Supporting Kibble-Zurek Mechanism in Quantum Ising Model through a Trapped Ion.

The Kibble-Zurek mechanism is the paradigm to account for the non adiabatic dynamics of a system across a phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. Our results support the Kibble-Zurek mechanism in the quantum regime and advance the quantum simulation of critical systems far-away from equilibrium.