Detection of Dynamical Phase Transitions in Real Time in Spinor Gases

We present a method to extract information about spin-dependent interactions and relative spinor phases from the observed spin population dynamics.  This method can be applied to systems experiencing unknown time-dependent interactions and is robust to initial estimates for the interactions.  Our results demonstrate the detection of dynamical phase transitions in real time via the relative spinor phase and the system energy in spinor gases subject to a variety of experimental sequences.  By informing our theoretical predictions with the extracted interactions, the observed nonequilibrium spin dynamics tuned by intricate spatial dynamics in a moving-lattice system can be well described over a wide range of conditions. This suggests that similar techniques could be applied to more thoroughly analyze other complex systems subject to time-dependent parameters, e.g., Floquet systems subject to periodically driven quadratic Zeeman energy, interactions, or spin-flopping fields.