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Chinese Physics Letters

Double Barrier Resonant Tunneling in Spin-Orbit Coupled Bose—Einstein Condensates

Zhi Li, Jianzhong Wang, Libin Fu

Published Jan 1, 2013• 6 citations
Publisher

Abstract

We study the double barrier tunneling properties of Dirac particles in spin-orbit coupled Bose—Einstein Condensates. The analytic expression of the transmission coefficient of Dirac particles penetrating into a double barrier is obtained. An interesting resonance tunneling phenomenon is discovered in the Klein block region which has been ignored before.

DOI
10.1088/0256-307x/30/1/010301

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We study the double barrier tunneling properties of Dirac particles in spin-orbit coupled Bose—Einstein Condensates. The analytic expression of the transmission coefficient of Dirac particles penetrating into a double barrier is obtained. An interesting resonance tunneling phenomenon is discovered in the Klein block region which has been ignored before.
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.
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.
Dirac particles can undergo perfect transmission through a sufficiently high potential barrier in the Klein zone. Although the perfect Klein tunneling (often referred to as the Klein paradox) is similar to the non-relativistic resonant transmission which occurs only when the kinetic energy exceeds the barrier, the underlying mechanism is believed to be fundamentally distinct. In this work, we show that for the relativistic double-barrier model the perfect-transmission curve can pass continuously from the above-barrier zone to the Klein zone. Additionally, in the Klein zone, perfect transmission occurs even for subcritical barrier heights, supported by both bound-state analysis and wave-packet dynamics. These findings suggest a connection between perfect Klein tunneling and resonant transmission, and provide new insights into the physical nature of the Klein paradox.
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.
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.
We investigate tunneling of excitations across a potential barrier separating two spin-1 Bose--Einstein condensates. Using mean-field theory at absolute zero temperature, we determine the transmission coefficients of excitations in the saturated magnetization state and unsaturated magnetization states. All excitations, except the quadrupolar spin mode in the saturated magnetization state, show the anomalous tunneling phenomenon characterized as perfect tunneling in the low-momentum limit through a potential barrier. The quadrupolar spin mode in the saturated magnetization state, whose spectrum is massive, shows total reflection. We discuss properties common between excitations showing the anomalous tunneling phenomenon. Excitations showing perfect tunneling have a gapless spectrum in the absence of the magnetic field, and their wave functions in the low-energy limit are the same as the condensate wave function.