Theory of nonlinear Landau-Zener tunneling

Details Theory of nonlinear Landau-Zener tunneling Theory of nonlinear Landau-Zener tunneling

2001-05-29

arxiv.org/abs/quant-ph/0105140v1

Phys. Rev. A Vol.66,023404 (2002)

Physics

Quantum Physics

9 figures

Scientific paper

10.1103/PhysRevA.66.023404

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 $C$ is above a critical value equal to the gap $V$ 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 $C/V-1$ and $\alpha $, 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 $C/V>>1$, we find a near unit probability for the transition between the adiabatic levels for all values of the crossing rate.

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