Fig. 1.

Sample structure and mode spectra of the resonators. (A) Scanning electron microscope image of a typical sample with a tilted view angle. Four contacts divide a suspended graphene ribbon into three mechanical resonators, $R_1$, $R_2$, and $R_3$, in a linear chain. (B) Schematic sample structure and measurement setup. A frequency-modulated microwave signal $V^{\text{FM}}$ is applied through one contact of the center resonator, and a lock-in amplifier detects the mixing current $I_{\text{mix}}$ at the modulation frequency of the inputted FM signal at another contact. The frequencies of the resonators are tuned by dc voltages on the gates, respectively. An arbitrary waveform generator (AWG) is connected to gate g1 to provide additional burst signals for the coherent oscillations. (C) The mixing current as a function of the driving frequency $f_{\text{d}}$ at $V_{\text{g}1}$ = 22 V. The measured linewidth of resonator $R_1$ is ${\gamma }_1/2\pi$ ∼ 1.20 kHz. Similarly, the linewidth of $R_2$ is ${\gamma }_2/2\pi$ ∼ 1.16 kHz and the linewidth of $R_3$ is ${\gamma }_3/2\pi$ ∼ 0.73 kHz (SI Appendix, Fig. S2) at a driving power of ∼− 60 dBm. (D) The mixing-current spectrum of resonators $R_1$ and $R_2$. Coupling strength as large as 11.5 MHz is observed. Here $V_{\text{g}2}$ = 17 V and $V_{\text{g}3}$ = 0 V. (E) Spectrum of all three resonators. Here $R_2$ is far off-resonance from $R_3$ with a detuning ${\mathrm{\Delta }}_{23}/2\pi$ ∼ 20 MHz, with $V_{\text{g}2}$ = 14 V, and $V_{\text{g}3}$ = 15 V. The dc voltage $V_{\text{g}1}$ is scanned over a wide range, to tune the resonant frequency of $R_1$ to cross the frequencies $f_{\text{m}2}$ and $f_{\text{m}3}$. A large avoided level crossing is observed when $f_{\text{m}1}$ approaches $f_{\text{m}2}$. A smaller energy splitting is observed when $f_{\text{m}1}$ approaches $f_{\text{m}3}$ due to the indirect coupling. (F) The measured indirect coupling strength ${\mathrm{\Omega }}_{13}/2\pi$ between $R_1$ and $R_3$ as a function of ${\mathrm{\Delta }}_{23}/2\pi$. D and E are obtained at a driving power of ∼− 40 dBm to have a better resolution.