Abstract
We study the quantum dynamics of a single impurity following its sudden immersion into a Bose–Einstein condensate. The ensuing formation of the Bose polaron in this general setting can be seen as impurity decoherence driven by the condensate, which we describe within a master equation approach. We derive rigorous analytical results for this decoherence dynamics, and thereby reveal distinct stages of its evolution from a universal stretched exponential initial relaxation to the final approach to equilibrium. The associated polaron formation time exhibits a strong dependence on the impurity speed and is found to undergo a critical slowdown around the speed of sound of the condensate. This rich non-equilibrium behavior of quantum impurities is of direct relevance to recent cold atom experiments, in which Bose polarons are created by a sudden quench of the impurity-bath interaction.
Highlights
Understanding the non-equilibrium dynamics of many-body systems remains an outstanding challenge in physics
While the quantum evolution of the Bose polaron has briefly been studied [31], in the present paper we show that the formation dynamics of the impurity towards the Bose polaron undergoes a critical slowdown for finite impurity momenta
We have studied the non-equilibrium dynamics of a quantum impurity immersed into a Bose–Einstein condensates (BECs)
Summary
Understanding the non-equilibrium dynamics of many-body systems remains an outstanding challenge in physics. Exciting new research directions include the dynamical emergence of thermal equilibrium in isolated quantum systems [1], and the observation of many-body localization [3], linked to the breakdown of ergodicity [4, 5] Another example is the polaron quasiparticle, which was originally introduced by Landau [6] to describe the interaction of electrons with the atomic crystal of a solid, and has since been employed to understand a broad range of problems in condensed matter physics [7]. While the quantum evolution of the Bose polaron has briefly been studied [31], in the present paper we show that the formation dynamics of the impurity towards the Bose polaron undergoes a critical slowdown for finite impurity momenta This is made possible by a master equation approach from which we derive rigorous results that reveal distinct evolution stages, as illustrated in figure 1(a). While analytical results are derived for weak impurity interactions, much of the identified characteristic features of the nonequilibrium impurity dynamics turn out to be of greater generality and occur for arbitrary coupling strengths
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