Pattern formation in one-dimensional polaron systems and temporal orthogonality catastrophe

TL;DR

This paper investigates the stationary and dynamical properties of one-dimensional Bose polarons, revealing how non-linear excitations and shock waves influence polaron behavior and the orthogonality catastrophe, especially under strong bath-impurity interactions.

Contribution

It introduces the Gross Ansatz approach to analyze the Bose polaron, highlighting the transition from quasi-particle to soliton regimes and generalizing the orthogonality catastrophe to unconfined systems.

Findings

Identification of the equilibrium state crossover from quasi-particle to soliton regimes.

Observation of the temporal orthogonality catastrophe under strong bath-impurity interactions.

Demonstration of momentum transfer via dispersive shock waves leading to reduced impurity velocity.

Abstract

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.