We realize the quantum regime of a surface acoustic wave (SAW) resonator by demonstrating vacuum Rabi mode splitting due to interaction with a superconducting artificial atom. Reaching the quantum regime is physically difficult and technologically challenging since SAW devices consist of large arrays of narrow metal strips. This work paves the way for realizing analogues of quantum optical phenomena with phonons and can be useful in on-chip quantum electronics.

The interaction of superconducting qubits with surface acoustic wave resonators in quantum regime has been achieved recently. It opens a new field of research – quantum acoustodynamics – and allows developing new types of quantum devices. The main challenge in this direction is to manufacture acoustic resonators in the gigahertz range. Here, we demonstrate that the structure of a hybrid acoustodynamic device can be significantly simplified, if we replace an acoustic resonator with a phononic crystal. Our crystal consists of narrow metallic stripes on a quartz surface. The artificial atom in turn interacts with a microwave transmission line. Therefore, two degrees of freedom of different nature, acoustic and electromagnetic, are coupled with a single quantum object. A scattering spectrum of propagating electromagnetic waves on the artificial atom visualizes acoustic modes of the phononic crystal. Our geometry allows realizing effects of quantum acoustics on a simple and compact system.

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We experimentally study a circuit quantum acoustodynamics system with a superconducting artificial atom coupled to both a two-dimensional surface acoustic wave resonator and a one-dimensional microwave transmission line. The strong coupling between the artificial atom and the acoustic wave resonator is confirmed by the observation of the vacuum Rabi splitting at the base temperature of dilution refrigerator. We show that the propagation of microwave photons in the microwave transmission line can be controlled by a few phonons in the acoustic wave resonator. Furthermore, we demonstrate the temperature effect on the measurements of the Rabi splitting and temperature induced transitions from high excited dressed states. We find that the spectrum structure of two-peak for the Rabi splitting could become into those of several peaks under some special experimental conditions, and gradually disappears with the increase of the environmental temperature T. The continuous quantum-to-classical crossover is observed around the crossover temperature T c, which is determined via the thermal fluctuation energy k B T and the characteristic energy level spacing of the coupled system. Experimental results agree well with the theoretical simulations via the master equation of the coupled system at different effective temperatures.