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Journal of Physics B Atomic Molecular and Optical Physics

Effects of periodic driving on asymmetric two-level systems coupled to dissipative environments

Garo Taft, Nancy Makri

Published Jan 28, 1998• 19 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/31/2/005

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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.
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 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.
We investigate Landau-Zener processes modeled by a two-level quantum system, with its finite bias energy varied in time and in the presence of a single broadened cavity mode at zero temperature. By applying the hierarchy equation method to the Landau-Zener problem, we computationally study the survival fidelity of adiabatic states without Born, Markov, rotating-wave, or other perturbative approximations. With this treatment it also becomes possible to investigate cases with very strong system-bath coupling. Different from a previous study of infinite-time Landau-Zener processes, the fidelity of the time-evolving state as compared with instantaneous adiabatic states shows nonmonotonic dependence on the system-bath coupling and on the sweep rate of the bias. We then consider the effect of applying a counterdiabatic driving field, which is found to be useful in improving the fidelity only for sufficiently short Landau-Zener processes. Numerically exact results show that different counterdiabatic driving fields can have very different robustness against environment effects. Lastly, using a case study, we discuss the possibility of introducing a dynamical decoupling field in order to eliminate the decoherence effect of the environment and, at the same time, to retain the positive role of a counterdiabatic field. Our work indicates that finite-time Landau-Zener processes with counterdiabatic driving offer a fruitful testbed to understand controlled adiabatic processes in open systems.
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.
A discretized path integral formulation of the real-time dynamics applicable to a general external field is derived for the driven spin-boson model to extend the recently developed real-time Quantum Monte Carlo algorithm to driven systems. Numerical results are obtained for a monochromatic periodic driving force and Ohmic dissipation with a high-frequency cutoff. The impact of an external driving field on the dissipative dynamics is examined for systems with a time-dependent bias as well as a time-dependent interstate coupling matrix element. This method is easily generalized to multistate tight-binding models.
We investigate the dynamics of Landau-Zener (LZ) transitions in an anisotropic, dissipative three-level LZ model (3-LZM) using the numerically accurate multiple Davydov D2Ansatz in the framework of the time-dependent variational principle. It is demonstrated that a non-monotonic relationship exists between the Landau-Zener transition probability and the phonon coupling strength when the 3-LZM is driven by a linear external field. Under the influence of a periodic driving field, phonon coupling may induce peaks in contour plots of the transition probability when the magnitude of the system anisotropy matches the phonon frequency. The 3-LZM coupled to a super-Ohmic phonon bath and driven by a periodic external field exhibits periodic population dynamics in which the period and amplitude of the oscillations decrease with the bath coupling strength.