Anomalous Hall conductivity from the dipole mode of spin-orbit-coupled cold-atom systems

TL;DR

This paper investigates how spin-orbit coupling in cold-atom systems influences dipole oscillations, revealing a link between oscillation phase differences and anomalous Hall conductivity, enabling experimental measurement of this property.

Contribution

It introduces a method to determine anomalous Hall conductivity in cold-atom systems via dipole oscillation phase analysis.

Findings

Different oscillation directions are coupled by spin-orbit interactions.

Phase differences relate to anomalous Hall conductivity.

Results suggest experimental measurement techniques.

Abstract

Motivated by recent experiments [Lin {\it et al.}, Nature {\bf 417}, 83 (2011)] that engineered spin-orbit coupling in ultra-cold mixtures of bosonic atoms, we study the dipole oscillation of trapped spin-orbit-coupled non-condensed Bose and Fermi gases. We find that different directions of oscillation are coupled by the spin-orbit interactions. The phase difference between oscillatory motion in orthogonal directions and the trapping frequencies of the modes are shown to be related to the anomalous Hall conductivity. Our results can be used to experimentally determine the anomalous Hall conductivity for cold-atom systems.