Collective and boson mapping description of a system of N Josephson junctions in a resonant cavity -: art. no. 214519

A system of N two-level Josephson junctions, interacting between themselves and with a single-mode cavity field, is described in terms of the superposition of fermionic and bosonic excitations. The results of the exact diagonalization are compared with the results of the Tamm-Dancoff approximation and with the results of a boson mapping. It is found that the boson mapping provides a suitable description of the spectrum, sum rules, and response function of the system. The dependence of the results upon the number of junctions, the excitation of the cavity modes, and the coupling strengths is investigated.