A density matrix method is used to obtain an exact solution for the reduced density matrix of the field in an arbitrary multimode m-photon absorption process. The results of some earlier specialized studies of photon statistics in multiphoton absorption process can be recovered from this solution.
Exact solutions of the master equations which describe single-mode m-photon absorption and m-photon emission processes in a two-level atomic system are obtained using a density-matrix approach. Some aspects of the photon statistics, e.g., antibunching, are discussed.
Abstract In order to continue and generalize the studies of the density matrix of a light field undergoing k‐photon absorption, in this paper we put the emphasis on the off‐diagonal elements. The solution obtained earlier for the diagonal elements describing the photon statistics can be found as a special case but will not be discussed again. The general solution calculated by recursion shows an asymptotic behaviour if the initial photon number is sufficiently high. Only the initial phase information survives. Illustrating the solution we start with coherent light and a generalized coherent state.
A simple procedure is described for computing steady-state excited vibrational state populations for multiphoton absorption processes in many-level systems. The procedure utilizes techniques already in the literature, i.e., expansion of the density matrix as a Fourier series in the frequency of the monochromatic radiation field, and introduction of linewidths and thermal relaxation by the addition of empirical terms to the density matrix time-development equation. Numerical computations can be carried out quickly on idealized systems, using commercially available band matrix inversion routines. A sample calculation for a 10-level, nine-photon process is presented.