Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

TL;DR

This paper provides an exact analytical solution for a two-mode atom-molecule Bose-Einstein condensate model, analyzing its scaling behavior, quantum dynamics, and coherence properties at zero temperature.

Contribution

It introduces an exact Bethe ansatz solution for the model and explores its scaling, coherence, and energy gap characteristics, including a parity effect.

Findings

Identified the threshold coupling for molecular BEC formation.

Discovered a parity effect in the energy gap depending on atomic number.

Revealed a smooth atomic to molecular BEC transition in quantum dynamics.

Abstract

We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.