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arXiv:quant-ph/0608164 · Physical Review Letters

Stochastic Resonance Phenomena in Quantum Many-Body Systems

Susana F. Huelga, Martin Bodo Plenio

Published Apr 24, 2007• 70 citations
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Abstract

We discuss stochastic resonance (SR) effects in driven coupled quantum systems. We construct dynamical and information-theoretic measures of the system's response that exhibit a nonmonotonic behavior as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations and identify parameter regimes where the breakdown of a linear response can be linked 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 is enhanced as a result of nearest-neighbor coupling. These results enlarge the domain where SR effects exist and should be observable in arrays of superconducting qubits.

DOI
10.1103/physrevlett.98.170601

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We discuss stochastic resonance (SR) effects in driven coupled quantum systems. We construct dynamical and information-theoretic measures of the system's response that exhibit a nonmonotonic behavior as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations and identify parameter regimes where the breakdown of a linear response can be linked 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 is enhanced as a result of nearest-neighbor coupling. These results enlarge the domain where SR effects exist and should be observable in arrays of superconducting qubits.
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.
We discuss stochastic resonance–like effects in the context of coupled quantum spin systems. We focus here on an information–theoretic approach and analyze the steady state quantum correlations (entanglement) as well as the global correlations in the system when subject to different forms of local decoherence. In the presence of decay, it has been shown that the system displays quantum correlations only when the noise strength is above a certain threshold. We extend this result to the case of a Heisenberg XY Z exchange interaction and revise and clarify the mechanisms underlying this behaviour. In the presence of pure dephasing, we show that the system always remains separable in the steady state. When both types of noise are present, we show that the system can still exhibit entanglement for long times, provided that the pure dephasing rate is not too large.
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 analyze quantum correlations arising in two coupled dimer systems in the presence of independent losses and driven by a fluctuating field. For the case of the interaction being of a Heisenberg exchange type, we first analytically show the possibility for stationary entanglement and then analyze its robustness as a function of the signal-to-noise ratio of the pump. We find that for a common fluctuating driving field, stochastic resonance effects appear as function of the ratio between field strength and noise strength. The effect disappears in the case of uncorrelated or separate pumps. Our result is general and could be applied to different quantum systems ranging from electron spins in solid state, to ions trap technologies and cold atom set ups.
The quantum dynamics of chains of superconducting qubits is analyzed under realistic experimental conditions. Electromagnetic fluctuations due to the background circuitry, finite temperature in the external environment, and disorder in the initial preparation and the control parameters are taken into account. It is shown that the amount of disorder that is typically present in current experiments does not affect the entanglement dynamics significantly. However, the effect of the environmental noise can modify entanglement generation and propagation across the chain. We study the persistence of coherent effects in the presence of noise and possible ways to efficiently detect the presence of quantum entanglement. We also discuss under which circumstances the system exhibits steady state entanglement for both short (N<10) and long (N>30) chains and show that there are parameter regimes where the steady state entanglement is strictly non-monotonic as a function of the noise strength. We present optimized schemes for entanglement verification and quantification based on simple correlation measurements that are experimentally more economic than state tomography.
We investigate the possibility of appearance of new phenomena derived from the influence of noise on quantum systems. As a starting point we study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement due to the noise. The new effect is that for particular initial states the time of disentanglement depends in a non-monotonous way on the strength of the noise. We find that it is shortest for an intermediate strength value of the noise. This we call "stochastic anti-resonance." Our new result indicates that there are noise values which are particularly harmful and should be avoided. This could lead to a better understanding of noisy perturbations and their role for optimal designing of quantum devices.