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Physical Review A

Coherent control of quantum tunneling in an open double-well system

Kewen Xiao, Wenhua Hai, Juan Liu

Published Jan 12, 2012• 23 citations
Publisher

Abstract

We investigate how to apply a high-frequency driving field to the quantum control of a single particle in an open double-well system. The linear stability analysis points out that the stability depends on the external-field parameters and the loss (or gain) coefficients of the system, and the instability leads to a transition of the Floquet quasienergy from real to complex values and results in decaying probabilities for the particle to be in the double well. By combining analytical solutions in the high-frequency approximation with numerical calculations based on an accurate model, we exhibit quantum-dynamical behavior of the particle such as Floquet oscillation, coherent destruction of tunneling, quasi-NOON-state population, partial one-particle tunneling, and the decay of the probabilities of occupation, which are due to the competition and balance between the quantum coherence and the loss (or gain) effect. The results suggest an experimental method for testing quantum motion in an open system by adjusting the driving field.

DOI
10.1103/physreva.85.013410

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We investigate how to apply a high-frequency driving field to the quantum control of a single particle in an open double-well system. The linear stability analysis points out that the stability depends on the external-field parameters and the loss (or gain) coefficients of the system, and the instability leads to a transition of the Floquet quasienergy from real to complex values and results in decaying probabilities for the particle to be in the double well. By combining analytical solutions in the high-frequency approximation with numerical calculations based on an accurate model, we exhibit quantum-dynamical behavior of the particle such as Floquet oscillation, coherent destruction of tunneling, quasi-NOON-state population, partial one-particle tunneling, and the decay of the probabilities of occupation, which are due to the competition and balance between the quantum coherence and the loss (or gain) effect. The results suggest an experimental method for testing quantum motion in an open system by adjusting the driving field.
Coherent control of quantum tunneling is investigated for a single atom held in a driven triple-well potential without tight-binding approximation. In the high-frequency regime within or without multiphoton resonance, we find the analytical solutions and their numerical correspondences, including the special Floquet states of invariant populations and the non-Floquet states of slowly varying populations. The Floquet quasienergy spectrum exhibits anticrossings and crossings for different values of the driving parameters, which are associated with different tunneling properties described by the non-Floquet states. Applying the presented results, we suggest a scheme for transporting a single atom between nonadjacent wells or between adjacent wells.
We investigate the coherent control of quantum tunneling for a single particle held in a driven double-well potential. For a moderate-frequency region, we demonstrate that the irregular quantum tunneling is associated with classically chaotic dynamics. A set of lower resonance-like frequencies is found, for which the coherent destruction of tunneling in the sense of the time average is illustrated numerically. For a high-frequency region, it is shown that the particle is located at the bottom of each well alternately for a long time and the time located in one well can be modulated by adjusting the driving field. The results could be useful for the experiments of controlling single-particle tunneling [see, e.g., E. Kierig, U. Schnorrberger, A. Schietinger, J. Tomkovic, and M. K. Oberthaler, Phys. Rev. Lett. 100, 190405 (2008).].
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.
Abstract In this paper, we study how to apply a periodic driving field to control stable spin tunneling in a non-Hermitian spin–orbit (SO) coupled bosonic double-well system. By means of a high-frequency approximation, we obtain the analytical Floquet solutions and their associated quasienergies and thus construct the general non-Floquet solutions of the dissipative SO coupled bosonic system. Based on detailed analysis of the Floquet quasienergy spectrum, the profound effect of system parameters and the periodic driving field on the stability of spin-dependent tunneling is investigated analytically and numerically for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, we find that the stable spin-flipping tunneling is preferentially suppressed with the increase of gain–loss strength. When the ratio of Zeeman field strength to periodic driving frequency Ω/ω is even, there is a possibility that continuous stable parameter regions will exist. When Ω/ω is odd, nevertheless, only discrete stable parameter regions are found. Under unbalanced gain and loss, whether Ω/ω is even or odd, we can get parametric equilibrium conditions for the existence of stable spin tunneling. The results could be useful for the experiments of controlling stable spin transportation in a non-Hermitian SO coupled system.
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.
Coherent control of quantum tunnelling is investigated analytically for two bosons held in a driven triple-well potential. In the high-frequency region within resonance, the non-Floquet states with slowly varying populations are constructed by the linear superposition of Floquet solutions. For the non-resonance case with appropriate reduced parameters, we obtain another set of analytical solutions and their numerical correspondences, which exhibits the selective tunnelling effect of atoms. Applying the presented analytical results, a scheme to transport two bosons from the first well to the third is suggested by adjusting the driving parameters.