Floquet scattering through a parity–time symmetric oscillating potential

We investigate the scattering of a particle from a trapping potential that is subjected to weak,parity–time symmetric periodic drivings.Using the Floquet theory,we derive the scattering matrix and calculate the transmittance of the incident particle.When the driving is purely coherent,our calculation recovers the known result and the transmission spectrum shows the familiar,bound-state-induced Fano resonances.When the driving is purely incoherent,we find the Fano resonances still occur,but the lineshape of each resonance is reversed compared to the coherent-driving counterpart.Intriguingly,the transmission resonances disappear when both the coherent and incoherent driving fields are present with equal amplitudes.This phenomena can be seen as a manifestation of the non-reciprocal coupling of Floquet channels in the frequency domain.Notably,when the frequency up-conversion is absent,the transmission is such as if there is no driving at all,even when the driving strength increases.