Topological Optical Parametric Oscillation

TL;DR

This paper demonstrates topological parametric oscillation in nonlinear resonator arrays, revealing robust quantum properties of edge modes and corner modes in driven out-of-equilibrium topological systems.

Contribution

It introduces a novel approach to induce and analyze topological parametric oscillation in nonlinear systems with complex eigenvalues only at the edges.

Findings

Parametric oscillation occurs in topological boundary and corner modes.

Quantum properties of edge modes are robust against certain disorders.

Edge modes exhibit squeezing dynamics below the oscillation threshold.

Abstract

Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in non-equilibrium scenarios is highly desirable and has led to the development of topological lasers. The topologically protected boundary states usually lie within the bulk bandgap, and selectively exciting them without inducing instability in the bulk modes of bosonic systems is challenging. Here, we consider topological parametrically driven nonlinear resonator arrays that possess complex eigenvalues only in the edge modes in spite of the uniform pumping. We show parametric oscillation occurs in the topological boundary modes of one and two-dimensional systems as well as in the corner modes of a higher-order topological insulator system. Furthermore, we demonstrate squeezing dynamics below the oscillation threshold, where the quantum properties of the topological edge modes are robust against certain disorders. Our work sheds light on the dynamics of weakly nonlinear topological systems driven out of equilibrium and reveals their intriguing behavior in the quantum regime.