Quantum coherent effects, phase transitions, and the dissipative dynamics of ultra small tunnel junctions

Abstract

The quantum dynamics of tunnel junctions with very small capacitance, such that k B T< e 2/2 C, is investigated. We derive the quantum mechanical description from the microscopic theory. It accounts for the macroscopic quantum effects associated with the coherent Cooper pair tunneling, and for the dissipation due to single-electron tunneling and normal current flow. The former is described by a periodic potential, which leads to energy bands and coherent Bloch oscillations of the voltage in response to an imposed current. The single-electron tunneling (SET) is stochastic, but the Coulomb interaction introduces coherence and leads to further oscillations of the voltage. In a Josephson junction with strong dissipation phase transitions occur, above which the quantum effects vanish or become very small. In this regime the junction behaves much like a classical superconducting junction. The features of the SET oscillations and their coexistence with Bloch oscillations, the phase transitions and the transport properties of the junctions are studied in detail.