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.

Crossover from a delocalized to localized atomic excitation in an atom–waveguide interface

“…We note a recent article which shows a detailed study of Rydberg excitation dynamics and their quantum correlations in the atom-waveguide interface without disorders [57]. The quasi-localization of excitation emerges when a long-range hopping in the exponentially decaying spin exchange interaction is used.…”

Diffusion of excitations and power-law localization in strongly disordered systems with long-range coupling

“…The presence of this Lieb-Robinson boundary has been observed in many theoretical and experimental studies [3][4][5][6][7][8][9][10][11][12], e.g. the first experimental evidence was achieved in the system of a one-dimensional quantum gas trapped in an optical lattice [5].…”

Undamped Rabi oscillations due to polaron-emitter hybrid states in non-linear photonic wave guide coupled to emitters

“…Ongoing research is exploring a variety of platforms, including nano-photonic lattices [1][2][3][4][5], plasmonic wave guides [6], and superconducting resonator arrays [7,8] coupled to atoms [9][10][11], quantum dots [12], quantum solid-state defects [13,14], or superconducting qubits [15][16][17][18][19]. Applications range from quantum information processing to quantum networking to quantum simulations [20][21][22][23][24][25][26]. Recent experimental milestones include the heralded creation of a single collective excitation in a chain of atoms coupled to a waveguide [27] and the demonstration of photon (anti-) bunching for weak atom-photon coupling by taking advantage of dissipation [28].…”