Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas

Abstract

We study the fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas using the field theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially suppressed beyond the thermal length. We obtain analytical expressions for the induced interaction at zero and finite temperature that are valid at arbitrary distances. We discuss experimental realizations as well as possible formation of bound states of two impurities, known as bipolarons.

14 pages, 1 figure; accepted to Physical Review B

References in corpus (6)

• Many-Body Physics with Ultracold Gases
• Bloch oscillations in one-dimensional spinor gas
• Bipolarons and multi-polarons consisting of impurity atoms in a Bose-Einstein condensate
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• Indirect forces between impurities in one-dimensional quantum liquids
• Impurity crystal in a Bose-Einstein condensate

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• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons
• Collective excitations of a Bose-Einstein condensate of hard-core bosons and their mediated interactions: from two-body bound states to mediated superfluidity
• Bound impurities in a one-dimensional Bose lattice gas: low-energy properties and quench-induced dynamics
• Impurities in a trapped 1D Bose gas of arbitrary interaction strength: localization-delocalization transition and absence of self-localization
• Two-dimensional Lorentz-violating Casimir effect
• Effective approaches to the dynamical properties of two distinguishable Bose polarons
• Effective two- and three-body interactions between dressed impurities in a tilted double-well potential