Bloch oscillations of bosonic lattice polarons

TL;DR

This paper investigates the non-equilibrium dynamics of impurity atoms in a BEC, revealing complex Bloch oscillations and drift behaviors of polarons, with analytical and numerical insights into their response to external forces.

Contribution

It introduces a variational mean-field approach to study polaron dynamics in optical lattices, providing new analytical expressions and highlighting differences from traditional models.

Findings

Non-linear drift velocity dependence on applied force.

Sub-Ohmic behavior for small forces in higher dimensions.

Analytical expression for heavy impurity atom drift velocity.

Abstract

We consider a single impurity atom confined to an optical lattice and immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the impurity with the phonon modes of the BEC leads to the formation of a stable quasiparticle, the polaron. We use a variational mean-field approach to study dispersion renormalization and derive equations describing non-equilibrium dynamics of polarons by projecting equations of motion into mean-field (MF) type wavefunctions. As a concrete example, we apply our method to study dynamics of impurity atoms in response to a suddenly applied force and explore the interplay of coherent Bloch oscillations and incoherent drift. We obtain a non-linear dependence of the drift velocity on the applied force, including a sub-Ohmic dependence for small forces for dimensionality d>1 of the BEC. For the case of heavy impurity atoms we derive a closed analytical expression for the drift velocity. Our results show considerable differences with the commonly used phenomenological Esaki-Tsu model.