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Journal of Physics A Mathematical and Theoretical

Coherent destruction of tunnelling in a symmetrical double well driven by a series of time dependent δ functions

Dipayan Seal, Pinaki Chaudhury, Subhasree Ghosh

Published Oct 21, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1751-8121/ac980c

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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.
The phenomenon of tunneling is investigated for a symmetric double-well potential perturbed by a monochromatic driving force. The analysis is based on a numerical treatment of the quantum map that propagates the system over one period of the external force, and of the spectrum of its eigenphases (quasienergies). The variety in the quasienergy spectrum, such as exact and avoided crossings, leads to novel forms of coherent tunneling. In particular, for specific parameter values of the driving force, we find almost complete localization of the wave packet in one of the wells.
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.
The roles of spatial symmetry and strength of external time-dependent perturbation on the dynamics of a quantum particle, initially localized in one of the wells of an asymmetric double-well potential are studied using the recently developed techniques incorporating quantum theory of motion and time-dependent Fourier grid Hamiltonian methods. The model used here includes a mimic of the related experimental situations which is considered as a perturbation to the static double-well potential. Analysis of localized and delocalized phase space structures and corresponding time-profile of tunneling probability reveal the recipe toward controlling the tunneling oscillations by modulating the parameters of applied perturbation. A study on a stochastic pulsating potential also reveals the root to the quantum localization, even in moderate field strength.
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.
The aim to control the internal and external degrees of freedom of quantum systems is of great interest for many fields of physics and chemistry. One opportunity to realize such a coherent control is provided by strong, time depended, external fields. In this work the experimental realization of a model-system is presented. The coherent control of the tunneling dynamics of single atoms by means of a time-periodic, external field is demonstrated. Depending on the parameters of the driving force the tunneling rate can be varied up to a total suppression of the tunneling process in the extreme. This type of dynamical localization is known as "coherent destruction of tunneling". The experimental setup allows a direct access to the tunneling dynamics of single atoms in a double well structure and enables great freedom concerning the parameters. Not only the double well potential, the driving frequency and the driving amplitude can be varied, but also the temporal and spatial symmetry of the driving. A coherent beam of slow, metastable argon atoms serves as source of particles, which can be detected spatially resolved enabling the direct observation of the tunneling dynamics in momentum space.