| Autor: |
Breu, Dennis, Marcos, Eric Vidal, Will, Martin, Fleischhauer, Michael |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We discuss impurities in a trapped one-dimensional Bose gas with arbitrary boson-boson and boson-impurity interactions. To fully account for quantum effects, in particular in the regime of strong boson-boson interactions, we employ numerical simulations based on the density-matrix renormalization group (DMRG) and analytic approximations exploiting the mapping to weakly interacting fermions. Mobile impurities in a box potential undergo a phase transition between a delocalized state and a solution localized at one of the potential edges upon increasing the impurity-boson interaction. While a mean-field ansatz based on coupled Gross-Pitaevski -- Schr\"odinger equations gives reasonable predictions of this transition, it also predicts the existence of a self-localized polaron solution, which we show to be an artifact of the underlying decoupling approximation. This demonstrates that impurity-boson correlations are important even in the limit of weak boson-boson interactions, where mean-field approaches are expected to work well. Furthermore we calculate the energy of a single polaron formed by a heavy impurity for arbitrary interaction strengths and give analytical approximations for large but finite boson-boson couplings. Finally we numerically determine the polaron-polaron interaction potential in Born-Oppenheimer approximation, which in the Tonks gas limit is oscillatory due to Friedel oscillations in the Bose gas. |
| Databáze: |
arXiv |
| Externí odkaz: |
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