  Quantum many body system in equilibrium can be effectively characterized
using the framework of quantum statistical mechanics. However, nonequilibrium
behaviour of quantum many body systems remains elusive, out of the range of
such a well established framework. Experiments in quantum simulators are now
opening up a route towards the generation of quantum states beyond this
equilibrium paradigm. As an example in closed quantum many body systems,
dynamical quantum phase transitions behave as phase transitions in time with
physical quantities becoming nonanalytic at critical times, extending important
principles such as universality to the nonequilibrium realm. Here, in solid
state quantum simulator we develop and experimentally demonstrate that
out-of-time-order correlators, a central concept to quantify quantum
information scrambling and quantum chaos, can be used to dynamically detect
nonoequilibrium phase transitions in the transverse field Ising model. We also
study the multiple quantum spectra, eventually observe the buildup of quantum
correlation. Further applications of this protocol could enable studies other
of exotic phenomena such as many body localization, and tests of the
holographic duality between quantum and gravitational systems.
