Probing Mechanics in Quantum Mechanics: Josephson Nano-Resonator Metamaterials

Abstract

The shrinking size of nanoelectromechanical systems causes traditional transduction methods such as AC voltage bias to become increasingly challenging, restricting their study to only a handful of groups. A remarkable solution may lie in the Josephson effect, where an AC supercurrent flows through two superconducting electrodes contacted by a weak link upon the application of a DC bias voltage. Proposals exist to suspend the weak link, forming a nanoelectromechanical resonator, and to couple its mechanical displacement to the AC supercurrent via a magnetic field, exciting mechanical oscillations using only DC voltage bias. Suspended devices invariably operate in the current bias regime due to their small impedance however, and experimental signatures of spontaneously induced mechanical resonance have been rare and inconclusive.

Using a resistively and capacitively shunted junction model, we show numerically and analytically how DC current bias may spontaneously excite mechanical oscillations within the suspended weak link in the presence of electromechanical coupling. At weak coupling this results in a huge mechanical voltage plateau and hysteresis loop in the DC current voltage characteristic, whilst at strong coupling we observe mechanically induced retrapping from the plateau to the superconducting state. After developing an analytical framework to understand these phenomena quantitatively and qualitatively, we derive models of both a parallel suspended junction array and an extended suspended junction. We investigate how coupling mechanical oscillations to Fiske modes and fluxons may fine-tune the mechanical properties of the system, and even cloak the oscillators from the supercurrent to suppress the mechanical amplitude.

Our proposals may be used for characterisation, precision metrology of small masses and forces, and to drive, detect, tune and cloak mechanical oscillations entirely in DC, enabling any group with access to suspended Josephson junctions and a cryostat to study nanoelectromechanical systems.