Strong-coupling Bose polarons in one dimension: Condensate deformation and modified Bogoliubov phonons

J Jager,M Will,M Fleischhauer,R Barnett

doi:10.1103/physrevresearch.2.033142

J Jager, M Will + Show 2 more

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https://doi.org/10.1103/physrevresearch.2.033142

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Abstract

We discuss the interaction of a quantum impurity with a one-dimensional degenerate Bose gas forming a Bose-polaron. In three spatial dimensions the quasiparticle is typically well described by the extended Fr\"ohlich model, in full analogy with the solid-state counterpart. This description, which assumes an undepleted condensate, fails however in 1D, where the backaction of the impurity on the condensate leads to a self-bound mean-field polaron for arbitrarily weak impurity-boson interactions. We present a model that takes into account this backaction and describes the impurity-condensate interaction as coupling to phonon-like excitations of a deformed condensate. A comparison of polaron energies and masses to diffusion quantum Monte-Carlo simulations shows very good agreement already on the level of analytical mean-field solutions and is further improved when taking into account quantum fluctuations.

Highlights

The polaron, introduced by Landau and Pekar [1,2] to describe the interaction of an electron with lattice vibrations in a solid, is a paradigmatic model of quasiparticle formation in condensed-matter physics
It is interesting to note that for η → ∞, Eq (8) approaches the energy of a dark soliton and the effective mass m∗ goes to infinity which is in contrast to results from the extended Fröhlich Hamiltonian [23]
Including quantum fluctuations leads to almost perfect agreement for the energy

Summary

INTRODUCTION

The polaron, introduced by Landau and Pekar [1,2] to describe the interaction of an electron with lattice vibrations in a solid, is a paradigmatic model of quasiparticle formation in condensed-matter physics. An arbitrarily weak deformation of the condensate leads to a self-localized impurity [37] This restricts the accuracy of the Fröhlich model to the perturbative regime. We follow a different approach, and expand the Bose quantum field about the exact mean-field solution in the presence of the mobile impurity in the Lee-LowPines (LLP) frame [39]. Such a treatment incorporates the backaction of the impurity already at the mean-field level as in Refs. We attribute this discrepancy to the existence of many-particle bound states in the attractive regime [23,33]

MODEL AND PROPER DEFINITION OF POLARON MASS

Mean-field equations in the presence of the impurity

Boundary conditions

QUANTUM FLUCTUATIONS

DISCUSSION AND SUMMARY