Mechanical frequency control in inductively coupled electromechanical systems

Thomas Luschmann,Rudolf Gross,Achim Marx,Hans Huebl,Alvaro Sanchez,Frank Deppe,Philip Schmidt

doi:10.1038/s41598-022-05438-x

Abstract

Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanical system, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (1) the bias magnetic flux applied perpendicular to the SQUID loop, (2) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring.

Highlights

10μm we can quantitatively describe by theoretical predictions
coplanar waveguide (CPW) resonator is short-circuited to ground via a dc-SQUID at one end
Since the inductance of the dc-SQUID depends on the applied flux, this in turn results in a modulation of the resonance frequency of the microwave resonator

Summary

Methods

All experiments are performed in a dilution refrigerator at a temperature of approximately 85 mK using spectroscopy schemes such as microwave transmission experiments and thermal sideband noise spectroscopy. A detailed description of the microwave detection setup can be found in Ref. 20. To apply the strong in-plane and the weak out-of-plane magnetic field to the nano-electromechanical circuit, we position the chip in a superconducting solenoid magnet and mount a small superconducting coil on the sample enclosure. While the IP superconducting solenoid is used to apply fields of up to 35mT, the field provided by the OOP coil is limited to 1 mT. The device is subject to fluctuations in the static magnetic field which are actively compensated by a feedback loop using the OOP coil as control entity

Results

Discussion

Conclusion