Non-local Josephson effect in Andreev molecules*

We propose the Andreev molecule, an artificial quantum system comprised of two closely spaced Josephson junctions. As in a real molecule, the coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction's "atomic" orbitals, the Andreev Bound States. One of the striking consequences of molecular hybridization is that the supercurrent flowing through one junction depends on the superconducting phase difference across the other junction. The energy spectrum of Andreev molecules have gaps which open as the inter-junction separation is reduced. The current-phase relations are non-local and demonstrate the possibility of a non-zero supercurrent at zero phase difference, a φ-junction. In order to synthesize and detect Andreev molecules, we propose experiments on devices fabricated only with conventional materials and standard nanofabrication techniques. Andreev molecules are a new class of superconducting quantum devices with potential applications in quantum information, metrology, sensing, and molecular simulation.