Tunneling ground state in the nonresonant superradiant phase transition

The low-lying levels in the eigenvalue spectrum of a nonresonant maser model are investigated at $T=0\mathrm{}°\mathrm{K}$ when the atom-photon coupling constant is strong enough to cause the appearance of the so-called superradiant phase transition in the thermodynamic properties of the system. The frequency of the field is assumed to be larger than the Larmor frequency of the pseudospins, and eigenfunctions and eigenvalues are found using a technique based on the theory of continuants. The eigenvalue spectrum turns out to consist of a set of slightly split doublets, and the corresponding eigenstates are such that the dynamical properties of the system in each doublet closely correspond to tunneling between equivalent energy configurations. The atoms are shown to be surrounded by a cloud of virtual photons which accompany them during the tunneling motion.