Direct Observation of Topology from Single-Photon Dynamics

Abstract

Topology manifesting in many branches of physics deepens our understanding on state of matters.Topological photonics has recently become a rapidly growing field since artificial photonic structures can be well designed and constructed to support topological states, especially a promising large-scale implementation of these states using photonic chips. Meanwhile, due to the inapplicability of Hall conductance to photons, it is still an elusive problem to directly measure the integer topological invariants and topological phase transitions for photons. Here, we present a direct observation of topological winding numbers by using bulk-state photon dynamics on a chip. Furthermore, we for the first time experimentally observe the topological phase transition points via single-photon dynamics. The integrated topological structures, direct measurement in the single-photon regime and strong robustness against disorder add the key elements into the toolbox of 'quantum topological photonics' and may enable topologically protected quantum information processing in large scale.The introduction of topology into condensed-matter and material sciences originates from the connection of integer quantum Hall conductances with topological Chern invariants [1], which greatly expands our knowledge on state of matters. With the birth of topological insulators, searching topological state of matters in solid state materials [2,3] and photonic systems [4,5] has recently become a leading research field. In contrast to the challenging experimental requirements for realizing topological states in solid state materials, photonic systems provide a convenient and versatile platform to design various topological lattice models and study different topological * meifeng@sxu.edu.cn † xianmin.jin@sjtu.edu.cn states, including topological insulator states [6-10] and topological Weyl points [11,12]. The found topological boundary states potentially can be utilized for developing inherently robust and efficient artificial photonic devices [13-16].In the view of fundamental physics, the topological invariant is a crucial parameter to characterize the topological matter state. In fermion systems, the topological invariant can be revealed by conductance measurements, while the concept of Hall conductance is inapplicable in photonic systems. New methods for directly detecting the topological invariants in topological photonics remain to be developed. The pioneering proposals in theory [17][18][19] and experimental observations have been dedicated in both integrated photonic lattices [20][21][22] and bulk optics [23][24][25][26].Different from the efforts made to detect the topological invariant based on probing Berry curvature [17,20], non-Hermitian photon loss [18,21] or the dynamics of edge states [19,22], we propose a new approach to directly detect the topological invariant via the bulk-state photon dynamics in the real space, which beyonds the physical picture where topological invariant is defined on the equilibrium Bloch state in the momentum spac...

Low-threshold topological nanolasers based on the second-order corner state

“…The investigation of topological photonics has become one of the most fascinating frontiers in recent years [1][2][3][4][5][6][7][8][9][10][11][12] . In addition to conventional passive and linear systems, exploring topological phenomena in highly nonlinear environments also has significance [13][14][15][16][17][18][19][20][21][22][23] .…”

Dynamic winding number for exploring band topology

“…Detecting topological invariants plays an important role in characterizing topological states. In Hermitian systems, the winding number (or Zak phase) has been directly measured by the mean chiral displacement in photonic quantum walks [33,34] and the Ramsey interferometry of cold atoms in superlattices [35]; The Chern number has been detected via the Hall response [36,37], the Thouless pumping [38,39], the Berry curvature [40], the spin polarization [41,42], the linking number [43,44] and the emerging ring structure in quenched dynamics [7]. However, several measurement approaches succeed in Hermitian systems fail in non-Hermitian systems.…”

Quantum Topological Photonics

“…c) Reproduced with permission. [ 188 ] Copyright 2019, American Physical Society. d) Reproduced under the terms of Creative Commons Attribution 3.0 License.…”