Roy Arkadev, Parto Midya, Nehra Rajveer, Leefmans Christian, Marandi Alireza
Department of Electrical Engineering, California Institute of Technology, Pasadena 91125, CA, USA.
Nanophotonics. 2022 Feb 24;11(8):1611-1618. doi: 10.1515/nanoph-2021-0765. eCollection 2022 Mar.
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 nonequilibrium 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.
拓扑绝缘体拥有受保护的边界态，这些边界态对无序具有鲁棒性，并且在费米子和玻色子系统中都有巨大的意义。在非平衡场景中利用这些拓扑效应是非常可取的，这也推动了拓扑激光器的发展。拓扑保护的边界态通常位于体能带隙内，在不引起玻色子系统体模不稳定的情况下选择性地激发它们具有挑战性。在此，我们考虑拓扑参数驱动的非线性谐振器阵列，尽管有均匀泵浦，但这些阵列仅在边缘模式中具有复本征值。我们表明，一维和二维系统的拓扑边界模式以及高阶拓扑绝缘体系统的角模式中都会出现参量振荡。此外，我们展示了低于振荡阈值时的压缩动力学，其中拓扑边缘模式的量子特性对某些无序具有鲁棒性。我们的工作揭示了非平衡驱动的弱非线性拓扑系统的动力学，并揭示了它们在量子领域中有趣的行为。
