In the three‐dimensional (3D) transversely symmetric oscillator, there are plentiful degeneracies and gaps in the quantum energy spectrum as a function of the ratio of the transverse to longitudinal frequency. It is theoretically verified that while...
In the three‐dimensional (3D) transversely symmetric oscillator, there are plentiful degeneracies and gaps in the quantum energy spectrum as a function of the ratio of the transverse to longitudinal frequency. It is theoretically verified that while the SU(2) interaction destroys the original degeneracies, numerous new degeneracies and gaps emerge around the original degeneracies to form a similar fine energy spectrum. The classical trajectories at the emergent degeneracies are analyzed to be localized on the 3D parametric surfaces which are constituted by the topologically invariant curves in the transverse tomography. The quantum coherent states are exploited to develop the wave functions that correspond to the 3D geometric surfaces in classical dynamics. Furthermore, the wave structures of the stationary coherent states at small quantum numbers are explored and found to display peculiar patterns with symmetries related to classical trajectories.
It is theoretically verified that while the SU(2) interaction destroys the original degeneracies in the three‐dimensional (3D) transversely symmetric oscillator, numerous new degeneracies and gaps emerge around the original degeneracies to form a fine energy spectrum. The classical trajectories at the emergent degeneracies are localized on the 3D parametric surfaces which are constituted by the topologically invariant curves in the transverse tomography. The quantum coherent states are developed to obtain the wave functions for manifesting the correspondence with the 3D geometric surfaces in classical dynamics. The feature of the theoretical coherent states can be linked to the formation of the experimental 3D structured laser modes.