Chiral quantum optics with V-level atoms and coherent quantum feedback

We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, and this direction is opposite for the two transitions. The waveguide is terminated by a mirror which coherently feeds the photon stream emitted by one transition back to the atom. First, we are interested in the dynamics of the atom in the Markovian limit where the time-delay in the feedback is negligible. Specifically, we study the conditions under which the atom evolves towards a pure "dark" stationary state, where the photons emitted by both transitions interfere destructively thanks to the coherent feedback, and the overall emission vanishes. This is a single-atom analog of the quantum dimer, where a pair of laser-driven two-level atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current state-of-the-art experiments. Second, we extend our study to non-Markovian regimes and investigate the effect of the feedback retardation on the steady-state.