Coherent control of dissipative dynamics in a periodically driven lattice array

We find a different mechanism for suppression of decay in an open one-dimensional lattice system, which originates from a dark Floquet state, a sink state to which the system is asymptotically driven, whose overall probability is determined only by the parameters of the periodic driving field. The zero-quasienergy of dark Floquet state is shown to be not a real zero, but a vanishingly small negative imaginary number which will cause undesirable physical effect in long-time evolution of quantum states, being extremely different from the conservative counterpart. Another intriguing finding is that the value of the system's effective decay, determined by the size of the nonzero imaginary part of the dark-Floquet-state-related quasienergy, depends not on how many localized lossy sites there are but on which one of the lossy sites is nearest to the driven site. Thus, for specially designed local dissipation, by controlling the driving parameters, it is possible for us to drive the system to a dark Floquet state with a much lower level of overall probability loss as compared to the undriven case and with good stability over longer evolution time. These results are applicable to the multisite lattice system with an odd number of sites and may be significant for long-time control of decay in a vast family of multistate physical systems with localized dissipation.