Direct observation of the optical Magnus effect with a trapped ion

We directly observe and spatially map an optical analog of the Magnus effect, where intrinsic spin-orbit-like coupling of light generates a spin-dependent transverse displacement of the atom-light interaction profile for a $^{40}$Ca$^+$ ion. Probed on a quadrupole transition using a tightly focused beam, we observe displacements of the maximum in the profile of the effective interaction by several 100 nm originating from intrinsic longitudinal electric field components beyond the paraxial approximation. The tight focus of the beam induces additional transverse polarization gradients, which we characterize through a phase-sensitive measurement and spatial maps for different beam configurations. The results establish the physical basis of polarization-gradient interactions relevant to optical tweezer-based quantum control.

💡 Research Summary

In this work the authors present the first direct observation of an optical analog of the Magnus effect using a single trapped 40Ca⁺ ion. The effect originates from intrinsic spin‑orbit‑like coupling that appears when a tightly focused Gaussian beam is treated beyond the paraxial approximation. In the non‑paraxial regime the beam acquires longitudinal electric‑field components and a local orbital angular momentum, which together with the beam’s spin (polarization) produce a transverse shift of the circular field components. When an atom is placed in such a field, the maximum of the atom‑light interaction profile is displaced laterally by a distance on the order of the optical wavelength divided by 2π or π, depending on the transition involved.

The experiment uses a 729 nm quadrupole transition (4S₁/₂ ↔ 3D₅/₂) of a single ion confined in a linear Paul trap with secular frequencies (1.18, 2.38, 2.07) MHz. The addressing beam is focused to a waist of w₀≈1.3 µm (2w₀≈2.6 µm) with a custom NA = 0.4 objective. Two crossed acousto‑optic deflectors (AODs) allow sub‑100 nm positioning of the beam in the focal plane. By scanning the beam across the ion and measuring the ground‑state population after a calibrated probe pulse, the spatial dependence of the quadrupole Rabi frequency for each Zeeman component (Δm = 0, ±1, ±2) is mapped.

For linear polarization (ε‖y) the authors find that the Δm = ±1 and Δm = ±2 transitions are shifted in the y‑direction by approximately ±λ/2π (≈115 nm) and ±λ/π (≈230 nm), respectively. Gaussian fits to line cuts give displacements of 240(16) nm for Δm = ±1 and 463(20) nm for Δm = ±2, in excellent agreement with the theoretical predictions λ/π and 2λ/π. The Δm = ±1 profiles exhibit a double‑lobe structure caused by transverse field gradients that persist even in the paraxial limit, whereas the Δm = ±2 profiles retain a single‑Gaussian shape.

When the beam is switched to right‑hand circular polarization, both Δm = ±1 and Δm = ±2 transitions are enhanced, and similar displacements are observed (151(21) nm for Δm = ±1 and 505(24) nm for Δm = ±2). Small deviations from the simulated values are attributed to residual polarization imperfections, mechanical drifts, and limited spatial sampling.

A key part of the study is the demonstration of a phase reversal between the two lobes of the Δm = +1 transition. By applying a π/2 pulse on the left lobe, moving the beam to the right lobe and applying a second π/2 pulse, the authors observe constructive interference (full π rotation) when both pulses address the same lobe and destructive interference when they address opposite lobes. The resulting ground‑state population versus beam position directly reveals the sign change of the Rabi frequency, confirming the presence of a transverse electric‑field gradient at the beam centre. Simulations show that, for modest power (10 µW) and the given waist, the carrier Rabi frequency can be suppressed while the gradient reaches Ω′≈2π × 76 Hz nm⁻¹, comparable to gradients used in two‑qubit gates.

The paper therefore establishes three important points: (1) non‑paraxial longitudinal field components generate a measurable spin‑dependent transverse shift of the atom‑light interaction; (2) this shift can be directly imaged with sub‑wavelength resolution and matches quantitative theoretical models; (3) the associated transverse polarization gradients produce controllable spin‑dependent forces that can be harnessed for quantum‑logic operations or mitigated to reduce unwanted motional coupling. These findings are highly relevant for the growing field of optical tweezers in neutral‑atom arrays and for advanced trapped‑ion gate schemes that rely on engineered polarization gradients.