Quantum Pyragas control: Selective-control of individual photon probabilities

Pyragas control allows to stabilize unstable states in applied nonlinear science. We propose to apply a quantum version of the Pyragas protocol to control individual photon-probabilities in an otherwise only globally accessible photon-probability distribution of a quantum light emitter. The versatility of quantum Pyragas control is demonstrated for the case of a two-level emitter in a pulsed laser-driven half cavity. We show that one- and two-photon events respond in a qualitatively different way to the half-cavity induced feedback signal. One-photon events are either enhanced or suppressed, depending on the choice of parameters. In contrast, two-photon events undergo exclusively an enhancement up to $50\%$ for the chosen pulse areas. We hereby propose an implementation of quantum Pyragas control via a time-delayed feedback setup.