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Journal of the Optical Society of America B

Transition dynamics of a bright soliton in a binary Bose–Einstein condensate

Li-Chen Zhao, Guoguo Xin, Zhan-Ying Yang

Published Nov 20, 2017• 8 citations

Abstract

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.

DOI: 10.1364/josab.34.002569

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We propose an experiment that would demonstrate nonlinear Josephson-type oscillations in the relative population of a driven, two-component Bose-Einstein condensate. An initial state is prepared in which two condensates exist in a magnetic trap, each in a different hyperfine state, where the initial populations and relative phase between condensates can be controlled within experimental uncertainty. A weak driving field is then applied, which couples the two internal states of the atom and consequently transfers atoms back and forth between condensates. We present a model of this system and investigate the effect of the mean field on the dynamical evolution.

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.

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.

Abstract We investigate Rosen-Zener tunneling for Bose-Einstein condensates in a triple-well potential within the framework of mean-field treatment. Firstly, we exactly calculate tunneling dynamics for triple-well in the linear case, where the population evolution of each well is robust, and all atoms are finally trapped in the single well, that is initially uploaded. In this case, tunneling dynamics are symmetrical when all atoms are populated in the first well and third well. However, as the nonlinear interaction is introduced, tunneling dynamics will be significantly changed. On the one hand, the symmetry will be broken, some atoms will not be confined to the starting well. On the other hand, nonlinear Josephson oscillation will be presented within a fixing interval. When the interaction exceeds this interval, the self-trapping solution emerges.