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arXiv:quant-ph/0001102 · Physical Review A

Quantum stochastic resonance in electron shelving

Susana F. Huelga, Martin Bodo Plenio

Published Oct 17, 2000• 25 citations
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Abstract

Stochastic resonance shows that under some circumstances noise can enhance the response of a system to a periodic force. While this effect has been extensively investigated theoretically and demonstrated experimentally in classical systems, there is complete lack of experimental evidence within the purely quantum-mechanical domain. Here we demonstrate that stochastic resonance can be exhibited in a single ion and would be experimentally observable using well mastered experimental techniques. We discuss the use of this scheme for the detection of the frequency difference of two lasers to demonstrate that stochastic resonance may have applications in precision measurements at the quantum limit.

DOI
10.1103/physreva.62.052111

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Stochastic resonance shows that under some circumstances noise can enhance the response of a system to a periodic force. While this effect has been extensively investigated theoretically and demonstrated experimentally in classical systems, there is complete lack of experimental evidence within the purely quantum-mechanical domain. Here we demonstrate that stochastic resonance can be exhibited in a single ion and would be experimentally observable using well mastered experimental techniques. We discuss the use of this scheme for the detection of the frequency difference of two lasers to demonstrate that stochastic resonance may have applications in precision measurements at the quantum limit.
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.
By means of a physically interesting example, it is shown how the mathematical theory of quantum stochastic calculus can be used in modelling physical systems. The example is the so-called electron shelving effect. The fluorescent light emitted by a single atom or ion presents periods of darkness if two transitions, one weak and one strong, are simultaneously driven. By a previously developed theory of counting processes, based on quantum stochastic differential equations, the full statistics of the emitted photons is obtained. In particular, the results on the duration of bright and dark periods, previously obtained by Cohen-Tannoudji and Dalibard (1986), are completely confirmed.
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.
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.
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.