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Chinese Physics Letters

Nonlinear Landau–Zener Tunnelling with Two and Three-Body Interactions

Wei Xiu-Fang, Rong-An Tang, Yong Wen-Mei, Xue Ju-Kui

Published May 1, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/25/5/012

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We investigate the Landau–Zener tunnelling of two-component Bose-Einstein condensates (BECs) in optical lattices. In the neighborhood of the Brillouin zone edge, the system can be reduced to two coupled nonlinear two-level models. From the models, we calculate the change of the tunnelling probability for each component with the linear sweeping rate. It is found that the probability for each component exhibits regular oscillating behavior for the larger sweeping rate, but for smaller rate the oscillation is irregular. Moreover, the asymmetry of the tunnelling between the two components can be induced by the unbalanced initial populations or the inequality of the two self-interactions when the cross-interaction between the components exists. The result can not be found in the single component BECs.
We theoretically investigate the energy band structure, nonlinear Landau–Zener tunneling dynamics and tunneling probability of spin-orbit coupled Bose–Einstein condensates in a one-dimensional accelerating optical lattice by using mean-field and two-mode approximation. The critical condition for the appearance of the loop structure is obtained numerically in parameter planes. When the intraspecies atomic interaction is less than the interspecies atomic interaction, the loop only appears in the lower band. In this case, Raman coupling inhibits the appearance of loop, while spin-orbit coupling (SOC) promotes the appearance of loop. If the intraspecies atomic interaction is larger than interspecies atomic interaction, the loop can appear in either the upper band or the lower band. In this case, Raman coupling promotes the loop appearing in the lower band, while SOC suppresses the loop appearing in upper band. Interestingly, when the interspecies atomic interaction is equal to the intraspecies atomic interaction, there is a critical atomic intercation value determined by the optical lattice depth, only when the intraspecies atomic interaction is greater than the critical value, the loop will occur only in lower band. Especially, the emergence of the loop structure destroys the Bloch oscillation of the system and results in the nonlinear Landau–Zener tunneling of the system. Furthermore, the Landau–Zener tunneling probability of the system is calculated, and it is found that the nonlinear Landau–Zener dynamics and the tunneling probability can be manipulated by SOC and Raman coupling.
We present our experimental investigations on the subject of dynamical nonlinearity-induced instabilities and of nonlinear Landau-Zener tunneling between two energy bands in a Rubidium Bose-Einstein condensate in an accelerated periodic potential. These two effects may be considered two different regimes (for small and large acceleration) of the same physical system and studied with the same experimental protocol. Nonlinearity introduces an asymmetry in Landau-Zener tunneling; as a result, tunneling from the ground state to the excited state is enhanced whereas in the opposite direction it is suppressed. When the acceleration is lowered, the condensate exhibits an unstable behaviour due to nonlinearity. We also carried out a full numerical simulation of both regimes integrating the full Gross-Pitaevskii equation; for the Landau-Zener effect we also used a simple two-level model. In both cases we found good agreement with the experimental results.
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.