The properties of an M-level equidistant radiator in the presence of SU(1,1) transition symmetry

We study the spontaneous emission of a multilevel equidistant excited quantum oscillator (nuclei, atoms, molecules) in case when the symmetry of the dynamical transitions between the levels is described by the SU(1,1) symmetry group. The results obtained are compared with those well-known for the SU(2) symmetry. It is shown that the equidistant radiator in the process of spontaneous decay in case of SU(1,1) symmetry exhibits either only acceleration or only a decrease of spontaneous emission rates, while in case of SU(2) symmetry the radiation pulse is similar to that for the Dicke superradiance. The exact steady-state solution for the atomic density operator for an equidistant radiator driven by a totally incoherent broad-band (chaotic) field for SU(1,1) symmetry group is obtained using the Fokker-Planck equation. It is found that for a strong field limit in case of SU(1,1) symmetry the fluctuations in the atomic population increase with the increasing of intensity of the external field and don not achieve their maximal value as in case of SU(2) symmetry. Moreover, in case of SU(1,1) transition symmetry we found that there is a superbunching effect for certain values of group parameter I, while in case of SU(2) symmetry only bunching and antibunching occur. It is found that for vanishing values of the external field intensity the second-order intensity correlation function has negative values. (authors)