Quantum versus classical regime in circuit quantum acoustodynamics

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