We investigate a superconducting quantum interference device (SQUID) based on carbon nanotubes in a fork geometry [J.-P. Cleuziou { \it et al.}, Nature Nanotechnology { \bf 1}, 53 (2006)], involving tunneling of evanescent quasiparticles through a superconductor over a distance comparable to the superconducting coherence length, with therefore ``non local'' processes generalizing non local Andreev reflection and elastic cotunneling. Non local processes induce a reduction of the critical current and modify the current-phase relation. We discuss arbitrary interface transparencies. Such devices in fork geometries are candidates for probing the phase coherence of crossed Andreev reflection.
Categories: cond-mat.mes-hall cond-mat.supr-con