Out-of-equilibrium dynamics of ultracold bosons in time- dependent random potentials

We investigate perturbatively the impact of time-dependent random potentials on a weakly interacting Bose gas at zero temperature. Generically, a random potential yields, on the ensemble average, a depletion of the condensate. It stems from the localization of bosons in the respective minima of the disordered landscape and is usually quantified by a Bose-glass order parameter [1] in close analogy to the well-known Edwards-Anderson order parameter for spin-glasses [2]. A time dependence of the random potential leads in addition to an out-of-equilibrium dynamics of the condensate depletion.\\ Here we study a smooth quench of a spatially delta-correlated disordered potential from an initial disorder-free state of a uniform Bose gas. Depending on the quench rise time we focus on two limiting cases: adiabatic and sudden quench. In the long-time limit the former scenario reproduces the static disorder equilibrium case [3], while the latter leads to the formation of a non-equilibrium steady state, which turns out to have an even larger condensate depletion.\\ [1] R. Graham and A. Pelster, Int. J. Bif. Chaos {\bf 19}, 2745 (2009)\\ [2] S. F. Edwards and P. W. Anderson, J. Phys. F {\bf 5}, 965 (1975)\\ [3] K. Huang and H.-F. Meng, Phys. Rev. Lett. {\bf 69}, 644 (1992)