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Journal of Modern Optics

The noise makes the signal: What a small fry should know about stochastic resonance

Vyacheslav Shatokhin, Thomas Wellens, Andreas Buchleitner

Published Apr 1, 2004• 3 citations
Publisher

Abstract

We are traditionally educated to consider noise a nuisance, hindering the transmission and detection of signals. Recently, however, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, the appropriate amount of noise can facilitate signal detection in noisy environments. Due to its simplicity and robustness, SR has been implemented by mother nature on almost any scale, from celestial mechanics to ion channels. The present mini-review outlines the basic mechanism underlying SR phenomena, and discusses recent quantum optical scenarios, in the deep quantum regime.

DOI
10.1080/09500340408233602

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We are traditionally educated to consider noise a nuisance, hindering the transmission and detection of signals. Recently, however, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, the appropriate amount of noise can facilitate signal detection in noisy environments. Due to its simplicity and robustness, SR has been implemented by mother nature on almost any scale, from celestial mechanics to ion channels. The present mini-review outlines the basic mechanism underlying SR phenomena, and discusses recent quantum optical scenarios, in the deep quantum regime.
Understanding the effect of noise on light’s behavior is crucial, as light plays a central role in the study of many systems. This thesis explores the interplay between light, matter, and noise, demonstrating how this interaction can lead to fascinating phenomena and practical applications in sensing, signal transmission, and computing. Chapter 1 provides an overview of the history of noise in physical systems and fundamental discoveries that shaped our understanding of noisy systems. The focus then shifts to optical systems, particularly nanophotonic sensors and devices, and introduces a basic model describing nonlinear optical resonators, pivotal in modern photonics. Chapter 2 delves into the stochastic dynamics of light in a coherently-driven Kerr-nonlinear optical cavity, drawing analogies between light dynamics in the cavity and Brownian particles in a scalar potential. While this analogy holds in linear, on-resonance conditions, it breaks down in nonlinear or off-resonance scenarios due to non-conservative forces. An effective equilibrium description is proposed, providing accurate results in limited regimes but failing in deep bistability. This breakdown is marked by significant changes in the intra-cavity field fluctuation spectrum. Our findings lay the groundwork for an effective thermodynamic description of coherently driven cavities, bridging stochastic thermodynamics and resonant optics. Chapter 3 introduces an innovative optical sensing approach using a single-mode Kerr-nonlinear resonator, achieving exceptional precision at a square-root singularity. This sensor leverages the dynamic hysteresis of the resonator, with intensity splitting at hysteresis endpoints scaling with the square root of perturbation strength. This novel method enhances sensing precision even in noisy environments and overcomes the traditional trade-off between precision and averaging time. Chapter 4 presents the first experimental demonstration of non-Markovian stochastic resonance (SR), showing how memory effects from a non-instantaneous nonlinear response can broaden the SR bandwidth significantly. We imprint a signal on a laser by modulating the cavity length of a thermo-optical cavity. SR is evidenced by a peak in the signal-to-noise ratio as a function of noise variance. Our insights suggest broader implications for noise-assisted processes in various natural and engineered systems with a non-instantaneous response. Chapter 5 and 6 explore complex dynamics emerging from memory effects in nonlinear resonators. Memory effects lead to stable limit cycles and self-sustained oscillations, both in nonlinear optical and mechanical systems. We demonstrate that memory effects can greatly enhance the ability of a nonlinear mechanical resonator to harvest energy from ambient vibrations. Chapter 7 challenges the belief that enhancing clock precision requires more energy, demonstrating that precision can be altered at constant energy by varying laser-cavity detuning in a laser-driven thermo-optical dimer. Stochastic simulations show that detuning changes the limit cycle's confining potential and the phase diffusion strength, explaining the changes in precision. Finally, Chapter 8 demonstrates enhanced performance of an all-optical flip-flop by leveraging noise, reducing switching energy by approximately 90% while maintaining 95% reliability. This approach uses noise as a resource, improving energy efficiency and reliability in optical systems and potentially extending to other platforms. Our findings pave the way for computational devices utilizing ambient fluctuations as a resource.
This paper proposes a novel approach to quantum sensing that fundamentally shifts the perspective on quantum noise. Instead of viewing it as an unwanted disturbance, we argue that quantum noise is a critical resource for extracting subtle environmental information. The core concept involves designing a quantum sensor that leverages the statistical properties of quantum noise to precisely measure and interpret its distribution, ultimately enabling the detection of extremely weak signals. This approach moves beyond traditional quantum sensing methodologies which often rely on minimizing noise. We present a theoretical framework and mathematical formalism for this concept, outlining the principles of operation and potential performance characteristics. The underlying mechanism hinges on the ability to correlate the statistical fluctuations of quantum noise with the underlying environmental signal. This work represents a significant departure from conventional thinking and offers a new paradigm for quantum sensing technology. ---
Stochastic resonance (SR) is experimentally demonstrated in an atomic optical bistable system consisting of three-level atoms in $\ensuremath{\Lambda}$-type configuration confined in an optical ring cavity. The optical bistable system with enhanced Kerr nonlinearity due to atomic coherence is driven by a periodic signal and a Gaussian white noise source with variable amplitude, and displays an improved output signal-to-noise ratio, a characteristic signature of SR. The measured results match qualitatively with the theoretical predictions of the generic model for the SR phenomenon.
A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation.