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Physica Scripta

Tunneling in a bistable system under rapid pumping

Malay Bandyopadhyay

Published Apr 29, 2008• 1 citation
Publisher

Abstract

With this work, I demonstrate the influence of a highly oscillating external field on the coherent tunneling of a quartic double-well potential. Extensive investigation on the tunneling rate of such a quantum system is made using the effective Hamiltonian formalism of (Rahav et al 2003 Phys. Rev. Lett. 91 110404; Rahav et al 2003 Phys. Rev. A 68 013820) for rapidly driven quantum systems. The present model explains the phenomena of chaos assisted tunneling (CAT), i.e. the enhancement of the tunneling rate. The two-level system (TLS) successfully explains the coherent destruction of tunneling (CDT). The effect of dissipation on CAT and CDT are also demonstrated in the present paper.

DOI
10.1088/0031-8949/77/05/055006

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With this work, I demonstrate the influence of a highly oscillating external field on the coherent tunneling of a quartic double-well potential. Extensive investigation on the tunneling rate of such a quantum system is made using the effective Hamiltonian formalism of (Rahav et al 2003 Phys. Rev. Lett. 91 110404; Rahav et al 2003 Phys. Rev. A 68 013820) for rapidly driven quantum systems. The present model explains the phenomena of chaos assisted tunneling (CAT), i.e. the enhancement of the tunneling rate. The two-level system (TLS) successfully explains the coherent destruction of tunneling (CDT). The effect of dissipation on CAT and CDT are also demonstrated in the present paper.
The interplay between classical chaos and quantum tunneling is examined in driven nonlinear systems, with emphasis on how semi classical phase space structures influence purely quantum transport phenomena. We show that, in the presence of external driving and stochastic perturbations, tunneling rates acquire an activated form determined by effective classical barriers, providing a transparent link between chaotic dynamics and quantum tunneling. Within this framework, chaos assisted tunneling and coherent destruction of tunneling emerge as closely related manifestations of the same underlying phase space restructuring and interference effects induced by driving. The results offer a unified perspective on tunneling control in non integrable systems and remain relevant for modern studies of driven quantum dynamics and decoherence resistant transport.
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.
We report on a direct visualization of coherent destruction of tunneling (CDT) of light waves in a double well system which provides an optical analog of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hänggi [Phys. Rev. Lett. 67, 516 (1991)10.1103/PhysRevLett.67.516]. The driven double well, realized by two periodically curved waveguides in an Er:Yb-doped glass, is designed so that spatial light propagation exactly mimics the coherent space-time dynamics of matter waves in a driven double well potential governed by the Schrödinger equation. The fluorescence of Er ions is exploited to image the spatial evolution of light in the two wells, clearly demonstrating suppression of light tunneling for special ratios between the frequency and amplitude of the driving field.
The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically.In our findings,when the system is with only repulsive twobody interactions or only three-body interactions,the tunneling will be suppressed;while in the case of the coupling between two- and three-body interactions,the tunneling can be either suppressed or enhanced.Particularly,when attractive three-body interactions are twice large as repulsive two-body interactions,CDT occurs at isolated points of driving force,which is similar to the linear case.Considering different interaction,the system can experience different transformation from coherent tunneling to coherent destruction of tunneling(CDT).The quasi-energy of the system as the function of the periodically driving force shows a triangular structure,which provides a deep insight into the tunneling dynamics of the system.
The second-order perturbation theory in the framework of the Kramers-Henneberger oscillating frame representation of the Hamiltonian [H. A. Kramers, Quantum Mechanics (North-Holland, Amsterdam, 1956); W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968)] is used to study the tunneling process in a periodically driven double-well potential. The eigenstates of the Floquet Hamiltonian are efficiently approximated when a field frequency is larger than a classical frequency of the time-averaged Hamiltonian. The conditions for coherent enhancement and suppression of tunneling are obtained when the standard perturbation theory fails. It is shown that the enhancement and suppression of tunneling is due to field-induced coupling between states of a one-period averaged effective potential.
Abstract The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunneling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunneling can be either suppressed or enhanced. Particularly, when attractive three-body interactions are twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunneling to coherent destruction of tunneling (CDT). The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunneling dynamics of the system.