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

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.

5 pages, 4 figures

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• Atom--Molecule Coherence in a Bose-Einstein Condensate
• Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates
• Quantum effects on the dynamics of a two-mode atom-molecule Bose-Einstein condensate
• Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates
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• On quantum phase crossovers in finite systems
• A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
• Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
• Exactly solvable models for multiatomic molecular Bose-Einstein condensates
• Exact ground-state correlation functions of an atomic-molecular boson conversion model
• A bosonic multi-state two-well model