization fluctuation of 3.0(4) mrad at nominal trap depth.

7. Design an AI system to optimize cooling parameters by iteratively adjusting tweezer polarizations based on the observation that the axial beam yields the largest temperature reduction and tuning them to achieve a common operating frequency near-resonant with the radial red sideband.

Optical tweezer arrays trapping ultracold atoms and molecules are a versatile quantum science platform with broad impact in quantum simulation, quantum computation, and quantum metrology. The polarization dependence of anisotropic vector and tensor light shifts offers a degree of freedom for precise quantum state engineering of trapped particles. Similarly, state-selective operations depend on the polarization of the addressing light through the atom--light coupling strength. Yet, methods for controlling the polarization of individual tweezers or local addressing beams remain an experimental challenge. Here, we demonstrate independent, site-resolved linear polarization rotation across an optical tweezer array by exploiting the local birefringence tunability of a spatial light modulator. Applying this capability to an array of 88 atoms, we homogenize differential light shifts imparted by the 813-nm tweezers to the narrow 1 S 0 cubed P 1 transition, enabling sideband cooling under a magic-angle condition. Furthermore, we show dynamic transport of trapped atoms across distinct polarization zones with high survival and preserved coherence. Finally, we characterize tweezer polarization noise and demonstrate closed-loop stabilization referenced to the atomic transition frequency, reaching mrad-level stability. Our work establishes a technique for manipulating polarization-sensitive atomic and molecular transitions in tweezer architectures, with immediate applications to optical tweezer clocks and multi-zone quantum processors.