Intrinsic lineshape of Josephson radiation from layered superconductors

Abstract

We consider the radiation from the BSCCO crystal, which is long in the $c$-axis ($z$) and $b$-axis ($y$) directions but short in the $a$-axis ($x$) direction, so that ${L}_{x}\ensuremath{\ll}{\ensuremath{\lambda}}_{\ensuremath{\omega}}$, ${L}_{y}>{\ensuremath{\lambda}}_{\ensuremath{\omega}}$, and ${L}_{z}<{\ensuremath{\lambda}}_{\ensuremath{\omega}}/2$, where ${L}_{x},{L}_{y},{L}_{z}$ are the crystal lengths along the $x,y,z$ directions, respectively, while ${\ensuremath{\lambda}}_{\ensuremath{\omega}}=2\ensuremath{\pi}c/{\ensuremath{\omega}}_{J}$ is the radiation wavelength and ${\ensuremath{\omega}}_{J}$ is the Josephson frequency. Metallic screens with lengths bigger than ${\ensuremath{\lambda}}_{\ensuremath{\omega}}$ are attached to the edges $\ifmmode\pm\else\textpm\fi{}{L}_{z}/2$ to separate the half-spaces $|x|>{L}_{x}/2$ and inject a dc interlayer current into the crystal. This bias current induces the Josephson oscillations with frequency ${\ensuremath{\omega}}_{J}$, which depends on the current. The oscillations result in the radiation from crystal edges $x=\ifmmode\pm\else\textpm\fi{}{L}_{x}/2$. Such a radiation has a backward effect on the Josephson oscillations and, as a result, the total radiation power ${\mathcal{P}}_{\mathrm{rad}}$ depends on the geometrical factor $a={\ensuremath{\epsilon}}_{c}{L}_{x}/{L}_{z}$ (${\ensuremath{\epsilon}}_{c}$ is the dielectric constant of crystal for the electric field along the $c$axis) so that ${\mathcal{P}}_{\mathrm{rad}}$ is proportional to the number of junctions squared only when $a\ensuremath{\gtrsim}1$. We show that both the super-radiation and the shunt capacitance attached to the screens introduce coupling of each junction with all others in the stack and, thus, stabilize the synchronized Josephson oscillations in all intrinsic junctions by forming the gap in the spectrum of fluctuation mode with nonzero momenta. To derive the linewidth of radiation, we account for pair-current fluctuations as well as fluctuations caused by quasiparticle currents. The gapless fluctuation mode with zero momentum related to the degeneracy with respect to the overall phase results in the broadening of the radiation line inversely proportional to the crystal volume. We estimate that the relative linewidth at 1 THz may be as narrow as ${10}^{\ensuremath{-}8}$ in the crystal with ${L}_{y}=300$ $\ensuremath{\mu}$m. The fluctuations with nonzero momenta result in the suppression of the radiation power characterized by the parameter similar to the Debye-Waller factor.