COMPETITION BETWEEN ONE-PHOTON AND 2-PHOTON ABSORPTION PROCESSES

We obtain an exact analytical solution to the master equation for the diagonal density matrix elements of the one-mode quantized held, when both one- and two-photon absorption processes are present. Explicit ex pressions 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 counterpar ts are considered in detail. The existence of the universal time-depen dent distribution of initially highly excited states is discovered, an d simple explicit expressions are given for some specific values of pa rameters. This distribution holds for times exceeding the transition t ime of the order of (D-2 (n) over bar(0))(-1), D-2, (n) over bar(0) be ing the two-photon absorption coefficient and the initial mean photon number, respectively. The transition time from any initial state to th e ground state is shown to be finite even for highly excited states, p rovided that D-2 not equal 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.