Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

Abstract

We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting, the impurity is injected in the fluid with some initial velocity v0, and we are interested in its velocity at infinite time, v,*,. We derive a rigorous upper bound on |vo -VoJ for initial velocities smaller than the generalized critical velocity. In the limit of vanishing impurity-fluid coupling, this bound amounts to v,* = v0, which can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling, the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting, a small constant force is exerted upon the impurity. We argue that two distinct dynamical regimes exist-backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. For fluids with u(|_ = vs (where vc\_ and vs are the Landau critical velocity and sound velocity, respectively), the latter regime is realized. For fluids with vcL < vs, both regimes are possible.Which regime is realized in this case depends on the mass of the impurity, a nonequilibrium quantum phase transition occurring at some critical mass. Our results are equally valid in one, two, and three dimensions.

La vitesse critique de Landau d'une particule dans un superfluide de fermions

“…Quand l'objet est une particule quasi ponctuelle faiblement couplée au superfluide, l'émission d'un anneau de vorticité reste de toute façon improbable aux vitesses inférieures à v L c [12]. 3 Pour une masse M finie et un couplage répulsif suffisamment faible entre l'impureté et le superfluide, il a été montré récemment qu'il existe une véri-table vitesse critique v c non nulle à la limite thermodynamique, sans considération de métastabilité, donc même pour un temps d'interaction arbitrairement long entre l'impureté et le superfluide [15]. Lorsque le couplage tend vers zéro, v c est obtenue en incluant dans (4) toutes les excitations possibles du superfluide, et pas seulement le nombre minimal d'excitations élémentaires, comme il sera fait ici.…”

Dissipative correlated dynamics of a moving impurity immersed in a Bose–Einstein condensate

“…In this latter context, Bloch-oscillations of impurities in the absence of a lattice [58], long-lived oscillations [59,60], as well as relaxation of moving impurities [53][54][55][56] have been observed in one-dimension. The majority of these investigations have been focusing on a Tonk-Girardeau gas of host atoms in homogeneous space.…”

Many-body quantum dynamics and induced correlations of Bose polarons

“…However, the non-equilibrium dynamics of impurities is far less explored and is expected to be dominated by correlation effects which build up in the course of the evolution [34-36, 39, 42-45]. Existing examples include the observation of self-trapping phenomena [46,47], formation of dark-bright solitons [6,42], impurity transport in optical lattices [48][49][50][51], orthogonality catastrophe events [35,52], injection of a moving impurity into a gas of Tonks-Girardeau bosons [53][54][55][56][57][58][59][60] and the relaxation dynamics of impurities [45,61,62]. Besides these investigations, which have enabled a basic description of the quasiparticle states in different interaction regimes, a number of important questions remain open and a full theoretical understanding of the dynamics specifically of Bose polarons is still far from complete.…”