The possibility of using coherent laser light to achieve product selectivity in chemical processes is an important goal of current research. In order to lead a chemical reaction toward the desired products one must overcome the consequences of intramolecular vibrational energy redistribution. Manipulating charge transfer in nanodevices requires controlling dissipative mechanisms such as electron-phonon interactions. In all the above cases, coupling to multidimensional environments is responsible for the inadequacy of simple control schemes.
In order to address such issues, we have recently focused on tunneling control and explored the interplay between time-dependent driving and dissipation with regard to the dynamics in a symmetric two-level system. Two questions appear relevant: First, is it possible to sustain large-amplitude coherent oscillations similar to those observed in dissipationless tunneling systems? Second, can an initially localized two-level system retain its localization for long periods in spite of its coupling to the dissipative environment?
Perhaps surprisingly, the answer to the first question is affirmative. We have shown that irradiation of a two-level system with a weak resonant laser field induces long-lived coherent tunneling motion whose amplitude exhibits a quantum stochastic resonance as a function of the two-level-system relaxation rate and the field strength. The phenomenon of quantum stochastic resonance can be described as the enhancement of response of a driven quantum mechanical system by quantum noise. The maximum oscillation amplitude at each temperature does not depend on the field strength, demonstrating the failure of linear response theory to describe this effect. Because sustaining coherent tunneling oscillations requires fairly weak fields, it should be readily observable in semiconductor double-quantum-well structures where damped charge oscillations have been monitored in recent experiments. This work is also relevant to single-charge tunneling phenomena which may prove important in future computer technology.
Unlike the effect of stochastic resonance in which the randomizing effects of dissipation can be overcome completely, our study concluded that coupling to dissipative environments always destroys localization eventually, although at a rate that, if the driving field is strong, can be very slow compared to that at which thermalization occurs in the absence of a field. At high temperature and intermediate friction the delocalization rate takes on a “universal” value which is largely independent of the parameters of the environment and of the specifics of the driving force, depending only on its overall strength. In this regime localized states can be stabilized for long periods without fine-tuning of external conditions. At low temperature and/or weak friction the tunneling dynamics is controlled by delicate phase relations which are gradually destroyed by the dissipative environment. In this regime competition between phase interference and dissipation results in nonmonotonic variation of the decay rate with friction and driving frequency.
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- D. E. Makarov and N. Makri, “Stochastic resonance and nonlinear response in double quantum well structures”, Phys. Rev. B 52, R2257-2260 (1995).
- N. Makri and L. Wei, “Universal delocalization rate in driven dissipative two-level systems at high temperature”, Phys. Rev. E 55, 2475-2479 (1997).
- N. Makri, “Stabilization of localized states in dissipative tunneling systems interacting with monochromatic fields”, J. Chem. Phys. 106, 2286-2297 (1997).
- G. Taft and N. Makri, “Effects of periodic driving on asymmetric two-level systems coupled to dissipative environments”, J. Phys. B 31, 209-226 (1998).
- K. Dong and N. Makri, “Quantum stochastic resonance in the strong field limit”, Phys. Rev. A 70, 042101 (2004).
- K. Dong and N. Makri, “Optimizing terahertz emission from double quantum wells”, Chem. Phys. 296, 273-279 (2004).