Figure 2. Device and characterization.

(a) False-colour image of the device. The cavity is coloured in dark yellow. The graphene flake is clamped in between niobium support electrodes (grey) and cross-linked poly(methyl metracylate) (turquoise). The scale bar is 5 μm. (b) Schematic cross-section of the graphene resonator along the white dashed dotted line in a. (c) Schematic of the measurement circuit. The graphene mechanical resonator is coupled to the superconducting LC cavity through the capacitance C_m. The separation d between the suspended graphene flake and the cavity counter electrode is controlled by the constant voltage V_g. The cavity is pumped with a pump tone at ω_p and the output signal is amplified at 3 K. (d) Reflection coefficient |S₁₁|² and (e) reflected phase Δφ₁₁ of the superconducting cavity of device A at V_g=3.002 V. The dark yellow lines are fits to the data using κ_int/2π=950 kHz and κ_ext/2π=850 kHz using equation (7) (see Methods). (f) Driven vibration amplitude of the graphene resonator of device A as a function of drive frequency. The driving voltage is 22 nV and V_g=3.002 V. The dark yellow line is a lorentzian fit to the data. (g) Resonant frequency ω_c/2π of the superconducting cavity as a function of V_g. (h) Resonant frequency ω_m/2π of the graphene resonator as a function of V_g. The black line is the V_g dependence of ω_m expected from electrostatic softening (see Supplementary Note 1).