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The double kicked rotor model is a physically realizable extension of theparadigmatic kicked rotor model in the study of quantum chaos. Even before theconcept of Floquet topological phases became widely known, the discovery of theHofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J.Gong, Phys. Rev. A 77, 031405 (2008)] already suggested the importance ofperiodic driving to the generation of unconventional topological matter. Inthis work, we explore Floquet topological phases of a double kicked rotor withan extra spin-1/2 degree of freedom. The latter has been experimentallyengineered in a quantum kicked rotor recently by loading Rb87 condensates intoa periodically pulsed optical lattice. Under the on-resonance condition, thespin-1/2 double kicked rotor admits fruitful topological phases due to theinterplay between its external and internal degrees of freedom. Each of thesetopological phases is characterized by a pair of winding numbers, whosecombination predicts the number of topologically protected 0 and\pi-quasienergy edge states in the system. Topological phases with arbitrarilylarge winding numbers can be easily found by tuning the kicking strength. Wediscuss an experimental proposal to realize this model in kicked Rb87condensates, and suggest to detect its topological invariants by measuring themean chiral displacement in momentum space.

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