Coherent Charge Oscillations in Tunnel Junctions

Small-capacitance junctions driven by a weak external current Ix may exhibit oscillations of the voltage with fundamental frequencies f2 = Ix/2e or f1 = Ix/e, thus reversing the role of current and voltage in comparison to the usual a.c. Josephson effect. These "Bloch" oscillations reflect the properties of the energy bands En(Qx), where Qx is an "external charge", and thus demonstrate the macroscopic quantum-mechanical nature of the system. Cooper pair tunnelling by itself would lead to 2e-periodic energy bands and band gaps. Quasi-particle tunnelling makes the bands e-periodic, but opens no further gaps. Depending on the strength of this process, the bands are qualitatively modified, with a phase transition occurring at a critical strength. The spectrum of the voltage oscillations reflects these modifications and the phase transition.