Semiclassical quantisation for a bosonic atom-molecule conversion system

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.

10 pages, 10 figures, corrected typos, further small changes, similar to published version

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Cited by in corpus (6)

• Excited-state quantum phase transitions
• Dynamics of interacting bosons using the Herman-Kluk semiclassical initial value representation
• Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
• Exact ground-state correlation functions of an atomic-molecular boson conversion model
• Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom-Diatomic Molecule Coexistence
• Walking with the atoms in a chemical bond : A perspective using quantum phase transition