Floquet Spectrum and Dynamics for Non-Hermitian Floquet One-Dimension Lattice Model

Periodically driven non-Hermitian quantum systems have become the center of interest in recent years due to their rich physical phenomena. In this work, we consider a one-dimensional non-Hermitian lattice model induced by partially asymmetric coupling with time-periodic and spatially periodic modulations upon on-site potentials. Within Floquet theorem, we obtain the Floquet quasienergy spectrum of this one-dimensional non-Hermitian system. We show that the robust zero-energy modes exist in the band gap from the real parts of quasienergy spectrum. Compared with the case of no modulations, two pairs of the conjugate imaginary parts are added, which can be attributed to the combined modulations upon the on-site potentials. With the increase of non-Hermitian degree, the imaginary parts of the spectra are enlarged. We also observe the dynamical characteristics that, for different kinds of tunneling amplitudes between lattices, the amplitude of evolution gradually either decays to zero or eventually stabilizes at one particular value. Our protocol, possible to realize in photonic lattices, may facilitate the engineering of novel Floquet topological phases in non-Hermitian systems.