Supersolid phase of a spin-orbit-coupled Bose-Einstein condensate: A perturbation approach
Authors: Martone G.I.; Stringari S.
Autors Affiliation: University Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France; Laboratoire Kastler Brossel, Sorbonne University, CNRS, ENS-PSL Research University, Collige de France; 4 Place Jussieu, 75005 Paris, France; INO-CNR BEC Center and Dipartimento di Fisica, Universita di Trento, I-38123 Povo, Italy
Abstract: The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.
Journal/Review: SCIPOST PHYSICS
Volume: 11 (5) Pages from: 092-1 to: 092-37
KeyWords: STRIPE PHASE; QUANTUM; SUPERFLUIDITYDOI: 10.21468/SCIPOSTPHYS.11.5.092