Publication:
Three-body repulsive forces among identical bosons in one dimension

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10.1103@PhysRevA.100.013614.pdf(389.93 KB)
Date
2019-07-12
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Authors
Valiente Cifuentes, Manuel
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Publisher
American Physical Society
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Física
DOI
https://doi.org/10.1103/PhysRevA.100.013614
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Description
© 2019 American Physical Society. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Published Manuscript, version of a Published Work that appeared in final form in Physical Review A . To access the final edited and published work see https://doi.org/10.1103/PhysRevA.100.013614
Abstract
I consider nonrelativistic bosons interacting via pairwise potentials with infinite scattering length and supporting no two-body bound states. To lowest order in effective field theory, these conditions lead to noninteracting bosons, since the coupling constant of the Lieb-Liniger model vanishes identically in this limit. Since any realistic pairwise interaction is not a mere delta function, the noninteracting picture is an idealization indicating that the effect of interactions is weaker than in the case of off-resonant potentials. I show that the leading-order correction to the ground-state energy for more than two bosons is accurately described by the lowest-order three-body force in effective field theory that arises due to the off-shell structure of the two-body interaction. For natural two-body interactions with a short-distance repulsive core and an attractive tail, the emergent three-body interaction is repulsive and, therefore, three bosons do not form any bound states. This situation is analogous to the two-dimensional repulsive Bose gas, when treated using the lowest-order contact interaction, where the scattering amplitude exhibits an unphysical Landau pole. The avoidance of this state in the three-boson problem proceeds in a way that parallels the two-dimensional case. These results pave the way for the experimental realization of one-dimensional Bose gases with pure three-body interactions using ultracold atoms.
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Citation
Physical Review A, 2019, Vol. 100, Issue 1 : 013614
URI
http://hdl.handle.net/10201/149437
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