Optimizing anharmonicity in nanoscale weak link Josephson junction oscillators.

We compute the current phase relation for superconducting weak links, with dimensions comparable to the zero temperature coherence length, connected to two and three dimensional superconducting electrodes. Our results indicate that 50-100 nm long aluminum nanobridges with three dimensional banks have sufficient anharmonicity for realizing low noise amplifiers and quantum bits. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits with potentially higher quality factor than tunnel junction devices due to the absence of a lossy oxide layer.