The Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model

Abstract

The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically.

arXiv commentContribution for the 30th International Colloquium on Group Theoretical Methods in Physics (Group30) in Ghent (Belgium)

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• Separable and entangled states in the high-spin XX central spin model
• Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics