Nonclassical light in two-photon Jaynes–Cummings model of a three-level atom with different dipole transitions

Abstract

We investigate two-photon interaction between an equidistant three-level atom and the quantized cavity field. It is supposed that dipole moment matrix transition elements between neighbouring energy levels d 12 and d 23 may be different. This problem generalizes Jaynes–Cummings model of a pair of indistinguishable two-level atoms interacting with the squeezed vacuum. Assuming that at initial moment the field is in the squeezed vacuum state, exact analytical solution for atom-field state-vector is found. With help of this solution quantum-statistical and squeezing properties of nonclassical light are studied as a function of parameter α = d 23/d 12. The numerical results are compared with those for the pair of indistinguishable two-level atoms. It is found that in proposed model, exact periodicity of squeezing revivals is violated by analogy with model of a pair of two-level atoms. The two limiting cases are examined. In first limiting case in which d 12 → d 23, quantum-statistical properties of single-mode cavity field remind those for the pair of indistinguishable two-level atoms. In second one d 12 → 0, quantum-statistical and squeezing features of proposed model are similar to those for single two-level atom model.