GENERATION OF THE NON-CLASSICAL STATES OF THE QUANTIZED CAVITY FIELD IN THE INTERACTION WITH TRAPPED EQUIDISTANT THREE-LEVEL ION

Abstract

The interaction between the laser cooled and trapped equidistant three-level atom (ion) and the quantized cavity field is investigated. The dipole moment matrix transition elements between the adjacent atomic energy levels d12 and d23 are assumed to be different. This model generalizes the problem of the pair of indistinguishable two-level atoms interacting with the squeezed vacuum which is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements. The exact analytical solution for the atom-field state-vector is found in the case in which at the initial moment t = 0, the single-mode cavity field is supposed to be in the squeezed vacuum state. With the help of this solution, the quantum-statistical and squeezing properties of the radiation field are studied. The obtained results are compared with those for the single two-level atom model. It should be noted that in the proposed model, the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one. The two limiting cases are analyzed. In the first limiting case in which d12 → d23 the quantum-statistical properties of the single-mode cavity field resemble those for the pair of indistinguishable two-level atoms. In the second one d12 → 0 the quantum-statistical and squeezing features of the proposed model are similar with those for the single two-level atom model.