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

Matija Čufar,Mingrui Yang,Elke Pahl,Joachim Brand

doi:10.3390/condmat7010015

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 of 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.

Highlights

The study of a single quantum impurity in a surrounding many-body medium has fascinated scientists for many decades [1,2]
Our results show that the yrast excitation energy is consistently lower in the presence of the spin impurity compared to the pure Bose gas at any value of η, as previously predicted [19,43]
Using the full configuration interaction quantum Monte Carlo (FCIQMC) method, we investigated the properties of the yrast states of Bose gases coupled with a mobile impurity in one spatial dimension

Summary

Introduction

The study of a single quantum impurity in a surrounding many-body medium has fascinated scientists for many decades [1,2]. Beyond the historical interest around the influence of the crystal lattice on the motion of an electron—the original “polaron” [3], or impurity atoms in superfluid helium [4]—there has recently been a surge of interest in the field of ultracold atoms, where interactions can be readily tuned with the help of Feshbach resonances [5] and excitation spectra probed with spectroscopic methods [6]. The prediction of Bloch oscillations in a onedimensional quantum liquid, even in the absence of a periodic potential [13,14], was debated [18,19] but eventually confirmed in an experiment with spin impurities in a onedimensional gas of cesium atoms [20]. Other experiments probing impurity physics in one-dimensional quantum gases employed spin impurities (where the impurity atoms have the same mass and only differ in a spin quantum number) [21,22], or different types of atoms [23,24]

Methods

Results

Conclusion