  Rotational Bose-Einstein condensates can exhibit quantized vortices as
topological excitations. In this study, the ground and excited states of the
rotational Bose-Einstein condensates are systematically studied by calculating
the stationary points of the Gross-Pitaevskii energy functional. Various
excited states and their connections at different rotational frequencies are
revealed in solution landscapes constructed with the constrained high-index
saddle dynamics method. Four excitation mechanisms are identified: vortex
addition, rearrangement, merging, and splitting. We demonstrate changes in the
ground state with increasing rotational frequencies and decipher the evolution
of the stability of ground states.
