Experimental Realization of the Rabi-Hubbard Model with Trapped Ions

TL;DR

This paper reports the experimental realization of the Rabi-Hubbard model using trapped ions, demonstrating quantum phase transitions and dynamics in a highly complex quantum system beyond classical simulation capabilities.

Contribution

It is the first experimental implementation of the Rabi-Hubbard model with up to 16 ions, enabling controlled study of its equilibrium and dynamical properties.

Findings

Observation of ground-state quantum phase transition.

Measurement of quantum dynamical evolution in various regimes.

Verification of the model Hamiltonian through experimental data.

Abstract

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 $2^{57}$, whose dynamics is intractable for classical supercomputers.