Superstripes and the excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate

TL;DR

This paper uses Bogoliubov theory to analyze the excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate in the stripe phase, revealing a double gapless band structure indicative of supersolid behavior.

Contribution

It provides a detailed theoretical prediction of the excitation spectrum and structure factors in a spin-orbit-coupled BEC, highlighting signatures of supersolidity and crystalline order.

Findings

Double gapless band structure as a signature of Bose-Einstein condensation

Divergent structure factor near the Brillouin zone indicating crystalline order

Sound velocities depend on Raman coupling and propagation direction

Abstract

Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases.