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

Dissipative quantum tunneling of two-level systems driven by dc-ac fields

Hao Wang, V. N. Freire, Xian-Geng Zhao

Published Aug 1, 1998• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.58.2632

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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.
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.
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.
The dynamical behavior of a two-level system coupled linearly to a dissipative bath of two-level systems whose tunneling splittings and coupling parameters are distributed according to an Ohmic spectrum is studied using numerical path integral methods as well as the noninteracting blip approximation for an equivalent harmonic environment characterized by a scaled spectral density. Comparisons with the behaviors of the conventional spin-boson model of similar coupling strength reveal a weaker quenching of coherence in the present case. Finally, the boundary in parameter space between coherent and incoherent dynamics is mapped.
We study the dissipative dynamics of a two-level system (TLS) exposed to strong ac driving. By combing Floquet theory with Van Vleck perturbation theory in the TLS tunneling matrix element, we diagonalize the time-dependent Hamiltonian and provide corrections to the renormalized Rabi frequency of the TLS, which are valid for both a biased and unbiased TLS and go beyond the known high-frequency and rotating-wave results. In order to mimic environmental influences on the TLS, we couple the system weakly to a thermal bath and solve analytically the corresponding Floquet-Bloch-Redfield master equation. We give a closed expression for the relaxation and dephasing rates of the TLS and discuss their behavior under variation of the driving amplitude. Further, we examine the robustness of coherent destruction of tunneling (CDT) and driving-induced tunneling oscillations (DITO). We show that also for a moderate driving frequency an almost complete suppression of tunneling can be achieved for short times and demonstrate the sensitiveness of DITO to a change of the external parameters.
We study the dissipative dynamics of a two-level system (TLS) exposed to strong ac driving. By combining Floquet theory with Van Vleck perturbation theory in the TLS tunneling matrix element, we diagonalize the time-dependent Hamiltonian and provide corrections to the renormalized Rabi frequency of the TLS, which are valid for both a biased and unbiased TLS and go beyond the known high-frequency and rotating-wave results. In order to mimic environmental influences on the TLS, we couple the system weakly to a thermal bath and solve analytically the corresponding Floquet-Bloch-Redfield master equation. We give a closed expression for the relaxation and dephasing rates of the TLS and discuss their behavior under variation of the driving amplitude. Further, we examine the robustness of coherent destruction of tunneling (CDT) and driving-induced tunneling oscillations (DITO). We show that also for a moderate driving frequency an almost complete suppression of tunneling can be achieved for short times and demonstrate the sensitiveness of DITO to a change of the external parameters.
The quantum behaviour of electrons in a two-level system under the influence of an AC-DC field is investigated. The closed-form solution of quasienergy is obtained, from which the exact level crossing is found to appear at a fan structure in the section (E, E 0 ) through the parameter space (E, E 0 , omega ), where E is the magnitude of the AC field, E 0 is the magnitude of the DC field, and omega is the frequency of the AC field. It is demonstrated that the emergence of the exact crossing of quasienergies is coincident with the onset of coherent destruction of tunnelling.