Observation of dynamical quantum phase transitions in spinor condensates with no correspondence in ground-state phase diagram

Dynamical quantum phase transitions are closely related to equilibrium quantum phase transitions for ground states. Here, we report an experimental observation of a dynamical quantum phase transition in a spinor condensate beyond this conventional wisdom. We observe that the quench dynamics exhibits a non-analytical change with respect to a control parameter in the absence of a corresponding phase transition for the ground state there. We make a connection between this singular point and a phase transition point for the highest energy level in a subspace with zero spin magnetization of a Hamiltonian. We further show the existence of dynamical phase transitions for finite magnetization corresponding to the phase transition of the highest energy level in the subspace with the same magnetization. Our results open a door for studying dynamical phase transitions beyond the conventional ground-state phase diagram and using them as a tool to probe the phase transitions at higher energy eigenlevels of many-body Hamiltonians.