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arXiv · 1505.03351

Semiclassical quantisation for a bosonic atom-molecule conversion system

Eva-Maria Graefe·Maria Graney·Alexander Rush
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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.

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Eva-Maria Graefe, Maria Graney, Alexander Rush. 2015-05-13. Semiclassical quantisation for a bosonic atom-molecule conversion system. https://doi.org/10.1103/physreva.92.012121

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