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 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.
We solve the three-boson problem with contact two-and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies.Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions.Combining these results with our three-body analytics, we extract the three-dimer scattering length close to the dimer-dimer zero crossing.In both considered cases the three-dimer interaction turns out to be repulsive.Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.
For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body
s-wave dimer, the Efimov effect takes place leading to the formation of an infinite number of three-body (Efimov) states. The lowest Efimov state crosses the three-body break-up threshold when the
s-wave two-body scattering length is $a\ensuremath{\approx}\ensuremath{-}9.73{r}_{\mathrm{vdW}}$,
rvdW being the van der Waals length. This article focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body
d-wave dimer, resulting in strong
d-wave interactions. In his paper [Phys. Rev. A 62, 050702(R) (2000)], Bo Gao predicted that for broad resonances the
d-wave dimer is always formed when $a\ensuremath{\approx}0.956{r}_{\mathrm{vdW}}$. Here we find that a single universal three-body state associated with the
d-wave dimer is also formed near the three-body breakup threshold at $a\ensuremath{\approx}1.09{r}_{\mathrm{vdW}}$, or alternatively
a2=0.902rvdW, where
a2 is the two-body
d-wave scattering length. The signature of such a universal three-body state is signaled experimentally by an enhancement of the three-body recombination rate. The three-body effective potential curves that are crucial for understanding the recombination dynamics are also calculated and analyzed. An improved method to calculate the couplings, effective potential curves, and recombination rate coefficients is presented.
We consider a three-boson system with resonant binary interactions and show that for sufficiently narrow resonances three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.
We consider the problem of a fixed impurity coupled to a small number
N of noninteracting bosons. We focus on impurity-boson interactions that are mediated by a closed-channel molecule, as is the case for tuneable interatomic interactions in cold-atom experiments. We show that this two-channel model can be mapped to a boson model with effective boson-boson repulsion, which enables us to solve the three-body
(N=2) problem analytically and determine the trimer energy for impurity-boson scattering lengths
a>0. By analyzing the atom-dimer scattering amplitude, we find a critical scattering length
a∗ at which the atom-dimer scattering length diverges and the trimer merges into the dimer continuum. We furthermore calculate the tetramer energy exactly for
a>0 and show that the tetramer also merges with the continuum at
a∗. Indeed, since the critical point
a∗ formally resembles the unitary point
1/a=0, we find that all higher-body bound states (involving the impurity and
N>1 bosons) emerge and disappear at both of these points. We show that the behavior at these ``multibody resonances'' is universal, since it occurs for any model with an effective three-body repulsion involving the impurity. Thus we see that the fixed-impurity problem is strongly affected by a three-body parameter even in the absence of the Efimov effect.
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.