Experimental observation of parity-symmetry-protected phenomena in the quantum Rabi model with a trapped ion

Symmetry is crucial for gaining insights into the fundamental properties of physical systems, bringing possibilities in studying exotic phenomena such as quantum phase transitions and ground state entanglement. Here, we experimentally simulate a highly controllable extended quantum Rabi model, capable of tuning into the ultra-strong or deep coupling regime, in a spin-motion-coupled trapped ion. We observe that the phonon driven by such a model with parity symmetry preserved (broken) would experience double (single) excitation in the ultra-strong coupling regime. Quantum phenomena such as strong ground state entanglement and quantum superposition in systems occur with parity symmetry, and these phenomena disappear following the symmetry breaking. We also find sensitive responses for the two-level system entropy and phonon Wigner function in the deep coupling regime, depending on the parameter across the symmetry transition point. This work offers the prospect of exploring symmetry-controlled quantum phenomena and their applications in high-precision quantum technologies.