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Journal of Physics A Mathematical and General

N-level atom and (N-1) modes: an exactly solvable model with detuning and multiphotons

A.M. Abdel-Hafez, A.‐S. F. Obada, Mahmoud Ahmad

Published Apr 21, 1987• 42 citations
Publisher

Abstract

A model is presented for the interaction between an N-level atom and (N-1) modes. Under the exact resonance condition between the modes with a detuning parameter, the Hamiltonian becomes solvable. The evolution operator is calculated and the time development for the photon number operators and the occupation numbers are obtained. Multiphoton processes are discussed.

DOI
10.1088/0305-4470/20/6/004

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A model is presented for the interaction between an N-level atom and (N-1) modes. Under the exact resonance condition between the modes with a detuning parameter, the Hamiltonian becomes solvable. The evolution operator is calculated and the time development for the photon number operators and the occupation numbers are obtained. Multiphoton processes are discussed.
We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).
A model is presented to investigate the problem of interaction between an N-level atom and N-1 modes of the field. The model includes detuning. Constants of motion are obtained. The evolution operator is calculated, and the probability distribution function for the photon numbers is computed for different initial atomic states. The characteristic functions are computed. Different statistical quantities concerning the photons or the atomic system are given. The case of a three-level atom and two modes is considered for its different configurations. The phenomenon of collapses and revivals is discussed for squeezed light, and the effect of squeezing is shown in this phenomenon.
The system of a three-level atom in the Ξ configuration coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time evolution operator for the system. Based on this su(3) structure, we also show that the system of a three-level atom in the Ξ configuration can be exactly transformed to an effective two-level Hamiltonian by an unitary transformation. Finally, we show that there exist an su (N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.