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College Physics

Nonlinear Landau-Zener tunnelling

Biao Wu

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The basic properties of the nonlinear Landau-Zener tunnelling,a new quantum tunnelling phenomenon is reviewed,which is discovered in interacting two-level systems,such as Bose-Einstein condensates in optical lattices and molecule magnets.It is found that the nonlinearity induced by the repulsive interaction can enhance the tunnelling probability compared to the usual linear Landdau-Zener tunnelling.When the nonlinearity is strong enough,the adiabaticity can break down:an infinitely small external linear force can cause finite tunnelling probability.

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The basic properties of the nonlinear Landau-Zener tunnelling,a new quantum tunnelling phenomenon is reviewed,which is discovered in interacting two-level systems,such as Bose-Einstein condensates in optical lattices and molecule magnets.It is found that the nonlinearity induced by the repulsive interaction can enhance the tunnelling probability compared to the usual linear Landdau-Zener tunnelling.When the nonlinearity is strong enough,the adiabaticity can break down:an infinitely small external linear force can cause finite tunnelling probability.
We investigate adiabatic Landau-Zener tunnelling in nonlinear three-level system. The levels and tunnelling probability are studied with respect to the nonlinearity. For weak nonlinearity, the structures of the levels are smooth and similar to their linear counterparts. However the eigenstates of the middle-level will be unstable for some system parameters, which leads to the adiabaticity to break down and the tunnelling probability chaotic. For strong nonlinearity, the structures of the levels are distorted, including double-ring-like distortion in lower-level and butterfly-like distortion in upper-level. The adiabaticity will be broken down more badly. Finally we give a possible application of the system in triple-well trapped Bose-Einstein condensates.
We present a comprehensive analysis of the Landau-Zener tunneling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunneling 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 the linear case. In particular, the tunneling 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 tunneling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunneling probability when the nonlinear ``internal field'' resonate with the external field. We also discuss the asymmetry of the tunneling 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.
We investigate the nonlinear Landau–Zener tunnelling of Bose–Einstein condensate (BEC) in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both analytically and numerically. The analytical eigenstates and the tunnelling probability are obtained, which are verified by numerical methods. It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.
We study tunneling of a Bose-Einstein condensates confined in a effective double-well potential (a single well with a spatially magnetic modulated scattering length, actually), called pseudo double-well trap, in which the interaction of atoms characterized by the s-wave scattering length a s can be widely tuned with a magnetic-field Feshbach resonance. As a result, corresponding to different nonlinear parameters, the energy levels of the nonlinear Schrödinger equation can have complex structures in their dependence on the bias between the wells. We discuss the emergence of looped levels, which lead to a breakdown of adiabaticity that the Landau-Zener transition probability does not vanish even in the adiabatic limit. Moreover, we also find that the Landau-Zener tunneling in the pseudo trap show many striking properties distinguished from that of the real trap model (where the barrier is created by the external potential). Possible experimental observation in an opticallyinduced photonic lattices in a photorefractive material is suggested.