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New Journal of Physics

Quantum stochastic resonance in parallel

Igor Goychuk, Peter Hänggi A

Published Aug 27, 1999• 19 citations

Abstract

A study of (aperiodic) quantum stochastic resonance (QSR) in parallel is put forward. By doing so, a generally stochastic input signal is fed into an array of parallel dissipative quantum two-level systems (TLS) and its integral response is studied against increasing temperature. The response is quantified by means of an information-theoretic measure provided by the rate of mutual information per element and, in addition, by the cross-correlation between the information-carrying input signal and the output response. For ohmic-like quantum dissipation, both measures exhibit QSR for biased two-level systems. Our prime focus here, however, is on the case with zero asymmetry between the two localized stable states. We then find that the mutual information measure exhibits QSR only for sufficiently strong dissipation ( > 3/2), as measured by the dimensionless ohmic friction strength . Moreover, the mutual information measure relates QSR within quantum linear response theory to the signal-to-noise-ratio (SNR) , being independent of the input driving frequencies in this limit. In contrast, the cross correlation measure connects QSR to a genuine synchronization phenomenon . For a single symmetric TLS, aperiodic QSR is exhibited in the cross-correlation measure for a Gaussian exponentially correlated input signal for > 1 already. Upon feeding the aperiodic input signal into a parallel array of unbiased TLS's, QSR successively emerges above the critical ohmic dissipation strength > 1/2 with increasing number n of parallel units. Thus, QSR can occur in parallel despite the fact that it does not occur in each individual, unbiased, TLS for < 1. This paradoxical phenomenon - which can be tested with an array of bistable superconducting quantum interference devices - constitutes a true quantum effect: it is due to the power-law dependence on temperature of the tunnelling rate and the stochastic linearization of quantum fluctuations with increasing number of parallel units.

DOI: 10.1088/1367-2630/1/1/314

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A study of (aperiodic) quantum stochastic resonance (QSR) in parallel is put forward. By doing so, a generally stochastic input signal is fed into an array of parallel dissipative quantum two-level systems (TLS) and its integral response is studied against increasing temperature. The response is quantified by means of an information-theoretic measure provided by the rate of mutual information per element and, in addition, by the cross-correlation between the information-carrying input signal and the output response. For ohmic-like quantum dissipation, both measures exhibit QSR for biased two-level systems. Our prime focus here, however, is on the case with zero asymmetry between the two localized stable states. We then find that the mutual information measure exhibits QSR only for sufficiently strong dissipation ( > 3/2), as measured by the dimensionless ohmic friction strength . Moreover, the mutual information measure relates QSR within quantum linear response theory to the signal-to-noise-ratio (SNR) , being independent of the input driving frequencies in this limit. In contrast, the cross correlation measure connects QSR to a genuine synchronization phenomenon . For a single symmetric TLS, aperiodic QSR is exhibited in the cross-correlation measure for a Gaussian exponentially correlated input signal for > 1 already. Upon feeding the aperiodic input signal into a parallel array of unbiased TLS's, QSR successively emerges above the critical ohmic dissipation strength > 1/2 with increasing number n of parallel units. Thus, QSR can occur in parallel despite the fact that it does not occur in each individual, unbiased, TLS for < 1. This paradoxical phenomenon - which can be tested with an array of bistable superconducting quantum interference devices - constitutes a true quantum effect: it is due to the power-law dependence on temperature of the tunnelling rate and the stochastic linearization of quantum fluctuations with increasing number of parallel units.

We investigate the low-temperature quantum stochastic resonance (QSR) phenomenon in a two-level system (TLS) which is coupled to an Ohmic heat bath. In contrast to common belief we find that QSR occurs also for symmetric (i.e., unbiased) TLS's if the viscous friction parameter alpha exceeds a critical value: We demonstrate that with respect to the spectral power amplification measure QSR always occurs for alpha>1; in contrast, the output signal-to-noise ratio exhibits an amplification only for alpha>3/2.

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.

In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.

We discuss stochastic resonance (SR) effects in weakly driven coupled quantum systems. We show that both dynamical and information theoretic measures of the system's response can be introduced that exhibit a non-monotonic behaviour as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations, showing that there are parameter regimes where the breakdown of a linear response can be associated to the presence of entanglement. We also show that a chain of coupled spin systems can exhibit an array-enhanced response, where the sensitivity of a single resonator to a weak driving signal is enhanced as a result of the nearest-neighbour coupling. These results enlarge the domain where SR effects exist and should be observable in state-of-the-art arrays of superconducting qubits.

A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.

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

{f}_{\text{QSS}}

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

{f}_{\text{QSS}},

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.