We perform a systematic study of the temporal dynamics emerging in the asymmetrically driven dissipative Bose-Hubbard dimer model. This model successfully describes the nonlinear dynamics of photonic diatomic molecules in linearly coupled Kerr resonators coherently excited by a single laser beam. Such temporal dynamics may include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. We have thoroughly characterized such dynamical states, their origin, and their regions of stability by applying bifurcation analysis and dynamical system theory. This approach has allowed us to identify and classify the instabilities, which are responsible for the appearance of different types of temporal dynamics.

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Self-pulsing and chaos in the asymmetrically driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis.

Self-oscillation and bifurcation as many-body dynamics solutions in a high-Q microresonator have induced substantial interest in nonlinear optics and ultrafast science. Strong mode coupling between clockwise (CW) wave and counterclockwise (CCW) wave induces mode-splitting and optical self-oscillation in the optical cavity. This study experimentally demonstrates the self-oscillation microcomb formation in a microresonator with strong backward Rayleigh scattering. When a pump laser sweeps across a resonance, both spontaneous symmetry breaking (SSB) and self-oscillation phenomenon are observed. The breathing soliton and stable soliton state can switch to each other through careful tuning of the pump detuning. Our experiments provide a reliable scheme for breather soliton microcomb generation. Meanwhile, the rich physics process enhances the comprehension of nonlinear optics in a cavity.

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Experimental Demonstration of Self-Oscillation Microcomb in a Mode-Splitting Microresonator

We demonstrate neuron-like spiking dynamics in the asymmetrically driven dissipative photonic Bose-Hubbard dimmer model which describes two coupled nonlinear passive Kerr cavities. Spiking dynamics appear due to the excitable nature of the system. In this context, excitable excursions in the phase space correspond to spikes in the temporal evolution of the field variables. In our case, excitability is mediated by the destruction of an oscillatory state in a global homoclinic bifurcation. In this type of excitability (known as type-I) the period of the oscillatory state diverges when approaching the bifurcation. Beyond this point, the system exhibits excitable dynamics under the application of suitable perturbations. We have also characterized the effect that additive Gaussian noise has on the spiking dynamics, showing that the system undergoes a coherence resonance for a given value of the noise strength. 

/pdf/neuronlike-spiking-dynamics-in-asymmetrically-driven-w3is9be9.pdf

Neuronlike spiking dynamics in asymmetrically driven dissipative nonlinear photonic dimers

We demonstrate neuron-like spiking dynamics in the asymmetrically driven dissipative photonic Bose-Hubbard dimmer model which describes two coupled nonlinear passive Kerr cavities. Spiking dynamics appear due to the excitable nature of the system. In this context, excitable excursions in the phase space correspond to spikes in the temporal evolution of the ﬁeld variables. In our case, excitability is mediated by the destruction of an oscillatory state in a global homoclinic bifurcation. In this type of excitability (known as type-I) the period of the oscillatory state diverges when approaching the bifurcation. Beyond this point, the system exhibits excitable dynamics under the application of suitable perturbations. We have also characterized the eﬀect that additive Gaussian noise has on the spiking dynamics, showing that the system undergoes a coherence resonance for a given value of the noise strength.

We study the dynamics emerging in the photonic driven dissipative Bose-Hubbard model describing two coupled Kerr cavities. By bifurcation analysis we identify rich dynamics, including oscillatory states, chaotic dynamics as well as spikes.

Self-pulsing and chaos in nonlinear photonic dimers

We experimentally investigate the nonlinear dynamics of two coupled fiber ring resonators, coherently driven by a single laser beam. We comprehensively explore the optical switching arising when scanning the detuning of the undriven cavity, and show how the driven cavity detuning dramatically changes the resulting hysteresis cycle. By driving the photonic dimer out-of-equilibrium, we observe the occurrence of stable self-switching oscillations near avoided resonance crossings. All results agree well with the driven-dissipative Bose-Hubbard dimer model in the weakly coupled regime.

Self-pulsing in driven-dissipative photonic Bose-Hubbard dimers

Self-Pulsing in driven-dissipative photonic Bose-Hubbard dimers

Despite its apparent simplicity, a pair of nonlinear coupled ring resonators exhibits a rich dynamics. These nonlinear photonic dimers have recently attracted interest in the context of emergent behaviors [1] , [2] . Here, we theoretically and experimentally study the bifurcation diagram and the self-pulsing dynamics of driven-dissipative photonic dimers with dissimilar detunings (∆ 1 , ∆ 2 ). We consider two passive fiber cavities, each composed of about L = 250 m of optical fiber with a net normal dispersion, coupled through a 95/05 fiber coupler. They are synchronously driven by a narrowband laser that pumps the first cavity through a 90/10 coupler. The detuning in each cavity can independently be set and/or scanned using piezoelectric fiber stretchers. The bifurcation structure of our system, neglecting dispersion, is computed by numerical continuation of the solutions of the canonical Bose-Hubbard dimer model [3] . A typical example of the main dynamical regions in the (∆ 2 , S )-phase diagram is shown in Fig. 1(a) for ∆ 1 = 3.1. Bistability is encountered in the green areas, while the self-pulsing region in which stable sustained oscillations arise is shown in red. Increasing the driving amplitude S , the self-pulsing appears near the level ( S ≈ 2.1) at which the avoided crossing couples the two equilibrium states of the driven cavity (at ∆ 2 ≈ 2). At larger power, when approaching the grey region by tuning ∆ 2 , the period of the oscillatory solution tends to infinity and, finally, the solution collapses through a Shil’nikov bifurcation. The experimental nonlinear resonance of cavity 1 (blue) and 2 (red) when scanning ∆ 2 are reported in Fig. 1(b) . We clearly observe a hysteresis cycle in the bistable region, then the finite self-pulsing region where the solution oscillates, in agreement with the Bose-Hubbard model. Stabilizing the second cavity at ∆ 2 = 2.4 [vertical black line in Figs. 1(a-b) ], the measurement of the intracavity power shows a stable oscillation in both cavities. Moreover, the reconstructed limit cycle (not shown) agrees very well with the numerical simulations of the model.

Jesus Yelo-Sarrion

Papers

Self-pulsing in driven-dissipative photonic Bose-Hubbard dimers

Self-pulsing and chaos in the asymmetrically driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis.

Self-Pulsing in driven-dissipative photonic Bose-Hubbard dimers

Self-pulsing and chaos in nonlinear photonic dimers

Self-Pulsing in Photonic Dimers