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arXiv:1911.00463 · Physical Review Letters

Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity

Z. Geng, K. J. H. Peters, Aurelien A. P. Trichet, Kiana Malmir, Radosław Kołkowski, Jason M. Smith, S. R. K. Rodríguez

Published Apr 15, 2020• 39 citations
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Abstract

We investigate, experimentally and theoretically, the dynamics of a laser-driven cavity with noninstantaneous effective photon-photon interactions. Scanning the laser-cavity frequency detuning at different speeds across an optical bistability, we find a hysteresis area that is a nonmonotonic function of the speed. In the limit of fast scans comparable to the memory time of the interactions, we demonstrate that the hysteresis area decays following a universal power law with scaling exponent -1. We further demonstrate a regime of non-Markovian dynamics emerging from white noise. This regime is evidenced by peaked distributions of residence times in the metastable states of our system. Our results offer new perspectives for exploring the physics of scaling, universality, and metastability, in non-Markovian regimes using arrays of bistable optical cavities with low quality factors, driven by low laser powers, and at room temperature.

DOI
10.1103/physrevlett.124.153603

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We experimentally explore the dynamical optical hysteresis of a semiconductor microcavity as a function of the sweep time. The hysteresis area exhibits a double power law decay due to the influence of fluctuations, which trigger switching between metastable states. Upon increasing the average photon number and approaching the thermodynamic limit, the double power law evolves into a single power law. This algebraic behavior characterizes a dissipative phase transition. Our findings are in good agreement with theoretical predictions for a single mode resonator influenced by quantum fluctuations, and the present experimental approach is promising for exploring critical phenomena in photonic lattices.
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The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature are studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics are completely determined by the propagating (retarded) and correlation Green functions. Comparing the non-Markovian behavior at finite temperature with those at the zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory effect can dramatically change the coherent and thermal dynamics of the cavity. We also numerically study the dissipation dynamics of the cavity through the mean mode amplitude decay and the average photon number decay in the microwave regime. It is shown that the strong coupling between the cavity and the reservoir results in a long-time dissipationless evolution to the cavity field amplitude, and its noise dynamics undergo a critical transition from the weak to the strong coupling due to the non-Markovian memory effect.
In this paper we discuss the influence of laser fluctuations on the hysteresis cycle in Optical Bistability. For the simplest case of an Absorptive Optical Bistability in a good cavity driven by an external laser light with non-white Gaussian amplitude fluctuations we derive a Fokker-Planck equation in the limit of large laser linewidth and good amplitude stabilization. This Fokker-Planck equation has a nonconstant diffusion term which shifts the most probable values of the steady state probability distribution from its deterministic positions. From the form of the steady state solution of the Fokker-Planck equation with non-white amplitude fluctuations we discuss the relative stability of the bistable branches. As in the case of quantum fluctuations the random amplitude of the laser field leads to a small range of values of the injected laser intensity in which the two bistable peaks have a comparable area. The transmitted field averaged with respect to the stationary distribution function coincides with one of the two deterministic branches except on the narrow transition region where we have large fluctuations.
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 systems, 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.