Dynamics of an M-level atom interacting with cavity fields: Effects of the level number on quantum collapse and revival

A quantum-mechanical theory is developed to treat the interaction of a multilevel atom with cavity fields of arbitrary detunings. The Hilbert space spanned by the energy eigenvectors is divided into subspaces specified by eigenvalues of the total excitation number, which is a constant of motion. Since the total Hamiltonian does not connect states in different subspaces, it can be diagonalized in each subspace independently. The time evolutions of the level occupation probabilities and the mean photon number are investigated numerically, and their variations with the atomic level number and the initial photon number are discussed. Their relation with the field squeezing is also discussed.