Abstract
We consider steady states of the one-mode quantized field interacting with two independent baths, each characterized by the one- and two-photon absorption and emission processes. In the absense of two-photon emission, using an exact analytical solution to the master equation for the diagonal elements of the density matrix in the Fock basis in terms of the confluent hypergeometric function, we obtain simple explicit expressions for the photon distribution function and for the factorial moments in the limiting cases of weak and strong two-photon absorption. If the two-photon absorption is strong enough, the steady state exhibits a sub-Poissonian photon statistics characterizing nonclassical behaviour, but Mandel's -parameter cannot be less . However, the distribution depends essentially on the temperature of the `one-photon bath'. For weak two-photon absorption, the stationary distribution is Gaussian, provided that the temperature of the `one-photon' bath is high enough. For an inversely populated `one-photon' bath, the -parameter is close to . In a generic case of nonzero two-photon emission probability, approximate asymptotic expressions for the factorial moments are found.
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