Trapped-ion Lissajous trajectories

TL;DR

This paper demonstrates how to generate and control Lissajous trajectories of a trapped ion using engineered spin-orbit interactions, revealing novel quantum motion phenomena and robustness against dissipation.

Contribution

It introduces a protocol for creating Lissajous curves with a trapped ion via engineered Rashba and Dresselhaus spin-orbit couplings, including bounded interactions and dissipation effects.

Findings

Successful generation of Lissajous trajectories in a trapped ion system.

Observation of an 'unusual' Zitterbewegung with cycloidal paths.

Trajectories remain robust under realistic dissipative conditions.

Abstract

Here we present a protocol for generating Lissajous curves with a trapped ion by engineering Rashba- and the Dresselhaus-type spin-orbit interactions in a Paul trap. The unique anisotropic Rashba $\alpha_{x}$, $\alpha_{y}$ and Dresselhaus $\beta_{x}$, $\beta_{y}$ couplings afforded by our setup also enables us to obtain an "unusual" Zitterbewegung, i.e., the semiconductor analog of the relativistic trembling motion of electrons, with cycloidal trajectories in the absence of magnetic fields. We have also introduced bounded SO interactions, confined to an upper-bound vibrational subspace of the Fock states, as an additional mechanism to manipulate the Lissajous motion of the trapped ion. Finally, we accounted for dissipative effects on the vibrational degrees of freedom of the ion and find that the Lissajous trajectories are still robust and well defined for realistic parameters.