Josephson tunnel junctions are widely used as nonlinear elements in superconducting circuits such as low noise amplifiers and quantum bits. However, microscopic defects in the oxide tunnel barrier can produce low and high frequency noise which can po
tentially limit the coherence times and quality factors of resonant circuits. Weak link Josephson junctions are an attractive alternative provided that sufficient nonlinearity can be engineered. 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 connected with three dimensional banks can be used to construct nonlinear oscillators for bifurcation amplification. We also show that under static current bias, these oscillators have a sufficiently anharmonic energy level structure to form a qubit. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits.
We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear bandstructure of graphene and deviates substantially from the usual metallic beh
avior. The effective band velocity of the Dirac fermions is found to be reduced by 4-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.
