Analog quantum simulation of generalized Dicke models in trapped ions. (arXiv:1802.01853v1 [quant-ph])

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.

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