Detecting dynamical quantum phase transition via out-of-time-order correlations in a solid-state quantum simulator

Abstract: 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.