Researchers Reveal 100nm Displacement Via the Optical Magnus Effect with an Ion

Researchers have, for the first time, directly observed the optical Magnus effect in a single trapped ion, demonstrating a spin-dependent displacement of light interacting with matter. Philip Leindecker, Louis P.H. Gallagher, and Edgar Brucke, from ETH Z urich and the PSI Quantum Computing Hub, alongside colleagues including Dominique Zehnder, Luka Milanovic, and Matteo Marinelli, achieved this by spatially mapping the effect on a calcium ion using a tightly focused laser beam. This observation, revealing displacements of up to several hundred nanometres, confirms the importance of considering intrinsic longitudinal electric field components and polarization gradients when manipulating atoms with light, paving the way for more precise control in emerging technologies like optical tweezers and quantum computing.

Spin-dependent atom displacement via focused light field polarisation gradients offers novel manipulation possibilities

Scientists have directly observed an optical analog of the Magnus effect, revealing a spin-dependent transverse displacement of the atom-light interaction profile for a single calcium-40 ion. These displacements originate from longitudinal electric field components beyond the standard paraxial approximation, a key innovation in understanding light-atom interactions.

The study employed a tightly focused Gaussian beam to induce transverse polarization gradients, which were then meticulously characterised using a phase-sensitive measurement and spatial maps for varying beam configurations. By utilising two crossed acousto-optic deflectors, the researchers achieved sub-100nm spatial resolution in positioning the laser beams, enabling precise mapping of the coupling strength for all components of the 729nm quadrupole transition from 4S1/2 to 3D5/2.

Experiments revealed the spin-dependent transverse displacement of the interaction profile, stemming solely from the Gaussian beam’s intrinsic longitudinal components, confirming theoretical predictions. This work establishes the physical basis of polarization-gradient interactions crucial for optical tweezer-based quantum control.

The observed shifts, predicted to lie between λ/2π and λ/π for different components of the quadrupole transition, demonstrate the potential for engineering transverse motional excitations. The research also characterizes additional transverse polarization gradients arising from the tight beam focus, leading to position-dependent selection rules for the quadrupole transition. These findings are particularly relevant as optical tweezers become increasingly central to atomic physics, enabling parallel trapping and control of large neutral-atom arrays and offering new avenues for high-fidelity trapped-ion gates.

Trapped ion manipulation and spatial mapping of optical quadrupole interactions enable precise quantum control

Scientists directly observed and spatially mapped an analog of the Magnus effect using a single 40Ca+ ion confined in a linear Paul trap with frequencies of 2π × (1.18, 2.38, 2.07) MHz. The research team initialized the ion in the 4S1/2, mj = +1/2 Zeeman level and cooled it close to the motional ground state via dark resonance and resolved sideband cooling techniques.

An optical tweezer beam, propagating along the z axis at 729nm, was then tuned to the quadrupole-allowed transitions between the 4S1/2, mj = +1/2 state and the Zeeman levels of the 3D5/2 state. The tweezer beam was focused to a diameter of 2w0 ≈2.6μm using a custom NA = 0.4 objective, and positioned in the focal plane using two crossed acousto-optic deflectors.

Researchers scanned the tweezer across the ion’s location to map the spatial dependence of the quadrupole interaction, simultaneously tracking and compensating for slow drifts in the ion’s position. A magnetic field of B = 0.4 mT was applied along the −x direction, inducing a Zeeman splitting of ≈6.72MHz within the 3D5/2 manifold.

For each measurement, the tweezer frequency was adjusted to resonantly drive a selected transition 4S1/2, mj ↔ 3D5/2, mj + ∆mj, with a probe interaction time of Tprobe. The final state was then discriminated via state-dependent fluorescence from a dipole transition at 397nm. The team normalized each transition’s spatial map to the maximum carrier Rabi frequency Ω0, extracting peak values of Ω0 = 2π×(7.7, 1.3, 0.7, 1.7, 16.7) kHz for ∆mj = (−2, . . . , +2). This protocol enabled direct spatial imaging of the spin-dependent atom, light interaction profile with sub-wavelength resolution, revealing transverse displacements of up to approximately ±λ/π ≈230nm for the ∆mj = ±2 coupling profiles.

Spin-dependent displacement maps intrinsic beam components in calcium ions with high fidelity

Scientists directly observed and spatially mapped an optical analog of the Magnus effect, demonstrating spin-dependent transverse displacement of the atom-light interaction profile for a calcium ion. Probed on a quadrupole transition with a tightly focused beam, the team measured displacements of the maximum interaction profile reaching several 100nm, originating from intrinsic longitudinal electric field components beyond the paraxial approximation.

These displacements arise from the interplay of induced and spin angular momentum, generating strong transverse polarization gradients and shifting circular field components off-axis. Experiments revealed the spatial profile of coupling strength for all components of the 729nm quadrupole transition from 4S1/2 to 3D5/2 in 40Ca+.

Researchers resolved the spin-dependent transverse displacement of the interaction profile, attributable solely to the Gaussian beam’s intrinsic longitudinal components. Measurements confirm that the observed shift is wavelength dependent, lying between λ/2π and λ/π for different components of the quadrupole transition.

Tests prove that the tight beam focus induces additional transverse polarization gradients, leading to position-dependent selection rules for the quadrupole transition. The team characterized these gradients using a phase-sensitive measurement and spatial maps for varying beam configurations. Data shows displacements of approximately ±λ/2π, equivalent to 115nm, for ∆mj = ±1, and ±λ/π, or 230nm, for ∆mj = ±2, in the y direction.

The breakthrough delivers sub-100nm spatial resolution in laser beam positioning, enabled by two crossed acousto-optic deflectors. Scientists achieved a maximum Rabi frequency of 2π × 16.7kHz for the ∆mj = +2 case, with scale factors of 2π × 7.7kHz for ∆mj = 0 and 2π × 1.3kHz for ∆mj = +1. These results establish the physical basis of polarization-gradient interactions relevant to tweezer-based quantum control and offer new routes to high-fidelity trapped-ion gates.

Magnus effect analogue reveals polarization-gradient driven atomic displacement in liquids

Scientists have directly observed and spatially mapped an analog of the Magnus effect, demonstrating a spin-dependent transverse displacement of the atom-light interaction profile for a calcium ion. This displacement, observed on a quadrupole transition using a tightly focused beam, resulted in shifts of several hundred nanometres in the maximum of the effective interaction profile.

These shifts originate from intrinsic longitudinal electric field components extending beyond the paraxial approximation. The research team characterised additional transverse polarization gradients induced by the tight beam focus through phase-sensitive measurements and spatial maps generated with varying beam configurations.

The findings establish the physical basis of polarization-gradient interactions, which are relevant to tweezer-based control of particles. Experiments were conducted using a trapped calcium-40 ion within a linear Paul trap, with a tightly focused laser beam tuned to a specific quadrupole transition. The polarization of the tweezer beam was carefully configured and monitored using a polarimeter, allowing for precise control over the interaction.

The authors acknowledge that ion drifts during measurements, on the order of 10nm, approached the limits imposed by the ion’s zero-point motion, representing a limitation of the current setup. Future research could focus on mitigating these drifts to further refine the precision of these measurements and explore the potential for manipulating atomic interactions with greater accuracy.