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AIP conference proceedings

Forced synchronization of a quantum dissipative dynamics

Igor Goychuk, Jesús Casado‐Pascual, Manuel Morillo, J. Lehmann, Peter Hänggi A

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We generalize the phenomenon of forced stochastic synchronization into the quantum domain within the framework of a paradigmatic spin‐boson model (tunneling charge, or flipping spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero‐temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.

DOI
10.1063/1.2759730

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We generalize the phenomenon of forced stochastic synchronization into the quantum domain within the framework of a paradigmatic spin‐boson model (tunneling charge, or flipping spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero‐temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.
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.
We demonstrate that the stochastic resonance phenomenon can occur in a pure quantum regime for a wider class of microscopic systems described by a dissipative anharmonic oscillator driven by two periodic forces. We apply a quantum-state diffusion method, and display the synchronization of quantum trajectories by the stochastic resonance process. The model proposed is accessible for experiments, and results in the formation of quantum states of the anharmonic oscillator, namely sub- and super-Poissonian statistics for time intervals exceeding the relaxation rate. We show that stochastic resonance phenomenon can be described in terms of the minimization of the quantum von Neuman entropy, and demonstrate the possibility of controlling both the dissipative dynamics and quantum statistics of anharmonic oscillator by two external periodic forces.
We report the observation of quantum stochastic synchronization (QSS) in a dissipative quantum system---a moderately damped current-biased Josephson junction. We show that when the junction is biased subcritically by a combination of a constant current and a small sinusoidal modulation signal, forced phase synchronization between the otherwise random, incoherent quantum tunneling and the signal may arise as a consequence of the interplay between quantum fluctuation and the weak periodic drive. It is found that optimal synchronization occurs at a signal frequency fQSS{f}_{\text{QSS}}fQSS​ that is comparable to the quantum tunneling rate. We also find a phenomenon called ``modulation induced suppression of quantum noise'': for signal frequency well below fQSS,{f}_{\text{QSS}},fQSS​, the power spectral density of escape time distribution of the junction could be reduced substantially from the floor level of the unmodulated system. Furthermore, we demonstrate that the application of a small signal with proper phase can suppress the average tunneling rate and enhance the stability of the metastable system. Our experimental results agree well with the numerical calculations without the use of adjustable parameters.
In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.
Abstract The zero and finite temperature tunneling dynamics of a periodically driven particle moving in a bistable potential with a fluctuating barrier is studied. We have focused on the influence of barrier fluctuation and thermal modulation on the tunneling processes in the presence of a driving field. At zero temperature, for a fixed strength of the driving field, both the tunneling probability and rate passes through a well‐defined minimum when plotted as a function of fluctuation frequency while it reveals a clear maximum as a function of driving frequency. However, at T > 0 the tunneling probability and rate show two maxima as a function of both fluctuation frequency and driving frequency. In both zero and finite temperature, the tunneling rate constant decreases with increasing fluctuation strength. So, the barrier fluctuation may enhance the stability of a periodically driven system. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
Abstract We explore dissipative quantum tunnelling, a phenomenon central to various physical and chemical processes, utilizing a model based on a double-well potential. This paper aims to bridge gaps in understanding the crossover from thermal activation to quantum tunnelling, a domain still shrouded in mystery despite extensive research. By numerically investigating a model derived from Caldeira–Leggett’s work on quantum Brownian motion, examining both Lindblad and stochastic Schrödinger dynamics, we offer new insights into the transition states in the crossover region. Contrary to a common belief that temperature strongly dampens all quantum effects, our findings reveal that under certain conditions temperature instead alters the nature of tunnelling from a deterministic and periodic process to a stochastic yet still very quantum phenomenon. This underscores the profound influence of quantum effects on transition rates and the critical role of temperature in modulating tunnelling behaviours. Additionally, we introduce a new model for quantum Brownian motion that takes Lindblad form and is formulated as a modification of the widely known model found in Breuer and Petruccione. In our approach, we remove the zero-temperature singularity resulting in a better description of low-temperature quantum Brownian motion near a potential minima. Despite these advancements, we recognize persistent challenges in accurately simulating the dynamics at extremely low temperatures for arbitrary potentials, particularly those that cannot be closely approximated locally by a quadratic function.