Condensates of Strongly-interacting Atoms and Dynamically Generated Dimers

TL;DR

This paper develops a method using the 1PI effective action to describe dimer condensates in strongly-interacting atomic systems, enabling analysis of both atom and dimer superfluid phases.

Contribution

It introduces an equivalent 1PI effective action incorporating a classical dimer field for better modeling of dimer condensates in atom systems.

Findings

The method accurately describes atom superfluid phase.

The dimer field approach simplifies analysis of dimer superfluid phase.

Results align with previous Bose gas studies near Feshbach resonance.

Abstract

In a system of atoms with large positive scattering length, weakly-bound diatomic molecules (dimers) are generated dynamically by the strong interactions between the atoms. If the atoms are modeled by a quantum field theory with an atom field only, condensates of dimers cannot be described by the mean-field approximation because there is no field associated with the dimers. We develop a method for describing dimer condensates in such a model based on the one-particle-irreducible (1PI) effective action. We construct an equivalent 1PI effective action that depends not only on the classical atom field but also on a classical dimer field. The method is illustrated by applying it to the many-body behavior of bosonic atoms with large scattering length at zero temperature using an approximation in which the 2-atom amplitude is treated exactly but irreducible $N$-atom amplitudes for $N \ge 3$ are neglected. The two 1PI effective actions give identical results for the atom superfluid phase, but the one with a classical dimer field is much more convenient for describing the dimer superfluid phase. The results are also compared with previous work on the Bose gas near a Feshbach resonance.