Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

TL;DR

This paper uses advanced numerical methods to analyze the energy states of a mobile impurity in a one-dimensional Bose gas, revealing different dynamical regimes and a super heavy depleton state.

Contribution

It provides the first exact numerical data for yrast states of a 1D Bose gas with a mobile impurity using FCIQMC, identifying distinct dynamical regimes and the super heavy depleton.

Findings

Identification of polaron, gray soliton, and depleton regimes.

Discovery of a super heavy depleton with negative effective mass.

Quantitative characterization of impurity dynamics in a 1D Bose gas.

Abstract

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension to exact diagonalization it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity's motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas.