Condensation of quasiparticles and density modulation beyond the superfluid critical velocity

Abstract

We extend our earlier study of the ground state of a bosonic quasiparticle Hamiltonian by investigating the effect of a constant external velocity field. Below a critical velocity the ground state is a quasiparticle vacuum, corresponding to a pure superfluid phase at zero temperature. Beyond the critical velocity energy minimization leads to a macroscopic condensation of quasiparticles at a nonzero wave vector ${\mathbf{k}}_{\mathbf{v}}$ parallel to the velocity $\mathbf{v}$. Simultaneously, physical particles also undergo a condensation at ${\mathbf{k}}_{\mathbf{v}}$ and, to a smaller extent, at $\ensuremath{-}{\mathbf{k}}_{\mathbf{v}}$. Together with the Bose-Einstein condensation at $\mathbf{k}=\mathbf{0}$, the three coexisting condensates give rise to density modulations of wave vectors ${\mathbf{k}}_{\mathbf{v}}$ and $2{\mathbf{k}}_{\mathbf{v}}$. For larger $|\mathbf{v}|$ our model predicts a bifurcation of ${\mathbf{k}}_{\mathbf{v}}$ with corresponding two pure condensates and no density modulation.