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Acta Physica Sinica

Klein tunneling in spin-orbit coupled Bose-Einstein condensate scattered by cusp barrier

Zhi Li, Hui Cao

Published Jan 1, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.7498/aps.63.110306

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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.
In this paper, the phenomenon of double barrier scattering in spin-orbit coupling Bose-Einstein condensate is studied and the analytical expression of transmission coefficient of the system is therefore obtained. On the basis of the above study, how to deal with Klein tunneling and bound Dirac particles is also discussed to devise an experimental scheme of trapping Dirac particles in captivity. Besides, numerical simulation of the barrier scattering pattern of Dirac particles is performed in this paper by the time splitting spectral method. Through the analysis of transmission situation of Dirac particles directing at the Klein barrier in both the center and margin part of blocked area and the study of the influence of non-linear interaction on the evolution of Dirac particles from both repelling and attracting effect, the conclusion can be drawn that although the influence of non-linear interaction on scattering property of particles is negligible to some extent, the strong non-linear interaction will completely destroy the momentum distribution of wave packets so that the result of barrier scattering of Dirac particles can be dramatically changed.
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.
The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective one-dimensional Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matter-wave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the noninteracting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.
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.
We calculate the tunneling process of a Dirac particle across two square barriers separated by a distance d, as well as the scattering by a double-cusp barrier, where the centers of the cusps are separated by a distance larger than their screening lengths. Using the scattering matrix formalism, we obtain the transmission and reflection amplitudes for the scattering processes of both configurations. We show that the presence of transmission resonances modifies the Lorentzian shape of the energy resonances and induces the appearance of additional maxima in the transmission coefficient in the range of energies where transmission resonances occur. We calculate the Wigner time delay and show how their maxima depend on the position of the transmission resonance.