Fig. 1: Superconducting circuit nano-electromechanical system with electrostatic and low-frequency access.

a False-color scanning electron microscopy image of a superconducting quarter-wavelength cavity (here for ω_c = 2π ⋅ 7.5 GHz), capacitively side-coupled to a coplanar waveguide feedline. The molybdenum-rhenium (MoRe) metallization is shown in blue and the silicon (Si) substrate in gray. b Zoom into the coupling capacitance region, where the mechanical nanobeam as part of the coupling capacitance is visible. The dimensions of the beam, which consists of MoRe on top of high-stress silicon-nitride (Si₃N₄), are 100 μm × 150 nm × 143 nm. c A magnified view of the suspended nanobeam. d Simplified circuit and measurement scheme, showing a lumped element circuit representation of the device as well as the microwave (MW) input and output lines (including a DC block and high electron mobility transistor amplifier shown as triangle) and the DC (directed current) input line connected to the microwave lines via a bias-tee. A more detailed version of the setup is given in Supplementary Note 1. e Cavity resonance data (black) and fit curve (orange). From the fit, we extract the cavity resonance frequency ω_c = 2π ⋅ 6.434 GHz and the internal and external linewidths κ_i = 2π ⋅ 370 kHz and κ_e = 2π ⋅ 5.7 MHz, respectively. f Resonance curve of the mechanical oscillator readout via the superconducting cavity. Data are shown as black dots, a Lorentzian fit as orange line. From the fit we extract the mechanical resonance frequency Ω_m = 2π ⋅ 1.4315 MHz and a quality factor Q_m = 195,000. g Optomechanically detected excitation spectrum of the nanobeam vs. applied DC voltage. The bright line resembling an inverted parabola represents the resonance of the in-plane mode, which was used everywhere throughout this paper. The thin second line around 1.48 MHz corresponds to the mechanical out-of-plane mode. The red dashed line at V_dc = −4 V indicates the voltage operation point we chose to use.