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Photonics North (PN)

Analytical Characterization of State Bifurcations in Kerr Resonators

Juan Diego Mazo-Vasquez, Julius Gohsrich, Flore K. Kunst, Lewis Hill

Published Jun 1, 2026• 0 citations
Publisher
DOI
10.1109/pn70808.2026.11657716

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Nonlinear phenomena such as optical bistability and spontaneous symmetry breaking play a central role in Kerr resonators, and are increasingly exploited in photonic integrated circuits for all-optical information processing. In this work, we present an analytical framework allowing to find the stationary states and their bifurcations for the propagating fields in Kerr ring and Fabry-Perot resonators, which can be generalized to other nonlinear systems. Using tools from nonlinear algebra, namely, polynomial resultants and Groebner bases, we derive compact polynomial expressions describing the system's full solution in both intensity and amplitude representations. The bifurcations follow directly from these expressions, and are additionally characterized as exceptional points of an auxiliary linear non-Hermitian system. Together, these results unify optical bistability and spontaneous symmetry breaking within a single analytical framework, and offer a route toward improved control of nonlinear optical systems, and the design of photonic devices.
Abstract Quantum annealing provides a promising way to solve combinational optimization problems where the solutions correspond to the ground state of the Ising Hamiltonian. We can implement quantum annealing using the Kerr nonlinear resonators (KNRs), with bifurcation phenomena emerging when subjected to a parametric drive. These bifurcated states can function as bases of qubits. Moreover, integrating four-body interactions between physical qubits enables the establishment of effective all-to-all long-range interactions between logical qubits, which is essential for practical quantum annealing. While theoretical proposals exist for creating four-body interactions within KNRs, there has not been experimental verification through their spectroscopic signatures. In this paper, we theoretically investigate the spectroscopic measurements of KNRs featuring four-body interaction. We identify six distinct frequencies exhibiting population changes by employing resonant driving on one resonator and weak driving on another. Analytical and numerical calculations validate these findings. Our study demonstrates the potential of spectroscopy in characterizing systems with four-body interactions, offering insights for realizing quantum annealing with Kerr parametric oscillators.
We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.