[Paper Review] Tunable transverse spin-motion coupling for quantum information processing

Adam West, Randall Putnam+2 more|arXiv (Cornell University)|Jul 20, 2020

Quantum Information and Cryptography37 references13 citations

TL;DR

This paper demonstrates tunable transverse spin-motion coupling in trapped ions by exploiting the transverse intensity gradient of a laser beam, enabling control over motional sideband strengths independent of longitudinal coupling. The method allows suppression of carrier transitions during sideband operations and vice versa, reducing off-resonant errors and improving gate fidelity in quantum information processing systems.

ABSTRACT

Laser-controlled entanglement between atomic qubits (`spins') and collective motion in trapped ion Coulomb crystals requires conditional momentum transfer from the laser. Since the spin-dependent force is derived from a spatial gradient in the spin-light interaction, this force is typically longitudinal -- parallel and proportional to the average laser $k$-vector (or two beams' $k$-vector difference), which constrains both the direction and relative magnitude of the accessible spin-motion coupling. Here, we show how momentum can also be transferred perpendicular to a single laser beam due to the gradient in its transverse profile. By controlling the transverse gradient at the position of the ion through beam shaping, the relative strength of the sidebands and carrier can be tuned to optimize the desired interaction and suppress undesired, off-resonant effects that can degrade gate fidelity. We also discuss how this effect may already be playing an unappreciated role in recent experiments.

Motivation & Objective

• To develop a method for controlling spin-motion entanglement in trapped ions beyond conventional longitudinal coupling.
• To address limitations in existing trapped ion systems where spin-motion coupling is fixed by beam propagation and electrode geometry.
• To demonstrate that transverse gradients in laser intensity can generate tunable spin-motion coupling perpendicular to the beam direction.
• To suppress off-resonant transitions by independently tuning carrier and sideband Rabi frequencies, thereby enhancing gate fidelity.

Proposed method

• Theoretical modeling of spin-motion coupling using a Taylor expansion of the laser beam's transverse intensity profile around the ion's equilibrium position.
• Derivation of effective Rabi frequencies for sidebands (first and second order) as a function of beam waist, ion position (d), and beam intensity gradient.
• Use of a Gaussian beam profile f(w, x) = exp(−2x²/w²) to model the spatial dependence of the laser-ion coupling, with beam offset d from the ion's equilibrium position.
• Numerical solution of the time-dependent Schrödinger equation to simulate Rabi spectroscopy and fit experimental data.
• Experimental validation using a single 138Ba+ ion in a surface-electrode trap with a co-propagating circularly polarized beam at 45° to the trap axis.
• Fitting of measured Rabi spectra by varying temperature, beam waist, and beam position to match theoretical predictions.

Experimental results

Research questions

• RQ1 Can transverse intensity gradients in a laser beam induce tunable spin-motion coupling in trapped ions?
• RQ2 Can the relative strength of carrier and motional sideband transitions be controlled independently via beam shaping and position?
• RQ3 To what extent does transverse spin-motion coupling affect gate fidelity in trapped ion quantum computing?
• RQ4 Is this effect already present and potentially detrimental in existing trapped ion experiments with tightly focused beams?

Key findings

• Transverse spin-motion coupling was experimentally observed in a single 138Ba+ ion using a co-propagating beam geometry, with clear motional sidebands visible at 25 kHz, 80 kHz, and 110 kHz.
• The strength of sidebands was tuned by adjusting the ion's temperature, which modulates the effective beam waist and position relative to the ion, in agreement with theoretical predictions.
• For a beam waist w = 1.5 µm and misalignment d ≈1.8 µm, the effective Lamb-Dicke parameter for first-order sidebands was ˜η(1) ≈0.017 on the target ion and ˜η(1) ≈0.030 on the neighboring ion.
• The model predicts that transverse coupling can lead to residual entanglement in linear ion traps, with a mean axial phonon occupation of ¯n ≈36 at the Doppler limit.
• Theoretical analysis shows that carrier and sideband Rabi frequencies can be independently suppressed by tuning beam position and profile, reducing off-resonant errors.
• The effect may already be contributing to crosstalk in existing experiments, such as in Debnath et al.'s 171Yb+ processor, where 4% crosstalk could be explained by d ≈1.8 µm beam misalignment.