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Chinese Physics Letters

Rosen–Zener Transition in a Nonlinear System for Two-Component Bose–Einstein Condensates in Optical Lattices

Jiang Xin, Mai-mai Lin, Sheng-Chang Li, Duan Wen-Shan

Published Jan 1, 2009• 3 citations
Publisher

Abstract

We study the Rosen–Zener transition (RZT) in a nonlinear system for two-component Bose–Einstein condensates in optical lattices. It is found that the percentage of the components could affect the quantum transition dramatically. For the component with large percentage it is equivalent that the effect of the nonlinearity is stronger, whereas for the component with small percentage the effect is weaker. We also find that the nonlinearity c 11 can affect the quantum transition dramatically. This is similar to that reported from Ref. [14]. Compared with one-component systems, however, the effect of the nonlinearity is decreased due to the two components of the BECs in optical lattices. Furthermore, the effect of the coupling nonlinearity between two components c 12 is studied. The component with large percentage is more affected by the nonlinearity than that with small-percentage component.

DOI
10.1088/0256-307x/26/1/013701

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We study the Rosen–Zener transition (RZT) in a nonlinear system for two-component Bose–Einstein condensates in optical lattices. It is found that the percentage of the components could affect the quantum transition dramatically. For the component with large percentage it is equivalent that the effect of the nonlinearity is stronger, whereas for the component with small percentage the effect is weaker. We also find that the nonlinearity c 11 can affect the quantum transition dramatically. This is similar to that reported from Ref. [14]. Compared with one-component systems, however, the effect of the nonlinearity is decreased due to the two components of the BECs in optical lattices. Furthermore, the effect of the coupling nonlinearity between two components c 12 is studied. The component with large percentage is more affected by the nonlinearity than that with small-percentage component.
Rosen–Zener transitions of two-component Bose–Einstein condensates in a nonlinear two-level system are studied. The intensities of interspecies interactions which can be adjusted by Feshbach resonance can affect the quantum transition dramatically. The percentage of both components also has an important effect on the quantum transition probabilities. It is also found that the quantum transition can be completely blocked by either strong interspecies interactions or large percentage of the component. In the sudden limit, the approximated transition probabilities for each component are obtained analytically. In the adiabatic limit, the equivalent classical Hamiltonian is obtained. The fixed points and the eigenenergy level structures are also obtained. Finally, for some special cases, the period of the rectangular oscillation as a function of the percentage of the number density and the interspecies interaction is obtained analytically. All the analytical results are compared with numerical simulations and good agreement is obtained.
We study the Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical expressions for the transition probability. Numerical explorations are made for a wide range of parameters of the general case. Possible applications of our theory to Bose-Einstein condensates (BECs) and solid-state physics are discussed.
Transition dynamics have been studied widely in two-mode Bose–Einstein condensate systems with linear coupling effects. Nonlinear interaction between atoms would induce a nonlinear Josephson oscillation, which admits an oscillation form different from the classical Josephson oscillation. Similar extensions for the Rosen–Zener transition and the Landau–Zener transition also suggest that a strong nonlinear strength would induce nonlinear-type transition dynamics, which is in sharp contrast to the linear process. Interestingly, here we show a standard Josephson oscillation that has a constant linear coupling strength, no matter how great the nonlinear interaction strength is. This characteristic is in sharp contrast to the nonlinear Josephson oscillation reported before in nonlinear coupled systems. By manipulating the linear coupling strength with the RF field, we demonstrate that the Rosen–Zener transition particles, with an invariant distribution profile, can be managed well under exponential and periodic forms. The nonlinear interaction strength is found to have no effect on the transition rate between atoms in the two components for the case where the inter- and intra-atomic interaction strengths are equal. Furthermore, we test the robustness of the transition dynamics against parameter deviations and noises in the initial condition. These results are helpful for controllable quantum state preparations.
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.