Photon density-density correlation spectrum of a three-level atom at high photon densities

The excitation spectrum arising from photon density-density correlations has been calculated for two types of a single three-level atom for which electronic transitions occur: from two different upper levels to a common lower one and from a common upper level to two different lower levels, respectively. Photon density-density correlations in such a system are described by the interference spectrum, which results from the beating between the two electronic transition frequencies. The spectral function has been calculated in the limit of high photon densities and consists of three pairs of bands, which are similar to those of the interference spectrum when the main peak at the frequency ω = Δ is missing, where Δ is equal to the frequency splitting between the excited states of the atom. The probability amplitude for the occurrence of each pair of bands depends on the parameter η = Δ2Ω2, where Ω is the Rabi frequency. Numerical values indicate that the probability amplitudes become negative, zero, or positive for different values of the parameter η. Using the spectral function, an expression has been derived for the photon density-density correlation function, which describes photon density-density correlations at two different times and at finite temperatures. In the limit of equal times, the mean square photon density distribution function has been calculated and discussed. At zero temperatures, numerical values for the mean square photon density distribution function indicate that it is positive for η<0.5, it vanishes for values of η approximately 0.7>η>0.5, and it becomes negative for η≥0.75. The possibility of observing photon density-density correlations is discussed.