Focus on topological physics: from condensed matter to cold atoms and optics

Abstract

The notions of a topological phase and topological order were first introduced in the studies of integer and fractional quantum Hall effects, and further developed in the study of topological insulators and topological superconductors in the past decade. Topological concepts are now widely used in many branches of physics, not only limited to condensed matter systems but also in ultracold atomic systems, photonic materials and trapped ions. Papers published in this focus issue are direct testaments of that, and readers will gain a global view of how topology impacts different branches of contemporary physics. We hope that these pages will inspire new ideas through communication between different fields.

Robustness of topologically sensitive harmonic generation in laser-driven linear chains

“…One of the fascinating research directions in condensed matter physics, cold atoms, and photonics are topological phases with interesting properties, and transitions between them [25]. From the strong-field laser perspective, there are only very few investigations on that subject to date [26][27][28][29][30].…”

Topological dipole Floquet solitons

“…Topological (non-Floquet) systems also allow the formation of Dirac [49], Bragg [50], and valley Hall [51] edge solitons. Even though such states may in principle be encountered in many physical systems, potentially including Bose-Einstein condensates in time-modulated potentials [52,53], only fundamental edge solitons with bell-shaped amplitude profiles have been reported to date. The only exception is Floquet dark-bright states introduced in [40], where opposite signs of the dispersion in two components dictate the dark structure of one of them -nevertheless still representing a fundamental state.…”

Real-space effects of a quench in the Su–Schrieffer–Heeger model and elusive dynamical appearance of the topological edge states

“…After a decade characterized by a remarkable effort to find signatures of these edge states in various materials, presently one of the most fascinating challenges in physics is the possibility to manipulate these states and to possibly encode information therein [19][20][21]. To this purpose, the implementation with cold atoms in optical lattices [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] offers a twofold advantage, namely a pretty reliable system isolation from the environmental decoherence, and an extremely precise control of the system Hamiltonian. In particular, it is possible to realize quantum quenches of the Hamiltonian parameters [40][41][42][43], both over the entire system and on a spatially localized portion.…”