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arXiv:1104.0444 · Physical Review A

Macroscopic Klein tunneling in spin-orbit-coupled Bose-Einstein condensates

Dan-Wei Zhang, Zheng‐Yuan Xue, Hui Yan, Z. D. Wang, Shi-Liang Zhu

Published Jan 19, 2012• 50 citations
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Abstract

We propose an experimental scheme to detect macroscopic Klein tunneling with spin-orbit-coupled Bose-Einstein condensates (BECs). We show that a nonlinear Dirac equation with tunable parameters can be realized with such BECs. Through numerical calculations, we demonstrate that macroscopic Klein tunneling can be clearly detected under realistic conditions. Macroscopic quantum coherence in such relativistic tunneling is clarified and a BEC with a negative energy is shown to be able to transmit transparently through a wide Gaussian potential barrier.

DOI
10.1103/physreva.85.013628

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We propose an experimental scheme to detect macroscopic Klein tunneling with spin-orbit-coupled Bose-Einstein condensates (BECs). We show that a nonlinear Dirac equation with tunable parameters can be realized with such BECs. Through numerical calculations, we demonstrate that macroscopic Klein tunneling can be clearly detected under realistic conditions. Macroscopic quantum coherence in such relativistic tunneling is clarified and a BEC with a negative energy is shown to be able to transmit transparently through a wide Gaussian potential barrier.
Ultracold atomic gases allows for the observation of interesting phenomena. In particular, with Bose-Einstein Condensates (BECs) it is possible to realise quantum tunnelling macroscopically. In this thesis the Spin-Orbit coupled BEC in [Phys. Rev. A 79, 043627 (2009)] is numerically solved with the Finite Element Method and the Besse relaxation scheme. The numerical scheme is applied to tunnelling of a BEC through a thin potential barrier. A partial a priori error estimate and a stability estimate is presented. Numerical solution is tested via a convergence and stability study.
The scattering process when spin-orbit coupled Bose-Einstein condensate gets through cusp barrier is numerically simulated by adopting time-split spectrum method; the Klein tunneling phenomena exist in the scattering process. The regions of Klein block and Klein tunneling will appear at higher barrier height as compared to the scattering process on getting through Gaussian barrier. In the Klein tunneling region, the transmission coefficient oscillates with the barrier height, and the oscillation amplitude decreases with increasing barrier height. Besides, the effect of non-linear atomic interaction has been discussed for different barrier heights as well.
Abstract We investigate the macroscopic quantum self-trapping (MQST) phenomenon of a spin–orbit-coupled Bose–Einstein condensate (BEC) in a double-well potential, emphasizing the critical behavior at the transition to MQST. We show that as the nonlinear parameter characterizing the atomic interaction increases, the spin–orbit-coupled BEC appears as MQST, manifesting an asymmetric distribution of the atom in two wells. Then, the effect of the initial condition on the critical behavior at the transition to MQST is given. Analytic expressions for the dependence of the transition parameters on the system parameters and the initial condition are derived, which are in agreement with our numerical simulations.
We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.
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.