Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems

A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A {\bf 77}, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A new class of driven systems without a link with the Harper model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hosftadter's butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.