The density matrix in the $P$ representation of a beam of radiation amplified by a two-photon amplifier has been derived up to the lowest order in the time-dependent perturbation theory without placing any restriction on the population of the state of the atom. It is shown that a laser beam containing noise in addition to the harmonic signal exhibits anticorrelation after being passed through such an amplifier, if less than one-sixth of the total number of atoms are maintained in the excited state.

• Received 19 September 1969

DOI:https://doi.org/10.1103/PhysRevA.1.1696