Competition between one- and two-photon absorption processes

We obtain an exact analytical solution to the master equation for the diagonal density matrix elements of the one-mode quantized field, when both one- and two-photon absorption processes are present. Explicit expressions for the time dependences of the factorial moments are found. The special cases of the initial Fock's, binomial, negative binomial, thermal, and coherent states, as well as of their even/odd counterparts are considered in detail. The existence of the universal time-dependent distribution of initially highly excited states is discovered, and simple explicit expressions are given for some specific values of parameters. This distribution holds for times exceeding the transition time of the order of (D2n-bar0)-1, D2, n-bar0, being the two-photon absorption coefficient and the initial mean photon number, respectively. The transition time from any initial state to the ground state is shown to be finite even for highly excited states, provided that D2≠0. Although the final stage of evolution is characterized by the sub-Poissonian statistics for any initial state, Mandel's parameter is shown to be very sensitive to small differences in high-order initial factorial moments at the intermediate stage. (author)