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The Journal of Chemical Physics

Stabilization of localized states in dissipative tunneling systems interacting with monochromatic fields

Nancy Makri

Published Feb 8, 1997• 42 citations
Publisher

Abstract

We study the dynamics of an initially localized symmetric two-level system coupled to high-temperature dissipative environments and driven by a strong time-periodic force which corresponds to high-frequency monochromatic light. Qualitative arguments based on the quantized representation of the radiation field predict a wealth of intriguing behaviors which are confirmed and quantified via accurate numerical path integral calculations. With the exception of very strong friction we find that high-frequency driving always helps stabilize localized states. At intermediate friction the delocalization rate approaches a “universal’’ limiting 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. This robust behavior implies that localized states can be stabilized in these systems without much finetuning of external conditions. In the weak friction regime the interplay between phase interference and dissipation results in nonmonotonic variation of the decay rate with friction and driving frequency. The path integral results are compared to those obtained earlier via analytical treatments.

DOI
10.1063/1.473345

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We study the dynamics of an initially localized symmetric two-level system coupled to high-temperature dissipative environments and driven by a strong time-periodic force which corresponds to high-frequency monochromatic light. Qualitative arguments based on the quantized representation of the radiation field predict a wealth of intriguing behaviors which are confirmed and quantified via accurate numerical path integral calculations. With the exception of very strong friction we find that high-frequency driving always helps stabilize localized states. At intermediate friction the delocalization rate approaches a “universal’’ limiting 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. This robust behavior implies that localized states can be stabilized in these systems without much finetuning of external conditions. In the weak friction regime the interplay between phase interference and dissipation results in nonmonotonic variation of the decay rate with friction and driving frequency. The path integral results are compared to those obtained earlier via analytical treatments.
We study the dynamics of initially localized states in biased dissipative TLSs evolving under a time periodic force simulating monochromatic light. Accurate numerical calculations are presented using an iterative procedure to evaluate realtime path integrals. In the high-temperature and moderate to high friction regime, the system exhibits exponential decay. In this regime the decay constant approaches a plateau value that depends only on the intensity of the driving field. Simple analytical calculations using a Landau-Zener approach predict correctly the value of the decay rate. Bias does not affect significantly the plateau value of the decay constant provided that the asymmetry is small relative to the amplitude of the driving field. In the low-friction regime, phase relations are important and there is nonmonotonic variation of the delocalization rate. Weak friction broadens the window for extending the lifetime of localized states. At very strong friction the decay rate diminishes monotonically.
The dynamics of a dissipative two-level system in a monochromatic field is studied numerically using an iterative path integral scheme that is based on the finite memory range of dissipative influence functionals. The focus of the paper is on the interplay between dissipation and field-induced localization or coherent tunneling. In accord with recent predictions based on approximate treatments, we find that weak dissipation can stabilize the localized state while strong dissipation destroys it. We also demonstrate the possibility of inducing and maintaining large-amplitude coherent oscillations by exploiting the phenomenon of quantum stochastic resonance. (c) 1995 The American Physical Society
The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.
We investigate how the combined effects of strong Ohmic dissipation and monochromatic driving affect the stability of a quantum system with a metastable state. We find that, by increasing the coupling with the environment, the escape time makes a transition from a regime in which it is substantially controlled by the driving, displaying resonant peaks and dips, to a regime of frequency-independent escape time with a peak followed by a steep falloff. The escape time from the metastable state has a nonmonotonic behavior as a function of the thermal-bath coupling, the temperature, and the frequency of the driving. The quantum noise-enhanced stability phenomenon is observed in the investigated system.
The tunneling dynamics of a dissipative two-level system that is strongly driven by elliptically polarized electric fields is investigated. The dissipative dynamics is governed within the noninteracting-blip-approximation for the stochastic forces by a generalized master equation (GME). With the focus being on viscous friction, we compare exact numerical solutions of the GME with analytical approximations to both the transient and the asymptotic, long-time periodic dynamics. Novel phenomena are identified: These are a selective control on localization (or, as well, on delocalization) of the tunneling dynamics, or the inversion of an initially induced localization by a static bias via multiphoton-assisted tunneling. These effects can be selectively tuned as a function of the eccentricity parameter p=Ey/Ex of corresponding field amplitudes. In particular, the case of a circularly polarized driving field with p=±1 yields a dramatic enhancement of the relaxation rate at resonances, when an integer multiple of the angular driving frequency matches the asymmetry energy induced by a static bias.
We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such dynamics: (1) the collapse and revival of oscillations in the population difference, (2) the simple exponential decay of the oscillations resulting in their steady state with the finite amplitude, and (3) the steady-state stabilization of the equally populated levels. The nonmonotonic Bessel-function-like dependence on the driving strength is also predicted for the decay rate of these oscillations. The features of this dependence are determined by the relative rates of energetic relaxation and pure dephasing.