EXACT STATIONARY PHOTON DISTRIBUTIONS DUE TO COMPETITION BETWEEN ONE-PHOTON AND 2-PHOTON ABSORPTION AND EMISSION

We consider steady states of the one-mode quantized field interacting with two independent baths, each characterized by the one-and two-phot on absorption and emission processes. In the absense of two-photon emi ssion, using an exact analytical solution to the master equation for t he diagonal elements of the density matrix in the Fock basis in terms of the confluent hypergeometric function, we obtain simple explicit ex pressions for the photon distribution function and for the factorial m oments in the limiting cases of weak and strong two-photon absorption. If the two-photon absorption is strong enough, the steady state exhib its a sub-Poissonian photon statistics characterizing nonclassical beh aviour, but Mandel's Q-parameter cannot be less -1/3. However, the dis tribution depends essentially on the temperature of the 'one-photon ba th'. For weak two-photon absorption, the stationary distribution is Ga ussian, provided that the temperature of the 'one-photon' bath is high enough. For an inversely populated 'one-photon' bath, the Q-parameter is close to 1/2. In a generic case of nonzero two-photon emission pro bability, approximate asymptotic expressions for the factorial moments are found.