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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Control of dissipative tunneling dynamics by continuous wave electromagnetic fields: Localization and large-amplitude coherent motion

Dmitrii E. Makarov, Nancy Makri

Published Dec 1, 1995• 59 citations
Publisher

Abstract

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

DOI
10.1103/physreve.52.5863

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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
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.
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.
The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is studied from the viewpoint of quantum optics by considering the photon statistics of a single mode cavity field which is strongly coupled to a two-level tunneling system (TS). As a function of the interaction time between TS and cavity the photon statistics displays the tunneling dynamics. In the semiclassical limit of high photon occupation number n, coherent destruction of tunneling is exhibited in a slowing down of an amplitude modulation for certain parameter ratios of the field. The phenomenon is explained as arising from interference between displaced number states in phase space which survives the large n limit due to identical ${\mathit{n}}^{\mathrm{\ensuremath{-}}1/2}$ scaling between orbit width and displacement. \textcopyright{} 1996 The American Physical Society.
We have studied the real-time dynamics of dissipative tunneling between two coupled diabatic surfaces. The interplay of tunneling, vibrational relaxation, dephasing, and resonances leads to various regimes of population dynamics, from coherent oscillations between the surfaces to exponential decay described by a rate constant. To describe these phenomena, we exploited recent efficient discretized-path-integral techniques; the two-surface system is treated exactly using a numerically constructed propagator, while the effects of the dissipative environment are incorporated through an influence functional. This procedure results in a low-dimensional integral, which is evaluated by quadrature. Use of a discrete-variable representation (DVR) allows us to replace continuous paths by paths that sample a small set of coordinate points; in particular, the conventional two-level-system approximation is shown to correspond to the limit of two DVR points. The specific features pertinent to nonadiabatic tunneling are discussed.
Coherent tunneling can be suppressed or enhanced by exciting a vibrational mode coupled to the tunneling coordinate. The localization in a two-level system (TLS) driven by a periodic force is obtained as a semiclassical limit for such a mode. We derive and test a semiclassical quantization rule that relates the quasienergies of a classically driven TLS with the energy splittings in the model of a TLS coupled to a quantum oscillator. The dissipative stabilization of a quasilocalized state and the possibility of localization by a quasiperiodic force are analyzed from this perspective.