Emergence of N-body tunable interactions in universal few-atom system

TL;DR

This paper investigates how tunable N-body interactions emerge in a universal three-atom system near a Feshbach resonance, revealing the influence of channel coupling and energy gaps on short-range three-body physics.

Contribution

It derives an effective three-body interaction in a three-atom system considering coupled channels and the energy gap, highlighting the violation of van der Waals universality in narrow Feshbach resonances.

Findings

Effective three-body interaction derived near vanishing scattering lengths

Channel coupling and energy gap influence short-range physics

Violation of van der Waals universality in narrow resonances

Abstract

A three-atom molecule AAB, formed by two identical bosons A and a distinct one B, is studied by considering coupled channels close to a Feshbach resonance. It is assumed that the subsystems AB and AA have, respectively, one and two channels, where, in this case, AA has open and closed channels separated by an energy gap. The induced three-body interaction appearing in the single channel description is derived using the Feshbach projection operators for the open and closed channels. An effective three-body interaction is revealed in the limit where the trap setup is tuned to vanishing scattering lengths . The corresponding homogeneous coupled Faddeev integral equations are derived in the unitarity limit. The s-wave transition matrix for the AA subsystem is obtained with a zero-range potential by a subtractive renormalization scheme with the introduction of two finite parameters, besides the energy gap. The effect of the coupling between the channels in the coupled equations is identified with the energy gap, which essentially provides an ultraviolet scale that competes with the van der Waals radius - this sets the short-range physics of the system in the open channel. The competition occurring at short distances exemplifies the violation of the ``van der Waals universality" for narrow Feshbach resonances in cold atomic setups. In this sense, the active role of the energy gap drives the short-range three-body physics.