Analog quantum simulation of generalized Dicke models in trapped ions

Abstract: We propose the analog quantum simulation of generalized Dicke models in trapped ions. By combining bicromatic laser interactions on multiple ions we can generate all regimes of light-matter coupling in these models, where here the light mode is mimicked by a motional mode. We present numerical simulations of the three-qubit Dicke model both in the weak field (WF) regime, where the Jaynes-Cummings behaviour arises, and the ultrastrong coupling (USC) regime, where rotating-wave approximation (RWA) cannot be considered. We also simulate the two-qubit biased Dicke model in the WF and USC regimes and the two-qubit anisotropic Dicke model in the USC regime and the deep-strong coupling (DSC) regime. The agreement between the mathematical models and the ion system convinces us that these quantum simulations can be implemented in the lab with current or near-future technology. This formalism establishes an avenue for the quantum simulation of many-spin Dicke models in trapped ions.