- An extended medium driven in a double Raman configuration generates Stokes and anti-Stokes fields that are described by coupled parametric oscillator equations with solutions that depend on input boundary operators and quantum noise operators. We identify the conditions where the boundary operators can be the substitute to the noise operators for describing two-photon cross correlation in forward and backward geometries. These conditions include short sample and small decoherence between ground states bc, and they are fulfilled by the spontaneous Raman electromagnetic induced transparency scheme (weak pump with large detuning). We verify the correspondence between the results from boundary and noise operators analytically and show that the correlation due to the boundary operators is typically smaller than that due to the noise operators. In general the noise operators are required to obtain the correct correlation, especially when the control laser field is weak and bc is finite. Explanations for the findings are given based on the physics represented by the boundary operators and noise operators. Similar conclusions are obtained for the Stokes and anti-Stokes intensities. 2007 The American Physical Society.