Research of the impact of group velocity dispersion on the second-order correlation of entangled light field

In the experiment presented in the paper, HBT (Hanbury-Brown and Twiss) interferometer is used to measure the second-order correlation function (G(2)) for two entangled photons, denoted as signal and idle ones, generated by the spontaneous parametric down-conversion process. When an extra optical fiber is inserted in the signal's path, the arrival times of these two photons are different, so that the length of the fiber can be estimated by measuring the time offset in the G(2) function. As the laser light we used is not monochromatic, the experimental result is affected by the group velocity dispersion (GVD). Light of different wavelength has different velocity and leads to different travelling time in the fiber. Through calculation, we find that the G(2) function of each wavelength has the same shape but different center time offset. Thus, the final G(2) function, as a superimposition of the functions with different wavelengths, is broadened in a long-distance measurement, which seriously reduces the estimation accuracy. We analyze this phenomenon in both theory and experiment, and the experimental results fit our theoretical simulations quite well. In the theoretical analysis, we find that the group velocity dispersion introduces an additional time offset to the final G(2) function which is proportional to the total time offset. In our experiment, this additional time offset is about 1% of the total time offset. In particular, this effect results in a 63600 ps extra time offset, which can be compensated in post process, with a time accuracy of about 1 ps. This paper focuses on the G(2) function affected by the group velocity dispersion, and also calculates the additional time offset produced by group velocity dispersion, and thus gives a method to compensate the additional time offset through calculation.