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Recently Yaakobi and co-workers [Phys. Rev. B 87, 144301 (2013)]theoretically studied four-wave mixing and parametric amplification in anonlinear transmission line consisting of capacitively shunted Josephsonjunctions. By deriving and solving the coupled-mode equations, they havearrived at the conclusion that in a wide frequency range around the pumpfrequency exponential parametric gain (in which the signal grows exponentiallywith distance) can be achieved. However, we have found a mathematical error intheir derivation of the coupled-mode equations (Equation (A13)), which leads tothe wrong expression of the gain factor and invalidates their conclusions onthe gain and bandwidth. In this comment, we present the correct expression forthe parametric gain. We show that for a transmission line with weak dispersionor positive dispersion ($\Delta k>0 $), as is the case discussed by Yaakobi etal, while quadratic (power) gain can occur around the pump frequency,exponential gain is impossible. Furthermore, for a transmission line withproper intrinsic or engineered dispersion, exponential gain occurs atfrequencies where the phase matching condition is met, while around the pumpfrequency the gain is still quadratic.

Comment on "Parametric amplification in Josephson junction embedded transmission lines"