Dynamics of Rydberg excitations and quantum correlations in an atomic array coupled to a photonic crystal waveguide

Abstract

We study the dynamics of up to two Rydberg excitations and the correlation growth in a chain of atoms coupled to a photonic crystal waveguide. In this setup, an excitation can hop from one atom to another via exponentially decaying exchange interactions mediated by the waveguide. An initially localized excitation undergoes a continuous-time quantum walk for short-range hopping, and for long-range hopping, it experiences quasilocalization. In addition, the inverse participation ratio reveals a superballistic diffusion of the excitation in short times, whereas, at a long time, it becomes ballistic. For two initially localized excitations, intriguing and complex dynamical scenarios emerge for different initial separations due to the competition between the Rydberg-Rydberg and exchange interactions. In particular, the two-point correlation reveals a light-cone behavior even for sufficiently long-range exchange interactions. Additionally, we characterize the growth of bipartite entanglement entropy, which exhibits a global bound if only one excitation is present in the dynamics. Finally, we analyze the effect of imperfections due to spontaneous emission from the Rydberg state into photons outside the waveguide and show that all of the physical phenomena we predict are well within experimental reach.