PC-symmetry-protected edge states in interacting driven-dissipative bosonic systems

Abstract

A main objective of topological photonics is the design of disorder-resilient optical devices. Many prospective applications would benefit from nonlinear effects, which not only are naturally present in real systems but also are needed for switching in computational processes, while the underlying particle interactions are a key ingredient for the manifestation of genuine quantum effects. A particularly attractive switching mechanism of dynamical systems are infinite-period bifurcations into limit cycles, as these set on with a finite amplitude. Here we describe how to realize this switching mechanism by combining attractive and repulsive particle interactions in a driven-dissipative Su-Schrieffer-Heeger model, such as realized in excitonic lasers and condensates so that the system displays a nonhermitian combination of parity and charge-conjugation (PC) symmetry. We show that this symmetry survives in the nonlinear case and induces infinite-period and limit-cycle bifurcations (distinct from a Hopf bifurcation) where the system switches from a symmetry-breaking stationary state into a symmetry-protected power-oscillating state of finite amplitude. These protected dynamical solutions display a number of characteristic features, among which are their finite amplitude at onset, their arbitrary long oscillation period close to threshold, and the symmetry of their frequency spectrum which provides a tuneable frequency comb. Phases with different transition scenarios are separated by exceptional points in the stability spectrum, involving nonhermitian degeneracies of symmetry-protected excitations.

References in corpus (15)

• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• Quantum fluids of light
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Topological photonic crystal nanocavity laser
• Polaritonic Feshbach Resonance
• Observation and control of nonlinear electromagnetic topological edge states
• Bistable topological insulator with exciton-polaritons
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• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Two-body physics in the Su-Schrieffer-Heeger model
• Frequency combs with weakly lasing exciton-polariton condensates
• Nonlinear mode competition and symmetry-protected power oscillations in topological lasers
• Superflow of resonantly driven polaritons against a defect
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Cited by in corpus (6)

• Nonlinear topological photonics
• Topological edge states and gap solitons in the nonlinear Dirac model
• Observation of edge solitons in topological trimer arrays
• Topological Phase Transition Independent of System Non-Hermiticity
• Inversion symmetric non-Hermitian Chern insulator
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point