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

Cooperative effects in the nonlinearly driven spin-boson system

Milena Grifoni, Maura Sassetti, Peter Hänggi A, Ulrich Weiß

Published Oct 1, 1995• 86 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.52.3596

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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.
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We investigate quantum stochastic resonance (QSR) in the periodically driven spin-boson system with Ohmic dissipation. For the special case \ensuremath{\alpha}=1/2 of the Ohmic coupling strength we present exact QSR results. For arbitrary Ohmic coupling, the amplitude and the phase of the nonlinear response function vs temperature are studied in a vast regime of temperatures and frequencies. It encompasses a dissipative-dominated incoherent tunneling regime, occurring at ``high'' temperatures and adiabatic driving, as well as coherent tunneling regimes, reached either at ``low'' temperatures or/and nonadiabatic frequencies. As a general feature, a principal maximum appears only in parameter regimes where incoherent tunneling dominates over coherent transitions. Moreover, for adiabatic driving, the nonlinear QSR exhibits a noise-induced suppression of higher harmonics accompanied by a characteristic phase change. \textcopyright{} 1996 The American Physical Society.
When an open quantum system is driven by an external time-dependent force, the coupling of the driving to the central system is usually included, whereas the impact of the driving field on the bath is neglected. We investigate the effect of a quantum bath of linearly driven harmonic oscillators on the relaxation dynamics of a quantum two-level system which is not directly driven. In particular, we calculate the frequency-dependent response of the system when the bath is subject to Dirac and Gaussian driving pulses. We show that a time-retarded effective force on the system is induced by the driven bath which depends on the full history of the perturbation and the spectral characteristics of the underlying bath. In particular, when a structured Ohmic bath with a pronounced Lorentzian peak is considered, the dynamical response of the system to a driven bath is qualitatively different than that of the undriven bath. Specifically, additional resonances appear which can be directly associated with a Jaynes-Cummings-like effective energy spectrum.