群速度色散对于纠缠光场二阶关联函数影响的研究

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

HBT干涉是量子测量中的一种重要手段,其通过计算光场的二阶关联函数而得到测量结果.在长距离测距中,光场的二阶关联函数会受到光纤中群速度色散的影响而发生展宽和平移,从而在一定程度上影响测量精度.本文主要针对二阶关联函数半高宽受群速度色散的影响,给出了半高宽与测量距离与群速度色散系数的关系.

In the experiment presented in the paper, HBT（Hanbury-Brown and Twiss） interferometer is used to measure the second-order correlation function（G2） 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 G2 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 G2 function of each wavelength has the same shape but different center time offset. Thus,the final G2 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 G2 function which is proportional to the total time offset. In our experiment, this additional time offset is about1% 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 G2 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.