Analytical expression is obtained for the cross-spectral density function of a Gaussian Schell-model (GSM) beam passing through an electromagnetic induced transparency (EIT) atomic vapor. The formula can be used in the study of the changes in the spectral density and spectral degree of coherence of the beam through the EIT atomic vapor. Numerical examples show that both the spectral density and the spectral degree of coherence of the GSM beam can be modulated by the Rabi frequency of the control light.
Temporal coherence of individual signal or idler beam, determined by the spectral correlation property of photon pairs, is important for realizing quantum interference among independent sources. Based on spontaneous four-wave mixing in optical fibers, we study the effect of chirp on the temporal coherence property by introducing a different amount of chirp into either the pulsed pump or individual signal (idler) beam. The investigation shows that the pump chirp induces additional frequency correlation into photon pairs; the mutual spectral correlation of photon pairs and the coherence of individual beam can be characterized by measuring the intensity correlation function
g(2) of the individual beam. To improve the coherence degree, the pump chirp should be minimized. Moreover, a Hong-Ou-Mandel--type two-photon interference experiment with the signal beams generated in two different fibers illustrates that the chirp of the individual signal (idler) beam does not change the temporal coherence degree, but affects the temporal mode matching. To achieve high visibility among multiple sources, apart from improving the coherence degree, mode matching should be optimized by managing the chirps of individual beams.
It is generally taken for granted that the spectrum of light does not change on propagation. This belief is implicit in all spectroscopy. In the last few years it was discovered that while such spectral invariance holds for radiation from commonly used sources it does not hold, in general, because the spectrum of emitted radiation depends not only on the source spectrum but also on the coherence properties of the source. It was found that in some cases the induced changes may be appreciable, possibly resulting in frequency shifts of spectral lines. It has also been demonstrated that similar spectral changes may be produced by scattering on media whose dielectric susceptibility is appropriately correlated.