  We propose the "Andreev molecule", an artificial quantum system composed of
two closely spaced Josephson junctions. The coupling between Josephson
junctions in an Andreev molecule occurs through the overlap and hybridization
of the junction's "atomic" orbitals, Andreev Bound States. A striking
consequence is that the supercurrent flowing through one junction depends on
the superconducting phase difference across the other junction. Using the
Bogolubiov-de-Gennes formalism, we derive the energy spectrum and non-local
current-phase relation for arbitrary separation. We demonstrate the possibility
of creating a $\varphi$-junction and propose experiments to verify our
predictions. Andreev molecules may have potential applications in quantum
information, metrology, sensing, and molecular simulation.
