Floquet topological phases in a spin-1/2 double kicked rotor

TL;DR

This paper investigates Floquet topological phases in a spin-1/2 double kicked rotor, revealing rich topological structures characterized by winding numbers and proposing an experimental detection method using Rb87 condensates.

Contribution

It introduces a spin-1/2 extension of the double kicked rotor model, analyzing its topological phases and proposing an experimental realization and detection scheme.

Findings

Topological phases characterized by pairs of winding numbers.

Existence of arbitrarily large winding number phases.

Experimental proposal using Rb87 condensates and mean chiral displacement measurement.

Abstract

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008)] already suggested the importance of periodic driving to the generation of unconventional topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1/2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading Rb87 condensates into a periodically pulsed optical lattice. Under the on-resonance condition, the spin-1/2 double kicked rotor admits fruitful topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected 0 and \pi-quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked Rb87 condensates, and suggest to detect its topological invariants by measuring the mean chiral displacement in momentum space.