Landau-Zener tunneling and quantum interference of Andreev states

Abstract

With the aid of a microscopic theory we derive an effective Hamiltonian that controls quantum dynamics of Andreev states in superconducting nanojunctions out of equilibrium. Resolving the corresponding Schrödinger-like equation we obtain the "wave functions" for Andreev levels and evaluate electric current across the junction in the presence of an external voltage bias. We demonstrate that quantum interference of Andreev states may yield pronounced coherent oscillations of the supercurrent as a function of the Josephson phase in junctions with barrier transmissions slightly below unity. Further implications of this novel effect are expected for junctions with diffusive barriers.