Driven nonlinear photonic cavities are widely studied because they exhibit many interesting effects, such as nonreciprocity, thermal effects, and frequency conversion. Specifically, adding noise to a modulated nonlinear system can lead to stochastic resonance (SR), which corresponds to periodic transitions between stable states. In this work, we study the outgoing power and spectra from a nonlinear-driven photonic cavity coupled to an external port. Using a Langevin framework, we show that the system temperature induces SR in the bistable regime, which we study in detail to exploit for enhanced frequency shift. In this way, the thermal fluctuations of the system itself can function as a driver for effective sideband generation, enabling shift efficiencies of up to 40%. We extensively explore various regimes in order to understand and maximize the process.
Driven nonlinear photonic cavities are widely studied because they exhibit many interesting effects, such as nonreciprocity, thermal effects, and frequency conversion. Specifically, adding noise to a modulated nonlinear system can lead to stochastic resonance (SR), which corresponds to periodic transitions between stable states. In this work, we study the outgoing power and spectra from a nonlinear-driven photonic cavity coupled to an external port. Using a Langevin framework, we show that the system temperature induces SR in the bistable regime, which we study in detail to exploit for enhanced frequency shift. In this way, the thermal fluctuations of the system itself can function as a driver for effective sideband generation, enabling shift efficiencies of up to 40%. We extensively explore various regimes in order to understand and maximize the process.
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.
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.
Understanding nonequilibrium transport and fluctuations driven by nonclassical light in nonlinear quantum optical systems is challenging. Here, we formulate a driven quantum master equation in the rotating frame combined with full counting statistics, retaining the drive-induced frequency shifts in the system-reservoir interactions and providing a unified description of drive-assisted incoherent transitions based on the rotated system dressed-basis. Applied to a Kerr resonator and a nonlinear Jaynes-Cummings model, the approach reveals pronounced multiphoton-resonant enhancement of the drive input energy current, with significant high peaks under two-photon driving compared to the single-photon case. The two-photon resonance relations are analytically obtained. Resonance structure in the nonlinear Jaynes-Cummings model nonlinearly relies on qubit-photon couplings, with additional dressed-state branches. A low-energy-state approximation attributes the resonant current enhancement to dressed-state hybridization and efficient activation of incoherent energy exchange processes. Beyond the average current, two-photon-driving induced energy exchange picture near resonance also substantially modifies the second-order current fluctuation and higher-order current cumulant, while increasing the time-normalized signal-to-noise ratio. Adding two-photon loss introduces extra incoherent photon-pair exchange pathways and further reshapes the current and its fluctuations. We hope these results may deepen interpretation of photon driving and quantum dissipation cooperatively governing nonequilibrium energy transport and fluctuations.
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.
Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well-described as ``Markovian,'' meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these system, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics should in the future lead to even richer possibilities than those discussed here for both classical and quantum light manipulations.
In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.