One-dimensional quantum walks with a time and spin-dependent phase shift

We investigate the role of a time and spin-dependent phase shift on evolution one-dimensional discrete-time quantum walks. By employing Floquet engineering, ($\phi$) is imprinted onto walker's wave function while it shifts from one lattice site to another. For walk driven by standard protocol we show with our numerical simulations that complete revivals equal periods occur in probability distribution for rational values factor, i.e., $\phi/2\pi = p/q$. an irrational value $\phi/2\pi$ results partial unpredictable periods, walker remains localized small region lattice. further split-step $\phi/2\pi$. In contrast case protocol, shows distribution. Furthermore, view experimental realization robustness against noise shift. Our signatures persist smaller parameter, vanish larger values. work important context computation where walks can be used control manipulate desired state demand.