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Theory of nonlinear Landau-Zener tunneling
A nonlinear Landau-Zener model was proposed recently to describe, among a
number of applications, the nonadiabatic transition of a Bose-Einstein
condensate between Bloch bands. Numerical analysis revealed a striking
phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear
parameter is above a critical value equal to the gap of avoided
crossing of the two levels. In this paper, we present analytical results that
give quantitative account of the breakdown of adiabaticity by mapping this
quantum nonlinear model into a classical Josephson Hamiltonian. In the critical
region, we find a power-law scaling of the nonadiabatic transition probability
as a function of and , the crossing rate of the energy levels.
In the subcritical regime, the transition probability still follows an
exponential law but with the exponent changed by the nonlinear effect. For
, we find a near unit probability for the transition between the
adiabatic levels for all values of the crossing rate.Comment: 9 figure