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

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.

Dynamical formation of two-fold fragmented many-body state induced by an impurity in a double-well

“…Substantial theoretical and experimental efforts have been recently focusing on strongly particle imbalanced cold atomic mixtures for both bosonic [28,29] and fermionic [30][31][32] settings where quasi-particle formation [33][34][35][36], and in particular polarons [37,38], can take place. Despite the quasi-particle concept, impurity systems can be proven very useful for probing transport phenomena [39][40][41][42], induced correlations [43][44][45][46], facilitate bound state formation [47][48][49][50][51], spontaneous generation of non-linear pattern formation [52][53][54] as well as study relaxation processes [55][56][57]. Overall, entanglement is supposed to be a crucial ingredient in these systems in part due to their few-body nature and also the non-negligible impurity-bath coupling.…”

Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces

“…The FCIQMC method has been used with success previously both for a wide array of fermionic models [79][80][81][82], as well as applied to bosons [83,84], however has not to date been applied to mixed-species systems. In particular, we believe that an application of FCIQMC to coupled electron-boson systems is particularly appealing, since it is not expected to require an explicit truncation of the bosonic mode occupation, allowing a sampling over all relevant bosonic degrees of freedom.…”