Josephson traveling-wave parametric amplifier with three-wave mixing

We develop a concept of the traveling-wave Josephson parametric amplifier exploiting quadratic nonlinearity of a serial array of one-junction SQUIDs embedded in a superconducting transmission line. The external magnetic flux applied to the SQUIDs makes it possible to efficiently control the shape of their current-phase relation and, hence, the balance between quadratic and cubic (Kerr-like) nonlinearities. This property allows us to operate in the favorable three-wave-mixing mode with minimal phase mismatch, an exponential dependence of the power gain on number of sections $N$, a large bandwidth, a high dynamic range, and substantially separated signal ($f_s$) and pump ($f_p$) frequencies obeying relation $f_s+f_i = f_p$, where $f_i$ is the idler frequency. An estimation of the amplifier characteristics with typical experimental parameters, a pump frequency of $12$ GHz, and $N = 300$ yields a flat gain of 20 dB in the bandwidth of 5.6 GHz.