Effective potential renormalization and polaronic mass shift in a trapped dynamical impurity-luttinger liquid system

TL;DR

This paper develops a theoretical framework combining semi-classical density wave theory and quantum Brownian motion to explain how external trapping potentials affect impurity mass and potential renormalization in one-dimensional Bose liquids, aligning with recent experiments.

Contribution

It introduces a novel combined semi-classical and quantum non-equilibrium approach to quantitatively describe impurity mass shift and potential renormalization in trapped Luttinger liquids.

Findings

The external trap causes a steeper effective potential for the impurity.

The theoretical model accurately reproduces recent experimental data.

The framework links density wave excitations to impurity dynamics.

Abstract

Recent experiments with cold atoms on the impurity motion in one-dimensional liquids of interacting bosons have revealed an interesting interplay between the polaronic impurity mass shift and the renormalization of the optical potential. We show that the influence of the external trap on the Bose gas leads to a steeper effective potential for the impurity. We propose a framework in which this potential renormalization and the mass shift can be quantitatively understood by combining a semi-classical theory of density wave excitations in the Luttinger liquid with the non equilibrium formalism of a quantum Brownian particle. The obtained theoretical results reproduce well recent experimental data.