Hybrid Josephson junctions – in which quantum conductors are used as weak links – offer a rich playground for novel quantum phenomena. They host localized fermionic states knowns as the Andreev bound states (ABS), which mediate the Josephson effect and carry the resulting supercurrent. When two such junctions are placed in close vicinity, the ABS wavefunctions hybridize, forming an Andreev molecule. In this regime, the Josephson effect becomes nonlocal: the supercurrent flowing through one junction depends directly on the superconducting phase applied across the other.
In this seminar, I will present our recent experimental realization [1] of an Andreev molecule built on ultraclean carbon nanotubes, which constitute elementary one-dimensional weak links. Using this platform, we observed a pronounced nonlocal Josephson response and demonstrated that it stems from the formation of delocalized Andreev molecular states extending across both junctions. Furthermore, we show that ground-state parity transitions induce characteristic π-phase shifts in the nonlocal response. Our findings demonstrate that the nonlocal Josephson effect offers a direct access into both the spatial structure and the global fermion parity of delocalized superconducting states.