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Abstract:
We present a detailed analysis of the Landau–Zener problem for
an interacting Bose–Einstein condensate in a time-varying double-well trap,
especially focusing on the relation between the full many-particle problem
and the mean-field approximation. Due to the nonlinear self-interaction a
dynamical instability occurs, which leads to a breakdown of adiabaticity and thus
fundamentally alters the dynamics. It is shown that essentially all the features of
the Landau–Zener problem including the depletion of the condensate mode can
be already understood within a semiclassical phase-space picture. In particular,
this treatment resolves the formerly imputed incommutability of the adiabatic
and semiclassical limits. The possibility of exploiting Landau–Zener sweeps to
generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover,
we study the influence of phase noise and propose a Landau–Zener sweep as a
sensitive yet readily implementable probe for decoherence, since the noise has
significant effect on the transition rate for slow parameter variations.
