Nonlinear adiabatic passage from fermion atoms to boson molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction Î" on the sweep rate α varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number N. The power law is linear, Î"â α, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Î"â α1/3 when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.