Impurities in a trapped 1D Bose gas of arbitrary interaction strength: localization-delocalization transition and absence of self-localization

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Main Authors: Breu, Dennis, Marcos, Eric Vidal, Will, Martin, Fleischhauer, Michael
Format: Preprint
Published: 2024
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author Breu, Dennis
Marcos, Eric Vidal
Will, Martin
Fleischhauer, Michael
author_facet Breu, Dennis
Marcos, Eric Vidal
Will, Martin
Fleischhauer, Michael
contents We discuss impurities in a one-dimensional Bose gas with arbitrary boson-boson and boson-impurity interactions. To fully account for quantum effects, we employ numerical simulations based on the density-matrix renormalization group (DMRG) and - in the regime of strong boson-boson interactions - the mapping to weakly interacting fermions. A mean-field description of the Bose polaron based on coupled Gross-Pitaevski -- Schrödinger equations predicts the existence of a self-localized polaron. We here show that such a solution does not exist and is an artifact of the underlying decoupling approximation. To this end we consider a mobile impurity in a box potential. Our work demonstrates that correlations between the impurity position and the bosons are important even in the limit where mean-field approaches are expected to work well. Furthermore we derive analytical approximations for the energy of a single polaron formed by a heavy impurity for arbitrary interaction strengths and large but finite boson-boson couplings which accurately reproduce DMRG results. This demonstrates that the polaron problem of a heavy impurity in a 1D Bose gas can be accurately approximated by a proper mean-field description plus a linearized treatment of quantum fluctuations for arbitrary boson-boson and impurity-boson couplings. Finally we determine the polaron-polaron interaction potential $V(r)$ in Born-Oppenheimer approximation for small and intermediate distances $r$, which in the Tonks gas limit is oscillatory due to Friedel oscillations in the Bose gas.
format Preprint
id arxiv_https___arxiv_org_abs_2408_11549
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Impurities in a trapped 1D Bose gas of arbitrary interaction strength: localization-delocalization transition and absence of self-localization
Breu, Dennis
Marcos, Eric Vidal
Will, Martin
Fleischhauer, Michael
Quantum Gases
Quantum Physics
We discuss impurities in a one-dimensional Bose gas with arbitrary boson-boson and boson-impurity interactions. To fully account for quantum effects, we employ numerical simulations based on the density-matrix renormalization group (DMRG) and - in the regime of strong boson-boson interactions - the mapping to weakly interacting fermions. A mean-field description of the Bose polaron based on coupled Gross-Pitaevski -- Schrödinger equations predicts the existence of a self-localized polaron. We here show that such a solution does not exist and is an artifact of the underlying decoupling approximation. To this end we consider a mobile impurity in a box potential. Our work demonstrates that correlations between the impurity position and the bosons are important even in the limit where mean-field approaches are expected to work well. Furthermore we derive analytical approximations for the energy of a single polaron formed by a heavy impurity for arbitrary interaction strengths and large but finite boson-boson couplings which accurately reproduce DMRG results. This demonstrates that the polaron problem of a heavy impurity in a 1D Bose gas can be accurately approximated by a proper mean-field description plus a linearized treatment of quantum fluctuations for arbitrary boson-boson and impurity-boson couplings. Finally we determine the polaron-polaron interaction potential $V(r)$ in Born-Oppenheimer approximation for small and intermediate distances $r$, which in the Tonks gas limit is oscillatory due to Friedel oscillations in the Bose gas.
title Impurities in a trapped 1D Bose gas of arbitrary interaction strength: localization-delocalization transition and absence of self-localization
topic Quantum Gases
Quantum Physics
url https://arxiv.org/abs/2408.11549