Experimental Realization of Rabi-Hubbard Model with Trapped Ions.

Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here we report an experimental realization of the Rabi-Hubbard model using up to $16$ trapped ions. With spin observables, we probe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamics in various parameter regimes. We verify the simulated Hamiltonian by comparing with theoretical results in small systems. For larger-size systems of $16$ ions and $16$ phonon modes, the effective Hilbert space dimension exceeds $2^{57}$, whose dynamics is intractable for classical supercomputers.