Quantum stochastic resonance in parallel

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 (α > 3/2), as measured by the dimensionless ohmic friction strength α. Moreover, the mutual information measure relates QSR within quantum linear response theory to the signal-tonoise-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 α > 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 α > 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 α < 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. ‡ On leave from Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine. New Journal of Physics 1 (1999) 14.1–14.14 PII: S1367-2630(99)03698-8 1367-2630/99/000014+14$19.50 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft