Release-free phononic crystal with strong microwave coupling

Phonons hold promise for storing and transferring quantum information, including in mechanically-mediated quantum interconnects between superconducting qubits and light. Phononic crystal cavities confine gigahertz sound to micron-scale volumes well matched to near-infrared light. So far, these devices have typically been suspended to suppress phononic radiation loss into the substrate, but suspension limits thermal anchoring leading to excess noise. Release-free phononic crystals have emerged as a way to address this challenge - but had yet to be shown compatible with strong electromechanical interactions. Here, we demonstrate a release-free phononic crystal cavity strongly coupled to a high-impedance microwave resonator, with an electromechanical coupling rate g_em/(2π) approx 30 MHz that exceeds both the mechanical and microwave loss rates, leading to a cooperativity up to mathcal{C} approx 180 on resonance. In addition, our lithium niobate phononic crystals reach quality factors above 10⁴ at millikelvin temperature on both silicon and sapphire substrates. Our results establish release-free phononic crystals as compact, scalable interfaces between microwaves and gigahertz sound for emerging sensing, communication, and computing systems.