Theory of Josephson Junction Resonators

Abstract

Superconductivity is a result of quantum coherence at macroscopic scales. Two superconductors separated by a metallic or insulating weak link exhibit the AC Josephson effect: the conversion of a DC voltage bias into an AC supercurrent. This current may be used to activate mechanical oscillations in a suspended weak link, acting as an electromechanical resonator. As the DC voltage bias condition is remarkably difficult to achieve in experiments, here the experimentally relevant purely DC current bias case is analyzed thoroughly. It shall be demonstrated that the Josephson effect can be exploited to activate and detect mechanical oscillations, eliminating the need for AC bias conditions that are generally required for nanoelectromechanical systems (NEMS). The coupling between the electronic and mechanical degrees of freedom may be tuned by an external magnetic field, allowing the exploration of the Josephson effect in two distinct coupling regimes. In the weak coupling regime, Shapiro-like plateaus and mechanically induced hysteresis loops develop in the junction's current-voltage (I-V) characteristic which allow for precision measurements of the resonator's resonance frequency by simple DC voltage measurements. In contrast, in the strong coupling regime there are sudden mechanically induced transitions to a zero voltage state which will be explained by energy sharing between the electronic and mechanical degrees of freedom. These transitions are intimately linked to the mechanical damping of the resonator, and may be used to determine the junction's quality factor, again with only DC voltage measurements. It is further revealed that these sudden transitions may be eliminated by using a setup consisting of two suspended weak links connected in parallel forming a superconducting quantum interference device (SQUID), and tuning the external magnetic flux appropriately. Finally, the quantum nature of Josephson junctions is explored more thoroughly by considering Bloch-like oscillations that develop in the junction. These oscillations, when coupled to mechanical vibrations, generate non-classical mechanical states that are intimately linked to the quantum dynamics of the junction.