Superfluidity breakdown and multiple roton gaps in spin-orbit-coupled Bose-Einstein condensates in an optical lattice

Abstract

We investigate the superfluid phases of a Rashba spin-orbit-coupled Bose-Einstein condensate residing on a two-dimensional square optical lattice in the presence of an effective Zeeman field Ω. At a critical value Ω=Ωc, the single-particle spectrum Ek changes from having a set of four degenerate minima to a single minimum at k=0, corresponding to condensation at finite or zero momentum, respectively. We describe this quantum phase transition and the symmetry breaking of the condensate phases. We use the Bogoliubov theory to treat the superfluid phases and determine the phase diagram, the excitation spectrum, and the sound velocity of the phonon excitations. A dynamically unstable superfluid regime occurring when Ω is close to Ωc is analytically identified and the behavior of the condensate quantum depletion is discussed. Moreover, we show that there are two types of roton excitations occurring in the Ω