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

Dynamics of the dissipative two-state system under ac modulation of bias and coupling energy

Milena Grifoni

Published Oct 1, 1996• 13 citations
Publisher

Abstract

We consider a driven dissipative two-state system subject to periodic modulation of both of its two parameters. The exact master equation that governs the dynamics is derived. Closed form analytical solutions are presented within the noninteracting-blip approximation for the stochastic forces, and for the exactly solvable case $\ensuremath{\alpha}=\frac{1}{2}$ of the Ohmic viscosity. We apply these results to a tight-binding particle with zero intrinsic bias. Selection rules are obeyed for arbitrary dissipation. For Ohmic dissipation, the effects of fast asymmetry modulation result in an overall reduction of quantum coherence and in a possible localization. On the contrary, a multiplicative modulation of the tunneling coupling leads to an exponential enhancement of tunneling.

DOI
10.1103/physreve.54.r3086

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We consider a driven dissipative two-state system subject to periodic modulation of both of its two parameters. The exact master equation that governs the dynamics is derived. Closed form analytical solutions are presented within the noninteracting-blip approximation for the stochastic forces, and for the exactly solvable case \ensuremathα=12\ensuremath{\alpha}=\frac{1}{2}\ensuremathα=21​ of the Ohmic viscosity. We apply these results to a tight-binding particle with zero intrinsic bias. Selection rules are obeyed for arbitrary dissipation. For Ohmic dissipation, the effects of fast asymmetry modulation result in an overall reduction of quantum coherence and in a possible localization. On the contrary, a multiplicative modulation of the tunneling coupling leads to an exponential enhancement of tunneling.
The time-dependent average population in a two-level system interacting with an Ohmic boson bath and driven by a dc-ac field is obtained. The study is performed within the noninteracting-blip approximation and for the high-frequency driving case. The integro-differential master equation and the exact formal solution for the average transition probability are obtained. The dissipative quantum decay and the transition temperature from the coherent to the incoherent motion are investigated. The effect of the external electric field on the the dissipative two-level system is found to destroy its coherence.
We study the nonlinear response of a periodically driven dissipative two-state system. The exact formal solution in the form of a series in the number of system transitions is derived. The series is summed in analytic form in the parameter region where incoherent transitions prevail. We also present the exact solution for the time evolution of the system in the entire region of temperatures and driving strength for a special value of the Ohmic viscosity. The destruction of quantum coherence by incoherent processes which are induced by the fluctuating and the driving forces is discussed on the basis of these solutions.
The dynamics of the density matrix of the two-state system under the influence of time-dependent deterministic and fluctuating forces is investigated. The exact formal solutions for the diagonal and off-diagonal elements are derived and transformed into coupled nonconvolutive master equations and integral relations. Thereby, the evolution of any observable relevant to the two-state system may be described. Solutions of the dynamical equations in analytic form are presented both for high and low temperatures. An iterative numerical method is put forward in which the familiar noninteracting-blip approximation is systematically improved by taking into account all bath-induced nearest-neighbor interblip correlations. The expanded treatment is found to be indispensable in studies of the dynamics of the off-diagonal elements at low temperatures. Finally, we discuss selection rules, as well as possibilities of control of tunneling, which occur in the presence of monochromatic driving.
We study the quantum dynamics of a periodically driven biased two-state system which additionally is subject to either Ohmic or to frequency-dependent damping. Within the noninteracting-blip approximation for the stochastic forces, the solution is given in terms of a series which is defined by recursion relations. Avoiding rotating wave and Markovian approximation, we deduce the solution in closed form for the important cases of high- and low-frequency driving. For low-frequency driving, the dynamics is governed by a rate equation with a time-dependent rate and with a time-dependent adiabatic equilibrium state. In the high-frequency case, we find novel cooperative effects, such as resonances in the spectral distribution near fractional values of the static detuning energy.
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.
Dynamics of a two-level system with Ohmic dissipation driven by a time-dependent cw field in the noninteracting-blip approximation are studied. It is found that at low temperatures when \ensuremath{\alpha}, a friction parameter, lies between 1/2 and 1, the localization predicted by Chakravarty [Phys. Rev. Lett. 49, 681 (1982)] and Bray and Moore [Phys. Rev. Lett. 49, 1546 (1982)] disappears, and the rate constant for tunneling of the particle increases with the intensity and frequency of the field. For 01/2 quantum coherence is observed, and the transition temperature from the coherent to the decay regime depends on the field intensity. When the intensity parameter approaches the zeros of the zeroth Bessel function coherence disappears. This transition from coherent to incoherent motion oscillates with the intensity of the field, giving rise to a cascade of transitions at different temperatures.