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Physical Review A

Stochastic resonance in quantum trajectories for an anharmonic oscillator

Hayk H. Adamyan, Suren B. Manvelyan, Gagik Yu. Kryuchkyan

Published Jan 5, 2001• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.63.022102

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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 propose an anharmonic oscillator driven by two periodic forces of different frequencies as a time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the framework of the statistical ensemble of quantum trajectories in a quantum state diffusion approach. The quantum dynamical manifestations of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement, are studied by numerical simulation of the ensemble averaged Wigner function and von Neumann entropy.
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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.
We consider a driven damped anharmonic oscillator that classically leads to a bistable steady state and to hysteresis. The quantum counterpart for this system has an exact analytical solution in the steady state that does not display any bistability or hysteresis. We use quantum-state diffusion theory to describe this system and to provide a new perspective on the lack of hysteresis in the quantum regime so as to study in detail the quantum to classical transition. The analysis is also relevant to measurements of a single periodically driven electron in a Penning trap where hysteresis has been observed.
We provide a detailed description of the response of an experimentally accessible, open, driven quantum system in its stationary state to a weak periodic signal. The system, a single mode of the quantized radiation field in coherent interaction with a sequence of two-level atoms and coupled to an environment of temperature T , is shown to exhibit stochastic resonance on output, under changes of T . Furthermore, at vanishing temperature, the transition rates between the metastable states of the radiation field remain finite and are set by the quantum noise level at . Consequently, signal enhancement and synchronization can be achieved even in this very quantum limit, for a properly tuned signal frequency.