Semiclassical quantisation for a bosonic atom-molecule conversion system

TL;DR

This paper develops a semiclassical approach to analyze a bosonic atom-molecule conversion system, linking mean-field dynamics with many-particle quantum features, and provides an analytic expression for the density of states at large particle numbers.

Contribution

It introduces a semiclassical quantisation method for a deformed $SU(2)$ algebra model of atom-molecule conversion, connecting mean-field and many-particle descriptions.

Findings

Semiclassical methods recover many-particle features from mean-field dynamics.

Analytic expression derived for the many-particle density of states.

Mean-field dynamics occur on a deformed Bloch sphere with a cusp singularity.

Abstract

We consider a simple quantum model of atom-molecule conversion where bosonic atoms can combine into diatomic molecules and vice versa. The many-particle system can be expressed in terms of the generators a deformed $SU(2)$ algebra, and the mean-field dynamics takes place on a deformed version of the Bloch sphere, a teardrop shaped surface with a cusp singularity. We analyse the mean-field and many-particle correspondence, which shows typical features of quantum-classical correspondence. We demonstrate that semiclassical methods can be employed to recover full many-particle features from the mean-field description in cold atom systems with atom-molecule conversion, and derive an analytic expression for the many-particle density of states in the limit of large particle numbers.