2019
DOI: 10.1088/1367-2630/ab1b8e
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The Casimir-like effect in a one-dimensional Bose gas

Abstract: The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross-Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induce… Show more

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Cited by 41 publications
(66 citation statements)
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“…Let us now consider the case of two fermionic impurities with the same spin state. Despite the Pauli exclusion principle which forbids any contact interaction between the two impurities, the formation of bipolarons is nevertheless possible owing to the non-local nature of the phonon-mediated interactions [90][91][92][93][94][95] , although the typical values of their pair binding energy are smaller compared to the spin singlet configuration.…”
Section: Results: ↑↑ Bipolaronmentioning
confidence: 99%
“…Let us now consider the case of two fermionic impurities with the same spin state. Despite the Pauli exclusion principle which forbids any contact interaction between the two impurities, the formation of bipolarons is nevertheless possible owing to the non-local nature of the phonon-mediated interactions [90][91][92][93][94][95] , although the typical values of their pair binding energy are smaller compared to the spin singlet configuration.…”
Section: Results: ↑↑ Bipolaronmentioning
confidence: 99%
“…On the contrary, the approaches of Refs. [11,12,17] describe well the quasiparticles at all momenta by the Bogoliubov spectrum (19), but treat the problem on the mean-field level and thus leads to the exponential interaction. In our recent work [19] we were able to account for the effect of quantum fluctuations within the Gross-Pitaevskii formalism, leading to the full crossover behavior of the induced interaction (see Appendix B) that contains both limits of short [Eq.…”
Section: Conclusion and Discussionmentioning
confidence: 99%
“…Effectively, we perform two expansions, one in √ γ and another in G √ γ/g as we explain more precisely in the following sections. However the result for the induced interaction will cover all distances since we are dealing with asymptotically exact Bogoliubov dispersion (19).…”
Section: Modelmentioning
confidence: 99%
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