Emergent limit cycles, chaos, and bistability in driven-dissipative atomic arrays

TL;DR

This paper investigates the complex dynamics of driven-dissipative atomic arrays, revealing conditions for steady states, bistability, limit cycles, and chaos, with finite arrays exhibiting rich behaviors due to light-induced interactions.

Contribution

It introduces a comprehensive analysis of the dynamical regimes in atomic arrays, including the emergence of chaos from deterministic interactions without external randomness.

Findings

Four dynamical regimes identified: steady state, bistability, limit cycles, chaos.

Chaotic behavior arises solely from drive and dissipation interplay, not external randomness.

Finite arrays can exhibit complex dynamics beyond mean-field predictions.

Abstract

We analyze the driven-dissipative dynamics of subwavelength periodic atomic arrays in free space, where atoms interact via light-induced dipole-dipole interactions. We find that depending on the system parameters, the underlying mean-field model allows four different types of dynamics at late times: a single monostable steady state solution, bistability (where two stable steady state solutions exist), limit cycles and chaotic dynamics. We provide conditions on the parameters required to realize the different solutions in the thermodynamic limit. In this limit, only the monostable or bistable regime can be accessed for the parameter values accessible via light-induced dipole-dipole interactions. For finite size periodic arrays, however, we find that the mean-field dynamics of the many-body system also exhibit limit cycles and chaotic behavior. Notably, the emergence of chaotic dynamics does not rely on the randomness of an external control parameter but arises solely due to the interplay of coherent drive and dissipation.