Non-Markovian dynamics of a single excitation within many-body dissipative systems

We explore the dynamics of N coupled atomic two-level systems embedded within a generic bosonic reservoir under specific system symmetries. In the regime of many atoms identically coupled to a single reservoir, we identify remarkable effects, notably that the initial configuration of the atomic excited-state amplitudes strongly impacts the dynamics of the system and can even fully sever the system from its environment. Additionally, we find that steady-state amplitudes of the excited states become independent of the specific structure of the bosonic reservoirs considered. The framework introduced is deployed to model a structured photonic reservoir associated with a photonic crystal, where it recaptures previous theoretical and experimental results for the superradiance rates even within the single-excitation regime. For the photonic band-gap system, our formalism predicts the generation of pairwise entanglement between initially uncorrelated atomic systems. Furthermore, it suggests that???with respect to a non-Markovian metric???the non-Markovianity of the aggregated many-atom system is modulated by the total number of atoms. This is due to a stark interplay between the Lamb shifting of the atomic transition energies due to their varying number and the increased number of atomic systems with resonant transition energies.

Automated summary

This study explores the dynamics of coupled atomic two-level systems within a generic bosonic reservoir. In the regime where many atoms are identically coupled to a single reservoir, interesting effects are identified, such as the strong impact of the initial configuration of atomic excited-state amplitudes on the system dynamics, which can even sever the system from its environment. Additionally, it is found that steady-state amplitudes of the excited states become independent of the specific structure of the bosonic reservoirs considered.