  The powerful terahertz emission from intrinsic Josephson junctions in high-Tc
cuprate superconductors has been detected recently. The synchronization of
different junctions is enhanced by excitation of the geometrical cavity
resonance. A key characteristic of the radiation is its linewidth. In this
work, we study the intrinsic linewidth of the radiation near the internal
cavity resonance. Surprisingly, this problem was never considered before,
neither for a single Josephson junction nor for a stack of the intrinsic
Josephson junctions realized in cuprate superconductors. The linewidth appears
due to the slow phase diffusion, which is determined by the dissipation and
amplitude of the noise. We found that both these parameters are resonantly
enhanced when the cavity mode is excited but enhancement of the dissipation
dominates leading to the net suppression of diffusion and dramatic narrowing of
the linewidth. The line shape changes from Lorentzian to Gaussian when either
the Josephson frequency is shifted away from the resonance or the temperature
is increased.
