Performance enhancement in Josephson traveling-wave parametric amplifiers by tailoring the relative distance between junctions

Josephson traveling-wave parametric amplifiers with heterogeneously spaced junctions are theoretically investigated. We consider unit cells with three junctions and characterize their interaction by spatially displaced fields defined by node fluxes. To solve this problem we define the system action and apply the variational principle to obtain the static action, which determines the equations of motion. This work shows that gain and bandwidth can be increased by modifying the relative distance between junctions within the same unit cell, thus increasing the effective nonlinear interaction. We find an optimal sub-unit-cell size ratio, which maximizes both gain and bandwidth, while equally spaced junctions offer minimum performance. Even though this method does not rely on phase matching, the same device can operate at different pump frequencies, it requires a very large number of JJs to achieve gains above 20 dB. We show that this method can be combined with resonant-phase matching and predicts an ideal gain above 29 dB on a 4-GHz bandwidth with 1998 junctions. Despite possible challenges fabricating devices at the optimal sub-unit-cell size with current technologies, substantial gain increase can still be achieved at suboptimal sizes.