Solution of the Dicke model for N = 3

Abstract

The N = 3 Dicke model couples three qubits to a single radiation mode via dipole interaction and constitutes the simplest quantum-optical system allowing for Greenberger–Horne–Zeilinger states. In contrast to the case N = 1 (the Rabi model), it is non-integrable if the counter-rotating terms are included. The spectrum is determined analytically, employing the singularity structure of an associated differential equation. While quasi-exact eigenstates known from the Rabi model do not exist, a novel type of spectral degeneracy becomes possible which is not associated with a symmetry of the system.