Beyond Adiabatic Elimination in Topological Floquet Engineering

  Yiming Pan  ,  Qingqing Cheng  ,  Shanghai Key Lab of Modern Optical System and Engineering Research Centre of Optical Instrument and System (Ministry of Education), University of Shanghai for Science and Technology, Shanghai 200093, CHINA  
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, ISRAEL

Manipulating and tailoring the intricate quasi-energy spectrum still remain a challenging issue in periodically-driven quantum systems. Here, we reported two typical spectral decompositions beyond the conventional adiabatic elimination, which enable to target the certain isolated quasi-energy bands by cutting-off the irrelevant far-off-resonant degrees of freedom. According to driving protocols in Floquet engineering, we classified the two non-adiabatic eliminations with Floquet driving frequency: namely, the quasi-adiabatic elimination, which non-adiabatically emerges at in-between driving frequency range, and in contrast the high-frequency-limited elimination, which requires rapidly-driven forces or modulations. Due to the failure of adiabatic condition, the protection mechanism of these driven eliminations is the first time to be demonstrated by selectively targeting the non-trivial isolated edge states via the bulk-edge correspondence, as a principle, from topological insulators and quantum field theories. Meanwhile, the near-field measurements using our well-fabricated photonic Floquet simulators correspondingly confirmed the observation of these eliminations and their stroboscopic dynamics. The non-adiabatic eliminations for Floquet quasi-energy spectrum are eventually proposed to open up the profound possibilities for artificially-controlling driven systems in topological Floquet engineering that may have numerous promising applications ranging from condensed matters to advanced photonics.