Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

Abstract

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially {equilibrated} Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part{, that actually corresponds to adiabatic switching on the disorder,} and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. {We also present an appropriate generalization to inhomogeneous trapped condensates.} Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

Binary Bose–Einstein condensates in a disordered time-dependent potential

“…Our time-dependent results can readily be extended to the case of trapped mixtures under the assumption that the disorder correlation length should be much smaller than the spatial extent of the atomic cloud [16,45]. We believe that our predictions open up new perspectives for an experimental demonstration of the peculiar interplay between the disorder and interaction in the non-equilibrium regime.…”

“…where erfc(x) is the complementary error function, ξ + = ξ/ δa + is the extended healing length for a symmetric mixture with short-range interactions, ξ = h/ √ 2mng, δa + = 1 + a 12 /a, and L = 4πh 4 / m 2 R 0 accounts for the Larkin length which is associated with the pinning energy due to the disorder [16,48,49]. For σ → 0, f (0) = √ 2, thus, the results of binary BECs with a weak delta-correlated disorder are recovered [1].…”

“…Moreover, it has been revealed that externally controlled spatiotemporal periodic drive constitutes an excellent platform for creating novel nonequilibrium states of quantum matter [13][14][15]. Recent study demonstrates that the condensate deformation is a signature of the non-equilibrium feature of steady states of a Bose gas in a temporally controlled weak disorder [16]. Quite recently, experimental realization of ultracold bosonic gases in dynamic disorder with controlled correlation time have been reported in reference [17], where the microscopic origin of friction and dissipation has been well illustrated.…”

“…To this end, we use the time-dependent perturbation theory. The perturbation method has proven to be a very useful and powerful tool to capture the main features of both equilibrium and non-equilibrium disordered single BECs [1,16,[25][26][27][28][29][30].…”