06-265 A.P. Itin, A.A. Vasiliev$, and S. Watanabe
Comment on "Nonlinear adiabatic passage from fermion atoms to boson molecules" (710K, Ps) Sep 18, 06
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Abstract. Dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms was considered recently in I.Tikhonenkov, E.Pazy {\it et al}, Phys. Rev. {\bf A 73}, 043605 (2006). In the mean-field limit, the system is reduced to a classical nonlinear Hamiltonian system with a slowly changing parameter. Analysis of the latter system was done incorrectly; the main results of the commented paper are inconsistent. Here we present accurate study of the mean-field dynamics of the model based on the rigorous separatrix crossing theory. In particular, for the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ the abovementioned Refs. predict the power-law $\Gamma \sim \alpha^{1/3}$ (in the case where the initial fraction of molecules is larger than the quantum fluctuations). Instead, $\Gamma$ is related to a quasi-random jump of an adiabatic invariant which can be calculated using a general method of the separatrix crossing theory and asymptotically $\sim\alpha$ .

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