Landau-Zener Tunnelling in a Nonlinear Three-level System

TL;DR

This paper analyzes Landau-Zener tunnelling in a nonlinear three-level quantum system, revealing nonzero tunnelling probabilities even in slow sweeps, and highlighting the effects of nonlinearity and resonance on tunnelling behavior.

Contribution

It provides a comprehensive analysis of nonlinear three-level Landau-Zener tunnelling, including analytical expressions and insights into nonlinearity effects and asymmetry.

Findings

Nonzero tunnelling probability in adiabatic limit.

Nonlinearity significantly affects tunnelling when resonant.

Tunnelling shows irregular sensitivity to sweep rate.

Abstract

We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunnelling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunnelling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunnelling probability when the nonlinear "internal field" resonate with the external field. We also discuss the asymmetry of the tunnelling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.