Scattering from a PT symmetric standing wave

We study the Kapitza–Dirac diffraction of a free beam particle in the presence of a PT symmetric standing wave. We discuss that the momentum and total probability are not conserved in the non-Hermitian scattering process. We show that the average momentum gain/loss does not vanish over a period even if the non-Hermitian optical potential changes periodically in time. We give the resonance conditions at which large momentum transfer is produced. -- Highlights: ► We show that non-Hermitian potential distinguishes right and left incoming waves. ► We discuss that the momentum and total probability are not conserved. ► We show that the time average of momentum gain/loss does not vanish over a period. ► We give the resonance conditions at which large momentum transfer is produced.