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arXiv:1908.05521 · Physical Review Applied

Enhancing the Speed and Sensitivity of a Nonlinear Optical Sensor with Noise

S. R. K. Rodríguez

Published Feb 13, 2020• 18 citations
arXivHTMLPDF

Abstract

We demonstrate how noise can be turned into a resource for optical sensing using a nonlinear cavity. The cavity is driven by a continuous-wave laser into the regime of optical bistability. Due to the influence of fluctuations, the cavity switches randomly between two metastable states. By analyzing the residence times in these two states, perturbations to the resonance frequency of the cavity can be detected. Here, such an analysis is presented as a function of the strength of the perturbation and of the noise. By increasing the standard deviation of the noise, we find that the detection speed increases monotonically while the sensitivity peaks at a finite value of the noise strength. Furthermore, we discuss how noise-assisted sensing can be optimized in state-of-the-art experimental platforms, relying solely on the minimum amount of noise present in the cavity due to its dissipation. These results open up new perspectives for the ultrafast detection of nanoparticles, contaminants, gases, or other perturbations to the resonance frequency of an optical resonator, at low powers and in noisy environments.

DOI
10.1103/physrevapplied.13.024032

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We demonstrate how noise can be turned into a resource for optical sensing using a nonlinear cavity. The cavity is driven by a continuous-wave laser into the regime of optical bistability. Due to the influence of fluctuations, the cavity switches randomly between two metastable states. By analyzing the residence times in these two states, perturbations to the resonance frequency of the cavity can be detected. Here, such an analysis is presented as a function of the strength of the perturbation and of the noise. By increasing the standard deviation of the noise, we find that the detection speed increases monotonically while the sensitivity peaks at a finite value of the noise strength. Furthermore, we discuss how noise-assisted sensing can be optimized in state-of-the-art experimental platforms, relying solely on the minimum amount of noise present in the cavity due to its dissipation. These results open up new perspectives for the ultrafast detection of nanoparticles, contaminants, gases, or other perturbations to the resonance frequency of an optical resonator, at low powers and in noisy environments.
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.
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In practical sensing tasks, noise is usually regarded as an obstacle that degrades the sensitivity. Fortunately, stochastic resonance can counterintuitively harness noise to notably enhance the output signal-to-noise ratio in a nonlinear system. Although stochastic resonance has been extensively studied in various disciplines, its potential in realistic sensing tasks remains largely unexplored. Here, we propose and demonstrate a noise-enhanced microwave sensor using a thermal ensemble of interacting Rydberg atoms. Using the strong nonlinearity present in the Rydberg ensembles and leveraging stochastic noises in the system, we demonstrate the stochastic resonance driven by a weak microwave signal (from several microvolts per centimeter to millivolts per centimeter). A substantial enhancement in the detection is achieved, with a sensitivity surpassing that of a heterodyne atomic sensor by 6.6 decibels. Our results offer a promising platform for investigating stochastic resonance in practical sensing scenarios.
Weak material nonlinearity at optical frequencies poses a serious hurdle to realizing optical bistability at low optical powers, which is a critical component for digital optical computing. In this paper, we explore the cavity enhancement of the second-order optical nonlinearity in order to determine the feasibility of few photon optical bistability. Starting from a quantum optical formalism of a doubly resonant cavity (required to meet the condition of phase matching), we derive a dynamic classical model of a cavity that is bistable at the fundamental mode. We analyze the optical energy and the switching speed as a function of the cavity quality factors and mode volumes and identify the regime where only ten's of photons are required to perform the switching. An unusual trend in the switching speed is also observed, where the speed monotonically decreases as the cavity linewidth increases. This is ascribed to the increase in the switching gain with increasing cavity linewidth.
Avalanche-based detection of small perturbations is commonplace in precision measurement devices from Geiger counters to single-photon avalanche detectors. Here, we expand this principle to sensing of light waves below the quantum shot noise limit, demonstrating numerically how atomic clouds trapped in photonic cavities can exhibit non-perturbative sensitivity to changes in the cavity field when the cavity mode is tuned to a parity-prohibited transition. We find that, when pumped by a continuous-wave laser, the atomic cloud creates emissions which amplify the initially sub-shot-noise fluctuation by two orders of magnitude. Crucially, this amplification is broadly tunable with respect to frequency and independent of atomic energy structure. Even more strikingly, our amplification mechanism preserves the phase imparted on the atoms by the original ultra-weak light wave, marking a qualitative improvement over conventional protocols. Our finding has implications for both quantum state characterization and detection of weak classical signals.
We investigate the influence of noise present in the periodic input signal of a passive optically bistable element. The thermally induced absorption nonlinearity of CdS crystals is used to achieve optically bi- stable behavior. By measuring the signal-to-noise ratio (S/N) of the noisy modulated input signal and of the output signal the phenomenon of stochastic resonance is found: With increasing noise strength the S/N increases up to a maximum value corresponding to the above resonance and then decreases again. The S/N of a noisy input can be enhanced by up to approximately 6 dB with this system. Furthermore, the cases of sinusoidal and rectangular modulation of the bistable element are compared.