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arXiv:2012.10429 · Physical Review A

Higher-order effective interactions for bosons near a two-body zero crossing

A. Pricoupenko, Dmitry S. Petrov

Published Mar 29, 2021• 16 citations
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Abstract

We develop the perturbation theory for bosons interacting via a weak two-body potential $V$, attractive and repulsive parts of which cancel each other. We find that the leading nonpairwise contribution to the energy emerges in the third order in $V$ and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of $V$. We apply our theory to a few particular two-body interaction potentials and calculate the leading two-body and three-body interaction corrections for tilted dipoles in quasi-low-dimensional geometries. We show that our approach is consistent with the many-body Bogoliubov treatment.

DOI
10.1103/physreva.103.033326

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We develop the perturbation theory for bosons interacting via a weak two-body potential VVV, attractive and repulsive parts of which cancel each other. We find that the leading nonpairwise contribution to the energy emerges in the third order in VVV and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of VVV. We apply our theory to a few particular two-body interaction potentials and calculate the leading two-body and three-body interaction corrections for tilted dipoles in quasi-low-dimensional geometries. We show that our approach is consistent with the many-body Bogoliubov treatment.
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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We calculate the effective three-body force for bosons interacting with each other by a two-body potential tuned to a narrow zero crossing in any dimension. We use the standard two-channel model parametrized by the background atom-atom interaction strength, the amplitude of the open-channel to closed-channel coupling, and the atom-dimer interaction strength. The three-body force originates from the atom-dimer interaction, but it can be dramatically enhanced for narrow crossings, i.e., for small atom-dimer conversion amplitudes. This effect can be used to stabilize quasi-two-dimensional dipolar atoms and molecules.
We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets and liquids. In particular, we study the role of effective three-body repulsion, in systems with weak attractive pairwise interactions. Its low-energy description is often argued to be equivalent to a model including only two-body interactions with non-zero range. Here, we show that, at zero temperature, the equations of state in both theories agree quantitatively at low densities for overall repulsion, in the gas phase, as can be inferred from the SSS-matrix formulation of statistical mechanics. However, this agreement is absent in the attractive regime, where universality only occurs in the long-distance properties of quantum droplets. We develop analytical tools to investigate the properties of the theory, and obtain astounding agreement with exact numerical calculations using the density-matrix renormalization group.
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The elastic scattering properties of three bosons at low energy enter the many-body description of ultracold Bose gases via the three-body scattering hypervolume DDD. We study this quantity for identical bosons that interact via a pairwise finite-range potential. Our calculations cover the regime from strongly repulsive potentials towards attractive potentials supporting multiple two-body bound states and are consistent with the few existing predictions for DDD. We present a numerical confirmation of the universal predictions for DDD in the strongly interacting regime, where Efimov physics dominates, for a local nonzero-range potential. Our findings highlight how DDD is influenced by three-body quasibound states with strong ddd-wave or ggg-wave characteristics in the weakly interacting regime.