Topological dynamics and excitations in lasers and condensates with saturable gain or loss

Abstract

We classify symmetry-protected and symmetry-breaking dynamical solutions for nonlinear saturable bosonic systems that display a non-hermitian charge-conjugation symmetry, as realized in a series of recent groundbreaking experiments with lasers and exciton polaritons. In particular, we show that these systems support stable symmetry-protected modes that mirror the concept of zero-modes in topological quantum systems, as well as symmetry-protected power-oscillations with no counterpart in the linear case. In analogy to topological phases in linear systems, the number and nature of symmetry-protected solutions can change. The spectral degeneracies signalling phase transitions in linear counterparts extend to bifurcations in the nonlinear context. As bifurcations relate to qualitative changes in the linear stability against changes of the initial conditions, the symmetry-protected solutions and phase transitions can also be characterized by topological excitations, which set them apart from symmetry-breaking solutions. The stipulated symmetry appears naturally when one introduces nonlinear gain or loss into spectrally symmetric bosonic systems, as we illustrate for one-dimensional topological laser arrays with saturable gain and two-dimensional flat-band polariton condensates with density-dependent loss.

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Cited by in corpus (18)

• Nonlinear topological photonics
• Active topological photonics
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions
• Topological edge states and gap solitons in the nonlinear Dirac model
• Nonlinear non-Hermitian higher-order topological laser
• Photonic Flatband Laser
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Dissipative analog of four-dimensional quantum Hall physics
• Non-Hermitian CT-Symmetric Spectral Protection of Nonlinear Defect Modes
• Dissipative nonequilibrium synchronization of topological edge states via self-oscillation
• Tunable two-dimensional laser arrays with zero-phase locking
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Topological protection in nonlinear optical dynamics with parity-time symmetry
• Supersymmetric non-Hermitian topological interface laser
• PC-symmetry-protected edge states in interacting driven-dissipative bosonic systems
• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces