Dynamics of a laser-cooled and trapped radiator interacting with the Holstein-Primakoff SU(1,1) coherent state

We study the interaction between a laser-cooled and trapped equidistant three-level atom (ion) and a single-mode cavity field. The dipole moment matrix transition elements between the adjacent atomic energy levels d12 and d23 are assumed to be different. This problem generalizes the model of a pair of indistinguishable two-level atoms. An intensity-dependent coupling is assumed between the three-level atom and the radiation field. In this situation, we suppose that at the initial moment the field is in the Holstein-Primakoff SU(1,1) coherent state and obtain the exact analytical solution for the atom-field state vector. The quantum-statistical and squeezing properties of the radiation field are investigated. The obtained results are compared with those for the single two-level atom model. We observe that the exact periodicity of the squeezing revivals that was observed in the case of the single two-level atom is violated in the model involving the equidistant three-level radiator with different dipole moment matrix transition elements. In other words, the exact periodicity of the physical quantities can be destroyed only when more than two levels of the single-atom model are taken into account. Two limiting cases are considered. In the first case, when d12 → d23, the quantum-statistical and squeezing properties of the single-mode cavity field are similar to those for a pair of indistinguishable two-level atoms. In the second case, when d12 → 0, the exact periodicity of the squeezing revivals takes place. This limiting case is equivalent to the single two-level atom model.