Dynamics of a many-particle Landau-Zener model: inverse sweep

Details Dynamics of a many-particle Landau-Zener model: inverse sweep Dynamics of a many-particle Landau-Zener model: inverse sweep

2009-02-19

arxiv.org/abs/0902.3351v1

Phys. Rev. A 79, 055602 (2009)

Physics

Condensed Matter

Other Condensed Matter

3 pages. Submitted to CEWQO 2009 on 14th February

Scientific paper

10.1103/PhysRevA.79.055602

We consider dynamics of a slowly time-dependent Dicke model, which represents a many-body generalization of the Landau-Zener model. In particular, the model describes narrow Feshbach resonance passage in an ultracold gas of Fermi atoms. Adiabaticity is destroyed when a parameter crosses a critical value, even at very slow sweeping rates of a parameter. The dynamics crucially depends on direction of the sweep. We apply our recent analysis [A.P. Itin, P. Torma, arXiv:0901.4778v1] to the "inverse" sweep through the resonance, corresponding (in a context of Feshbach resonance passage) to dissociation of molecules. On a level of the mean-field approximation, the dynamics is equivalent to a molecular condensate formation from Bose atoms within a two-mode model. Mapping the system to a Painlev\'e equation allows us to calculate deviation from adiabaticity at very slow sweeps analytically.

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