Experimental Realization of the 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, the 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 and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 257, whose dynamics is intractable for classical supercomputers.

Automated summary

Quantum simulation is an important tool for studying strongly correlated many-body systems. The Rabi-Hubbard model, a hybrid of two fundamental models in quantum optics and condensed matter physics, demonstrates rich physics through local spin-boson interactions and long-range boson hopping competition. Experimental realization of the Rabi-Hubbard model using up to 16 trapped ions allowed for controlled study of its equilibrium properties and quantum dynamics, with verification of the model's predictions through theoretical and experimental comparisons.