  In a quantum dot hybrid superconducting junction, the behavior of the
supercurrent is dominated by Coulomb blockade physics, which determines the
magnetic state of the dot. In particular, in a single level quantum dot singly
occupied, the sign of the supercurrent can be reversed, giving rise to a
pi-junction. This 0-pi transition, corresponding to a singlet-doublet
transition, is then driven by the gate voltage or by the superconducting phase
in the case of strong competition between the superconducting proximity effect
and Kondo correlations. In a two-level quantum dot, such as a clean carbon
nanotube, 0-pi transitions exist as well but, because more cotunneling
processes are allowed, are not necessarily associated to a magnetic state
transition of the dot. In this proceeding, after a review of 0-pi transitions
in Josephson junctions, we present measurements of current-phase relation in a
clean carbon nanotube quantum dot, in the single and two-level regimes. In the
single level regime, close to orbital degeneracy and in a regime of strong
competition between local electronic correlations and superconducting proximity
effect, we find that the phase diagram of the phase-dependent transition is a
universal characteristic of a discontinuous level-crossing quantum transition
at zero temperature. In the case where the two levels are involved, the
nanotube Josephson current exhibits a continuous 0-pi transition, independent
of the superconducting phase, revealing a different physical mechanism of the
transition.
