Anisotropic dynamics of a spin-orbit coupled Bose-Einstein condensate

TL;DR

This paper investigates the anisotropic excitation spectrum of a spin-orbit coupled Bose-Einstein condensate, revealing how sound velocity and roton minima relate to phase transitions and dynamic behavior.

Contribution

It provides a detailed analysis of the excitation spectrum and dynamic anisotropy in spin-orbit coupled BECs, including a hydrodynamic model for collective oscillations.

Findings

Sound velocity quenched along spin-orbit direction

Roton minimum indicates transition to stripe phase

Strong anisotropy in dynamic behavior

Abstract

By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.