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