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arXiv:1701.03144 · Journal of Physics Conference Series

Topological view of quantum tunneling coherent destruction

Alex E. Bernardini, Mariana Chinaglia

Published Aug 1, 2017• 0 citations
arXivHTMLPDF

Abstract

Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.

DOI
10.1088/1742-6596/880/1/012038

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Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.
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We investigate the coherent control of a single particle held in a quartic double well with a symmetric or asymmetric driving and exhibit time evolutions of relative probability of the particle in one of the double-well wells. It is shown analytically and numerically that the coherent destruction of tunneling could occur only for the symmetric intense driving, and application of the asymmetric sawtooth driving leads to an increase in the tunneling rate. The results agree with the recent experimental data reported by Kierig et al. [Phys. Rev. Lett. 100, 190405 (2008)]. We also exhibit the effect of multiple photon resonances on the tunneling through a dc field. Finally, we demonstrate a connection between the classically chaotic barrier crossing and quantum tunneling numerically.
Abstract It is analytically and numerically shown that the coherent tunnelling between the individual wells of a symmetrical double well potential can be totally suppressed when it is driven by a periodic series of δ function in time, depending on the time period and strength of the δ function. We have applied time dependent perturbation theory to have an understanding over the process. In absence of any kind of perturbation, the average position of the particle makes a sinusoidal oscillation between two wells. With the application of a periodic δ function, the amplitude and the frequency of the oscillation both get modified. In this article we have explored how the frequency and strength of the applied perturbation controls the quantum dynamics of tunnelling and finally, how these parameters drive the system towards a complete stand still situation, which is described as coherent destruction of tunnelling.
We report on the first direct observation of coherent control of single-particle tunneling in a strongly driven double-well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the driving parameters such as frequency, amplitude, and even the space-time symmetry. Our experimental findings are in quantitative agreement with the predictions of the corresponding Floquet theory and are also compared to the predictions of a simple two mode model. Our experiments reveal directly the critical dependence of coherent destruction of tunneling on the generalized parity symmetry.
We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.