  We explore the role played by the quantum relative phase in a well-known
model of atom-field interaction, namely, the Dicke model. We introduce an
appropriate polar decomposition of the atom-field relative amplitudes that
leads to a truly Hermitian relative-phase operator, whose eigenstates correctly
describe the phase properties, as we demonstrate by studying the positive
operator-valued measure derived from it. We find the probability distribution
for this relative phase and, by resorting to a numerical procedure, we study
its time evolution.
