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arXiv:cond-mat/0508483 · Physica D Nonlinear Phenomena

Quantum dynamics and delocalization in coherently driven one-dimensional double-well system

Akira Igarashi, Hiroaki S. Yamada

Published Aug 31, 2006• 13 citations
arXivHTMLPDF
DOI
10.1016/j.physd.2006.07.022

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We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.
This paper presents the first experimental evidence of the transition from dynamical localization to delocalization under the influence of a quasiperiodic driving on a quantum system. A quantum kicked rotator is realized by placing cold atoms in a pulsed, far-detuned, standing wave. If the standing wave is periodically pulsed, one observes the suppression of the classical chaotic diffusion, i.e., dynamical localization. If the standing wave is pulsed quasiperiodically, dynamical localization is observed or not, depending on the driving frequencies being commensurable or incommensurable. One can thus study the transition from the localized to the delocalized case as a function of the effective dimensionality of the system.
Levitated particles trapped in double-well potentials provide a promising platform for exploring quantum dynamics beyond the harmonic regime. We show that such systems exhibit a distinctive quantum signature arising from tunneling-assisted interference. Unlike classical dynamics, where the two wells are disconnected, in the quantum case, quantum tunneling enables eigenstates to delocalize into the other well, creating nonzero overlaps between adjacent eigenstates that introduce low-frequency components into the evolution of the mean particle position. By comparing quantum and classical dynamics of particles in one-dimensional double-well potentials, we demonstrate that this interference is uniquely quantum and can be identified through the oscillation of the average position alone. We further relate the observed spectral peaks to the structure of the energy eigenvalues. The effect provides a promising probe of the quantum signature of levitated particle motion, and has fundamental importance as it predicts the demonstration of two major phenomena of quantum mechanics, quantum tunneling and quantum interference, at the same time and on the same system.