Correlated Dephasing in a Piezoelectrically Transduced Silicon Phononic Waveguide

Nanomechanical waveguides offer a multitude of applications in quantum and classical technologies. Here, we design, fabricate, and characterize a compact silicon single-mode phononic waveguide actuated by a thin-film lithium niobate piezoelectric element. Our device directly transduces between microwave frequency photons and phonons propagating in the silicon waveguide, providing a route for coupling to superconducting circuits. We probe the device at millikelvin temperatures through a superconducting microwave resonant matching cavity to reveal harmonics of the silicon waveguide and extract a piezoelectric coupling rate $g/2\pi= 1.1$ megahertz and a mechanical coupling rate $f/2\pi=5$ megahertz. Through time-domain measurements of the silicon mechanical modes, we observe energy relaxation timescales of $T_{1,\text{in}} \approx 500$ microseconds, pure dephasing timescales of $T_\phi \approx {60}$ microseconds and dephasing dynamics that indicate the presence of an underlying frequency noise process with a non-uniform spectral distribution. We measure phase noise cross-correlations between silicon mechanical modes and observe detuning-dependent positively-correlated frequency fluctuations. Our measurements provide valuable insights into the dynamics and decoherence characteristics of hybrid piezoelectric-silicon acoustic devices, and suggest approaches for mitigating and circumventing noise processes for emerging quantum acoustic systems.