Towards a platform for many-body spin emulation: Cavity quantum acoustic device in the multi-mode strong coupling regime

Coupling many qubits to a dense cavity spectrum has been proposed as a means of engineering finite-range interactions among many qubits for analog quantum emulation. Although the circuit quantum electrodynamics (cQED) architecture is perhaps the most advanced quantum information technology, building a system of many qubits coupled to a multi-mode cavity is hindered by the mismatch of scales between the transmons and the electromagnetic modes. Here we investigate an acoustic analog of cQED by replacing the electromagnetic resonators with acoustic cavities. In particular, we couple a single tunable transmon to a 300 micron long surface acoustic wave (SAW) resonator. We show that the resonator supports a dense spectrum of high-Q microwave-frequency modes that couple piezoelectrically to the transmon through an interdigitated SAW transducer. For some modes, the qubit-cavity coupling reaches 6.5 MHz, exceeding the cavity loss rate 200 kHz, qubit linewidth 1.1 MHz, and the free spectral range 4.8 MHz, placing the device in both the strong coupling and strong multi-mode regimes. Crucially, we observe that the qubit linewidth strongly depends on its predicted emission of propagating phonons, and identify operating frequencies where the emission rate is suppressed.