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The powerful terahertz emission from intrinsic Josephson junctions in high-Tccuprate superconductors has been detected recently. The synchronization ofdifferent junctions is enhanced by excitation of the geometrical cavityresonance. A key characteristic of the radiation is its linewidth. In thiswork, we study the intrinsic linewidth of the radiation near the internalcavity resonance. Surprisingly, this problem was never considered before,neither for a single Josephson junction nor for a stack of the intrinsicJosephson junctions realized in cuprate superconductors. The linewidth appearsdue to the slow phase diffusion, which is determined by the dissipation andamplitude of the noise. We found that both these parameters are resonantlyenhanced when the cavity mode is excited but enhancement of the dissipationdominates leading to the net suppression of diffusion and dramatic narrowing ofthe linewidth. The line shape changes from Lorentzian to Gaussian when eitherthe Josephson frequency is shifted away from the resonance or the temperatureis increased.

Linewidth of the electromagnetic radiation from Josephson junctions near cavity resonances