Measurement of a Topological Edge Invariant in a Microwave Network

Hu, Wenyi; Pillay, Jason C.; Wu, Kan; Pasek, Michael; Shum, Perry Ping; Chong, Yidong

doi:10.1103/physrevx.5.011012

Cited by 196 publications

(217 citation statements)

References 47 publications

Supporting

Mentioning

208

Contrasting

Order By: Relevance

“…This situation stands in sharp contrast to that of static two-dimensional systems, where the existence of chiral edge states is intimately tied to the topological structure of the system's bulk bands, as captured by their Chern numbers [34]. A system exhibiting this anomalous behavior was recently realized using microwave photonic networks [35,36].…”

Section: Introductionmentioning

confidence: 83%

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

et al. 2016

View full text Add to dashboard Cite

We show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

show abstract

Section: Introductionmentioning

confidence: 83%

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

et al. 2016

View full text Add to dashboard Cite

show abstract

“…5, and is conceptually similar to the experiment previously reported in Ref. 24. The network is designed according to the topological pumping configuration shown in Fig.…”

Section: Methodsmentioning

confidence: 97%

“…Previously, we have shown that such a network, constructed from radio frequency (RF) cables, couplers, and phase shifters, can be used to implement a topological pump. 24 The windings arXiv:1703.01293v1 [physics.class-ph] 3 Mar 2017…”

mentioning

confidence: 99%

See 1 more Smart Citation

Exceptional points in a non-Hermitian topological pump

et al. 2017

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…A direct implication of this result is the interface state formed by two PCs with different topological invariants. Recently, interface states in some non-Hermitian systems have been reported [47][48][49]. It is known that for Hermitian systems there is a rigorous mathematical relationship that connects the quantized Zak phase of the bulk bands with the formation of interface states [44].…”

Section: Band Inversion In 1d Pt -Symmetric Pcmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

View full text Add to dashboard Cite

Non-Hermitian systems with parity-time-(PT )-symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT -symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT -broken phase can reenter into a PT -exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT -exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

show abstract

Measurement of a Topological Edge Invariant in a Microwave Network

Cited by 196 publications

References 47 publications

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

Exceptional points in a non-Hermitian topological pump

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

Contact Info

Product

Resources

About