Non-Hermitian Floquet topological phases in the double-kicked rotor

Abstract

Dynamical kicking systems possess rich topological structures. In this work, we study Floquet states of matter in a non-Hermitian extension of double kicked rotor model. Under the on-resonance condition, we find various non-Hermitian Floquet topological phases, with each being characterized by a pair of topological winding numbers. A generalized mean chiral displacement is introduced to detect these winding numbers dynamically in two symmetric time frames. Furthermore, by mapping the system to a periodically quenched lattice model, we obtain the topological edge states and unravel the bulk-edge correspondence of the non-Hermitian double kicked rotor. These results uncover the richness of Floquet topological states in non-Hermitian dynamical kicking systems.

Perspective on topological states of non-Hermitian lattices

“…To close this section we note that there are a few studies that examine the interplay between non-Hermiticity and driving in models with gains and losses [160][161][162][163], or others with non-reciprocal interactions [164].…”

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

“…The mean chiral displacement (MCD) refers to the time-averaged chiral displacement of a wavepacket in a lattice, where is the sublattice symmetry operator and is the position operator of the unit cell. The MCD was first introduced as a dynamical probe to the winding numbers of 1D topological insulators in the symmetry classes AIII and BDI [ 98 ], and later extended to Floquet systems [ 93 , 99 , 100 ], two-dimensional systems [ 101 ], many-body systems [ 102 ], systems in other symmetry classes [ 84 ], and recently also to non-Hermitian systems [ 50 , 51 , 53 ]. In the meantime, the MCD has also been measured experimentally in photonic [ 98 , 103 ] and cold atom [ 104 , 105 ] setups.…”

“…Recently, the study of non-Hermitian physics has been extended to Floquet systems, in which the interplay between time-periodic driving fields and gains/losses or nonreciprocal effects could potentially yield topological phases that are unique to driven non-Hermitian systems [ 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 ]. In early studies, various non-Hermitian Floquet topological phases and phenomena have been discovered, including non-Hermitian Floquet topological insulators [ 49 , 50 , 53 , 54 , 55 ], superconductors [ 52 ], semimetals [ 63 ], and skin effects [ 56 , 57 ]. Meanwhile, the time-averaged spin texture and mean chiral displacement have been suggested as two dynamical tools to extract the topological invariants of non-Hermitian Floquet systems [ 49 , 50 , 51 , 53 ].…”

“…In early studies, various non-Hermitian Floquet topological phases and phenomena have been discovered, including non-Hermitian Floquet topological insulators [ 49 , 50 , 53 , 54 , 55 ], superconductors [ 52 ], semimetals [ 63 ], and skin effects [ 56 , 57 ]. Meanwhile, the time-averaged spin texture and mean chiral displacement have been suggested as two dynamical tools to extract the topological invariants of non-Hermitian Floquet systems [ 49 , 50 , 51 , 53 ]. These discoveries extend the boundary of nonequilibrium phases of matter to driven non-Hermitian systems, and shed light on new approaches for the detection of their intriguing features.…”

Detecting topology through dynamics in interacting fermionic wires

“…[20][21][22] it was shown theoretically and confirmed experimentally that the MCD of a localized single-particle excitation above the vacuum state converges in the long-time limit to the chiral invariant of one-dimensional static, periodically-driven, and even disordered systems. Since then, the MCD has found a myriad of applications in very different single-particle systems [23][24][25][26][27][28][29][30][31].…”