Exceptional points in a non-Hermitian topological pump

Abstract

We investigate the effects of non-Hermiticity on topological pumping, and uncover a connection between a topological edge invariant based on topological pumping and the winding numbers of exceptional points. In Hermitian lattices, it is known that the topologically nontrivial regime of the topological pump only arises in the infinite-system limit. In finite non-Hermitian lattices, however, topologically nontrivial behavior can also appear. We show that this can be understood in terms of the effects of encircling a pair of exceptional points during a pumping cycle. This phenomenon is observed experimentally, in a non-Hermitian microwave network containing variable gain amplifiers.

Perspective on topological states of non-Hermitian lattices

“…Because of the complex shape of the energy Riemann surfaces in the vicinity of an exceptional point (see figure 2), which also lead to a breakdown of the adiabatic theorem, there are many counter-intuitive properties such as a strong dependence on the parameter λ close to those points, or the phenomenon dubbed chiral state conversion [72][73][74] 4 . This has fueled fascinating experiments with microwaves [42][43][44][45][74][75][76], optical waveguides [77], nuclear magnetic resonance [78], and also in optomechanical systems [79]. Exceptional points lead to intriguing phenomena such as unidirectional invisibility [80], single-mode lasers [81,82], or enhanced sensitivity in optics [83][84][85].…”

“…Topological effects are intrinsic to features unique to non-Hermitian Hamiltonians such as the topological structure of exceptional points, points in parameter space where the eigenvalues and eigenvectors coalesce (the non-Hermitian counterpart of Hermitian degeneracies), and have been studied for a few decades [42][43][44][45][46]. The focus of the present new wave of interest is, however, on a different aspect: given a non-Hermitian lattice, a system where a motif is periodically repeated in space, what is the phenomenology and how do we classify the topological nature of the resulting states?…”

Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory

“…EPs have been discussed in electronics [20], optomechanics [13,21,22], acoustics [23,24], plasmonics [25], and metamaterials [26]. The concept of EPs has been successfully applied in the description of dynamical quantum phase transitions and topological phases of matter in open quantum systems (see, e.g., [27][28][29][30][31][32][33][34][35][36]).…”

Geometric characterization of non-Hermitian topological systems through the singularity ring in pseudospin vector space

“…In recent years, increased attention has been placed on the topological properties of non-Hermitian phases, which behave very differently from Hermitian topological phases of matter . In non-Hermitian systems, different energy bands can intersect at exceptional points (EPs) where two or more eigenmodes coalesce and form an incomplete Hilbert basis, even when the Hamiltonian remains non-vanishing 2,3,[24][25][26] . Another fascinating phenomenon is the non-Hermitian skin effect (NHSE), where eigenmodes all accumulate along the boundaries due to non-Hermitian pumping 1,4,5 , leading to a modification to the conventional bulk-boundary correspondence (BBC) [9][10][11]18 .…”