Non-equilibrium disordered Bose gases: condensation, superfluidity and dynamical Bose glass

In an equilibrium three-dimensional (3D) disordered condensate, it is well established that disorder can generate an amount of normal fluid rho(n) equaling to 4/3 of rho(ex), where rho(ex) is a sum of interaction-induced quantum depletion and disorder-induced condensate deformation. The concept that the superfluid is more volatile to the existence of disorder than the condensate is crucial to the understanding of the Bose glass phase. In this work, we show that, by bringing a weakly disordered 3D condensate to non-equilibrium regime via a quantum quench in the interaction, disorder can destroy superfluid significantly more, leading to a steady state of Hamiltonian H-f in which the rho(n) far exceeds 4/3 of the rho(ex). This suggests the possibility of engineering Bose glass in the dynamic regime. Here, we refer to the dynamical Bose glass as the case where in the steady state of quenched condensate, the superfluid density goes to zero while the condensate density remains finite. As both the rho(n) and rho(ex) are measurable quantities, our results allow an experimental demonstration of the dramatized interplay between the disorder and interaction in the non-equilibrium scenario.