Exact results for a model of a three-level atom

Siamak Khademi, Ghasem Naeimi, Samira Alipour +1 more

Semi-quantum or full-quantum electromagnetically induced transparency has been fully studied for three-level atoms in a weak field approximation method, where probe field is very wea ker than the coupling field. The weak field approximation is no t valid in full-quantum model where the number of coupling photons is not so large. In the present article, the master equations for the interaction of two-mode photons with a three-level Λ -type atom are exactly solved and the exact dispersion and absorption spectra for the probe beam photons are also obtained analytically. The results of the exact scheme are compared with the corresponding results in the weak field approximation method in full-quantum and semi-classi cal models.

Denis A. Demidov, N. K. Solovarov

D. A. M. Abo-Kahla, M. M. A. Ahmed, A. T. M. Makram-Allah

Ravinder Rupchand Puri

An unified approach to the dynamics of a class encompassing several widely encountered models of a two-level and of a three-level atom interacting with a quantized electromagnetic field is developed. The approach is based on separating the dependence of the dynamics on the field and the atomic operators by expressing the unitary evolution operator in the basis of the atomic operators. The evolution operator then resembles the one for the atoms in an externally applied classical field. The exactly solvable examples of the deterministic, as well as fluctuating, time-dependence of the atom-field coupling are discussed. The issue of an effective two-level description for a three-level system is also analysed. The proposed method not only provides an unified approach to the models belonging to the class considered but is found to uncover several new results even for simple widely studied models.

V. I. Koroli, Victor V. Zalamai

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 d 12 and d 23 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 d 12 → d 23 , 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 d 12 → 0, the exact periodicity of the squeezing revivals takes place. This limiting case is equivalent to the single two-level atom model.