  The analysis of single-mode photon fluctuations and their counting statistics
at the superradiant phase transition is presented. The study concerns the
equilibrium Dicke model in a regime where the Rabi frequency, related to a
coupling of the photon mode with a finite-number qubit environment, plays a
role of the transition's control parameter. We use the effective Matsubara
action formalism based on the representation of Pauli operators as bilinear
forms with complex and Majorana fermions. Then, we address fluctuations of
superradiant order parameter and quasiparticles. The average photon number, the
fluctuational Ginzburg-Levanyuk region of the phase transition and Fano factor
are evaluated. We determine the cumulant generating function which describes a
full counting statistics of equilibrium photon number. Exact numerical
simulation of the superradiant transition demonstrates quantitative agreement
with analytical calculations.
