  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 with
correspondence in an excited state phase diagram, instead of the ground state
one. We observe that the quench dynamics exhibits a non-analytical change with
respect to a parameter in the final Hamiltonian 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 using
dynamical phase transitions as a tool to probe physics at higher energy
eigenlevels of many-body Hamiltonians.
