Experimentally testing quantum critical dynamics beyond the Kibble-Zurek mechanism

Pioneered in the cosmological setting, the Kibble-Zurek mechanism (KZM) describes the universal dynamics across a phase transition, leading to the breakdown of adiabatic dynamics and the formation of topological defects. The authors present an experimental study of the universal critical dynamics of a 1D quantum Ising chain driven across the paramagnet-to-ferromagnet phase transition using a trapped-ion quantum simulator, and characterize the probability distribution of topological defects, which is found in excellent agreement with theoretical predictions. The Kibble-Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one-dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.