Non-Markovian dynamics of collective atomic states coupled to a waveguide

When atoms are optically coupled to a one dimensional waveguide, they can interact through macroscopic distances. The retardation effects inherent to field propagation and the associated delay in information backflow between the atoms result in a departure from the familiar Markovian dynamics. We study the case of two two-level atoms coupled along a waveguide. One remarkable feature of the dynamics in this regime is the formation of long-lived bound states in the continuum (BIC),(30) that refer to a hybrid diatomic molecule bound together by propagating modes of a field. In particular, we study the probability of reaching such a bound states of the system starting in an initially anti-symmetric state of the emitters.