a Schematics of the device. The artificial atom is simultaneously coupled to electromagnetic and acoustic systems. Microwave photons excite an artificial atom (qubit). The atom in turn generates phonons into the phononic crystal. b Schematic representation of the sample. Electromagnetic waves propagate through a coplanar transmission line and interact with an artificial atom shaped as a transmon. The qubit shunting capacitance consists of Np = 140 identical electrode pairs (metallic stripes). The corresponding mechanical substrate surface oscillations are shown by color gradients. c Micrograph of the sample. Thin structures of the phononic crystal and the SQUID are shown in the insets.