Entanglement Properties and Dynamics of Collectively Dissipating Multilevel Atom Arrays

Abstract

Achieving an efficient and controllable atom-light interface is essential for quantum technologies. In this context, subwavelegnth atomic arrays provide a promising platform, as collective radiance effects can be exploited to achieve an enhanced atom-light coupling and a higher fidelity in certain quantum optics protocols. In such systems, constructive (superradiance) and destructive (subrradiance) interference between the scattered photons enables to suppress spontaneous emission into undesired optical modes, while enhancing it into desired, detectable modes. In this work, we explore how these ideas, originally developed for two-level atoms, can be extended to multilevel structures with a focus on Λ-type atoms with one excited state and two degenerate ground states. To this end, we generalize the open quantum spin model to multilevel atoms and apply it to Λ systems. We study the collective radiative properties and the entanglement of Dicke states, using a mapping onto SU(3) algebra. Furthermore, we analyse how finite-size effects and coherent interactions modify collective radiance, leading to the emergence of darker states in the two excitation manifold of Λ-systems, compared to the case of two-level atoms, for an atom number N ≥ 10. We also study the dissipative Dicke dynamics for a fully inverted initial state, showing that the evolution is restricted to the symmetric sector. In the finite-size array case in presence of coherent interactions, we identify a peak in the dynamical evolution of entanglement, coinciding with the superradiant burst and find that the system reaches a non-trivial entangled steady state.