The Effect of Mechanical Resonance on Josephson Dynamics

Abstract

We study theoretically dynamics in a Josephson junction coupled to a mechanical resonator looking at the signatures of the resonance in d.c. electrical response of the junction. Such a system can be realized experimentally as a suspended ultra-clean carbon nanotube brought in contact with two superconducting leads. A nearby gate electrode can be used to tune the junction parameters and to excite mechanical motion. We augment theoretical estimations with the values of setup parameters measured in the samples fabricated. We show that charging effects in the junction give rise to a mechanical force that depends on the superconducting phase difference. The force can excite the resonant mode provided the superconducting current in the junction has oscillating components with a frequency matching the resonant frequency of the mechanical resonator. We develop a model that encompasses the coupling of electrical and mechanical dynamics. We compute the mechanical response (the effect of mechanical motion) in the regime of phase bias and d.c. voltage bias. We thoroughly investigate the regime of combined a.c. and d.c. bias where Shapiro steps are developed and reveal several distinct regimes characteristic for this effect. Our results can be immediately applied in the context of experimental detection of the mechanical motion in realistic superconducting nano-mechanical devices.

18 pages, 11 figures

References in corpus (9)

• A tunable carbon nanotube electromechanical oscillator
• Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
• Theory of ground state cooling of a mechanical oscillator using dynamical back-action
• Cooling a nanomechanical resonator with quantum back-action
• Strong coupling between single-electron tunneling and nano-mechanical motion
• Quantum analysis of a linear DC SQUID mechanical displacement detector
• Cooling of a suspended nanowire by an AC Josephson current flow
• Detection of qubit-oscillator entanglement in nanoelectromechanical systems
• Superconductive pumping of nanomechanical vibrations

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• Robust continuous-variable entanglement of microwave photons with cavity electromechanics
• Bistability and Displacement Fluctuations in a Quantum Nano-mechanical Oscillator
• Charge-vibration interaction effects in normal-superconductor quantum dots
• Nano-mechanics driven by Andreev tunneling
• Strong mechanically-induced effects in DC current-biased suspended Josephson junctions
• Pumping and cooling of nanomechanical vibrations generated by Cooper pair exchange