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Physica B Condensed Matter

Nonlinear Landau–Zener tunneling under biharmonic driving

Xiaobing Luo, Senping Luo, Jun Xu, Jinwang Chen

Published Feb 17, 2011• 1 citation
Publisher
DOI
10.1016/j.physb.2011.02.030

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In this work, we investigate the influence of colored noise originating from a heat bath on nonlinear Landau-Zener (LZ) tunneling. The nonlinearity might arise intrinsically from many-body mean-field atomic self-interactions or Kerr nonlinearities in optical systems. Contrary to the well-established picture of thermally enhanced quantum tunneling within the linear LZ paradigm, ensemble statistics of our numerical simulations demonstrate that nonlinearity can give rise to thermally suppressed LZ tunneling: the tunneling probability of the nonlinear LZ system decreases as the amplitude of the colored noise increases beyond a critical value. Analytically, the Wiener-Hermite expansion facilitates elucidation of the intrinsic mechanism accounting for the nonmonotonic dependence of tunneling probability on noise amplitude. We compare these behaviors with stochastic resonance responses and clarify that the two phenomena stem from distinct physical mechanisms. In addition, we obtain approximate solutions in the weak- and strong-noise limits and discuss the implications of our theory.
Nonlinear Landau-Zener tunneling is an important nonlinear phenomenon. We propose to stimulate the nonlinear tunneling in a spin-orbit-coupled spinor Bose-Einstein condensate. The system provides an experimentally tunable nonlinearity as well as multiple avoided crossings with tunable gap size in nonlinear dispersion relations. The nonlinearity generates tilted cusp and loop structures around the avoided crossings, and the physical consequence of these nonlinear structures is the nonlinear Landau-Zener tunneling. The spin-momentum locking induced by the spin-orbit coupling leads to a time-resolved observation of the nonlinear tunneling by measuring atom populations.
We theoretically study the band structure, tunneling dynamics, and tunneling probability of tunable spin-orbit-coupled Bose-Einstein condensates under the periodic driving of Raman coupling. The time-independent Floquet Hamiltonian is obtained in the high-frequency approximation. It is found that the periodic driving can effectively tune spin-orbit coupling and nonlinear interaction. The system is mapped to a standard nonlinear two-level model, and the critical condition for the appearance of the loop in energy band structure and the width of the loop are obtained analytically. When the interspecies atomic interaction is equal to the intraspecies atomic interaction, there is no loop. However, when the intraspecies atomic interaction is smaller (larger) than the interspecies atomic interaction, the loop appears in the lower (upper) energy band. In this case, both spin-orbit coupling and Raman coupling will suppress the appearance of loop. In particular, the critical condition for the appearance of loop structure can be controlled by adjusting external driving. We also study the tunneling dynamics of Bose-Einstein condensate with tunable spin-orbit coupling. More importantly, by tuning the periodic driving, the tunneling dynamics of the system and the location of nonlinear Landau-Zener tunneling can be controlled. We also find that the spin components of the system can be reversed. Finally, the Landau-Zener tunneling probability of the system is calculated. The research shows that the periodic driving can effectively change the tunneling probability of the system.