Dynamical localization in a non-Hermitian Floquet synthetic system

We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain. The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation. In the Hermitian case, strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy. We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization. Moreover, the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter. Interestingly, the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value. The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most. The exponential localization length decreases with the increase of the non-Hermitian parameter, unveiling the underlying mechanism of the enhancement of the dynamical localization by non-Hermiticity.