Abstract
AbstractThe concept of topology is universally observed in various physical objects when the objects can be described by geometric structures. Although a representative example is the knotted geometry of wavefunctions in reciprocal space for quantum Hall family and topological insulators, topological states have also been defined for other physical quantities, such as topologically distinct Fermi surfaces and enhanced lattice degrees of freedom in hyperbolic geometry. Here, we investigate a different class of topological states – topological geometry of dynamical state trajectories – in non-Hermitian and nonlinear optical dynamics, revealing topologically protected oscillation quenching mechanisms determined by parity–time (PT) symmetry. For coupled systems composed of nonlinear gain and loss elements, we classify the topology of equilibria separately for unbroken and broken PT symmetry, which result in distinct oscillation quenching mechanisms: amplitude death and oscillation death. We then show that these PT-symmetric quenching mechanisms lead to immunity against temporal perturbations, enabling the applications of topologically protected laser modulation and rectification. The observed connection between the topological geometry of dynamical states, oscillation quenching phenomena in dynamical systems theory, and PT symmetry provides a powerful toolkit for noise-immune signal processing.
Highlights
Topological degrees of freedom (DOF) have provided a new phase of matter, including quantized bulk conductance and topological insulators [1]
For coupled systems composed of nonlinear gain and loss elements, we classify the topology of equilibria separately for unbroken and broken PT symmetry, which result in distinct oscillation quenching mechanisms: amplitude death and oscillation death
We theoretically studied the topological nature of nonlinear optical dynamics with PT symmetry, which is manifested by the topological invariance of the trajectory in the optical state space
Summary
Topological degrees of freedom (DOF) have provided a new phase of matter, including quantized bulk conductance and topological insulators [1]. The recent developments in parity–time (PT) symmetry [25, 26] and topological physics [2, 27] have established new design freedom in nonlinear and non-Hermitian optical dynamics: suppressed time reversals [28], optical isolation [29], amplified Fano resonances [30], single-mode lasing [31], quenching behaviors [32] in nonlinear PT-symmetric systems, and topological zero modes in Su–Schrieffer–Heeger chains [33]. Our results can be readily implemented with electric circuits and acoustics
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