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/2π= 1.1 megahertz and a mechanical coupling rate f/2π=5 megahertz. Through time-domain measurements of the silicon mechanical modes, we observe energy relaxation timescales of T1,in ≈ 500 microseconds, pure dephasing timescales of T_φ ≈ 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.