Theory of the Josephson Junction Laser

We develop an analytic theory for the recently demonstrated Josephson Junction laser [Cassidy, et al, Science 355, 939 (2017) ]. These devices are built with standard transmon-waveguide technology and are potentially useful as gigahertz sources for quantum computing applications. By working in the time-domain representation (rather than the frequency-domain) a single non-linear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.