中国激光, 2021, 48 (3): 0312001, 网络出版: 2021-02-02   

基于波长到时间映射快速测量纠缠光子相位匹配波长的实验方法 下载: 1160次

Experimental Method for Fast Measuring the Phase-matched Wavelengths of Entangled Photons by Wavelength-to-Time Mapping
李百宏 1,2夏志广 1,2项晓 2,3,*靳亚晴 2,3权润爱 2,3董瑞芳 2,3,**刘涛 2,3张首刚 2,3
作者单位
1 西安科技大学理学院, 陕西 西安 710054
2 中国科学院国家授时中心中国科学院时间频率基准重点实验室, 陕西 西安 710600
3 中国科学院大学天文与空间科学学院, 北京 100049
摘要
准相位匹配有利于实现高效的自发参量下转换, 它由非线性晶体的极化周期和依赖于温度的折射率决定。为了确定特定波长处所需的晶体温度,需要测量相位匹配波长随晶体温度的变化关系。单色仪的传统测量方法具有测量精度较低且耗时长等缺点。提出了一种实验方法,该方法能快速准确测量纠缠光子相位匹配波长随晶体温度变化的关系。在信号和闲置光路中先后加入色散元件, 通过测量纠缠光子对到达时间关联峰值处的时间延迟随晶体温度的变化关系, 利用波长到时间的映射关系将其转化为波长随晶体温度的变化关系。给出了周期极化铌酸锂(PPLN)波导和周期极化磷酸氧钛钾(PPKTP)晶体的实验测量结果,测量精度优于0.1 nm, 测量时间约为几分钟。测量精度受限于单光子探测器的抖动时间和色散元件色散量的大小。原则上,抖动时间越小,色散量越大,测量精度越高。最后讨论了Sellmeier方程计算的结果与实验结果存在差异的可能原因。所提方法可以用来校准相位匹配波长与晶体温度的关系及极化周期,并有望实现温度依赖的Sellmeier方程的修正或改进。
Abstract

Objective The entangled photons generated by the spontaneous parameter down-conversion (SPDC) process have wide applications in quantum precision measurement, quantum spectroscopy, quantum imaging, quantum teleportation, and quantum security communications. However, one can only obtain a highly efficient SPDC when the phase-matching condition (conservation of momentum) is satisfied. In general, only a few birefringent crystals can meet the phase-matching condition, however the phase-matched wavelength (PMW) and bandwidth of entangled photons are limited. Afterwards, the quasi-phase matching (QPM) technology is proposed to solve the limitation problem of a birefringent crystal by artificially modulating the polling periods of the crystal. QPM is determined by the polling period and the refractive index of the crystal. The crystal temperature can be used to adjust the refractive index and different crystal temperatures are corresponding to different PMWs. To determine the crystal temperature at the required PMW, it is necessary to know the relationship between the PMW and crystal temperature. The temperature-dependent Sellmeier equation can be used to estimate this relationship. However, the Sellmeier equations of many nonlinear crystals are still unknown. Even if the Sellmeier equation is known, there is still a discrepancy between the estimated result and the experimental result in some special wavelengths and temperature ranges since the coefficients in the Sellmeier equation come from some empirical values. Thus, it needs to be revised or improved continuously. Therefore, it is necessary to use some experimental methods to accurately measure the PMW of the entangled photons in the SPDC process. In experiments, a monochromator is usually used to measure the spectrum of entangled photons and thus the relationship between the PMW and the crystal temperature is obtained. However, owing to the scanning for different wavelengths at different crystal temperatures, the measurement is low-accuracy and time-consuming, especially for the entangled broadband spectra.

Methods Herein, we propose an alternative experimental method for fast measuring the PMW of entangled photons versus crystal temperature. It utilizes the wavelength-to-time mapping (WTTM) technology with a dispersive element to realize a fast measurement. In the experimental setup (Fig. 1), the fiber Bragg grating is successively inserted in the signal and idler paths. By adjusting the crystal temperature, one can obtain the two curves of the time delay between arrival time of signal and idler photons versus crystal temperature. Further, based on the wavelength-to-time mapping relation, these two curves can be converted into those of the PMWs of the signal and idler photons versus the crystal temperature. Before the experiment, we first calibrate the WTTM relation by measuring the idler wavelength as a function of the time delay, in which the programmable filters and FBG are together input in the idler path. The utilized SPDC sources are generated from a 10 mm long, type-II periodically poled LiNbO3(PPLN, Fig. 2) waveguide and a periodically poled KTiOPO4(PPKTP, Fig. 3) crystal pumped by a continuous wave distributed Bragg reflector laser (DBR laser) at 780 nm. A half-wave plate is used to optimize the SPDC efficiency by adjusting the polarization of the pump laser. After filtering out the residual pump beam using two long-pass filters (LPFs), the signal and idler photons are focused and then coupled into a fiber polarization beam splitter (FPBS). With the help of another half-wave plate, the signal and idler are separated into two polarization-orthogonal fiber paths marked using s and i, respectively. The coincidence count measurement is accomplished using a time-correlated single-photon counting module. According to our experimental results, we obtain a linear relation between the idler wavelength and the time delay, i.e., τ-=893203-523.6l. With this relation, we can estimate the FBG with Dl=-(523.6 ± 2.2) ps·nm -1 at 1560 nm.

Results and Discussions As examples, the experimental results are given with a PPLN waveguide (Fig. 2) and a PPKTP crystal (Fig. 3), which provides a proof for our proposed method. A measurement resolution better than 0.1 nm in Fig. 2 is obtained owing to the use of two superconducting nanowire single-photon detectors (SNSPDs) with the maximum standard deviation of 47 ps from the five measurements of full-width half-maximum (FWHM) of G(2). A measurement resolution better than 0.27 nm in Fig. 3 is obtained owing to the use of two semiconductor single-photon detectors with the maximum standard deviation of 143 ps using the same FBG. The measurement resolution in Fig. 2 is better than that in Fig. 3, because the SNSPDs the former used can provide lower time jitters. The resolution is limited by the time jitters of the detectors and the magnitude of the dispersive elements. In principle, the smaller the jitter of the detector and the larger the amount of dispersion, the higher the resolution. Compared with the traditional method using a monochromator (a few hours), this method only takes a few minutes.

Conclusions In conclusion, we propose an alternative experimental method for fast measuring the PMW of entangled photons versus crystal temperature based on the WTTM technology. A measurement resolution better than 0.1 nm is obtained in our experiment and the measurement time is reduced significantly (only a few minutes) if compared with that of the traditional method using a monochromator (a few hours). In addition, we analyse the discrepancy between the theoretical and experimental results and discuss some possible applications. The proposed method can be applied to calibrate the poling period of crystals and the relation between PMW and crystal temperature, and is expected to modify or improve the temperature-dependent Sellmeier equations of nonlinear crystals.

李百宏, 夏志广, 项晓, 靳亚晴, 权润爱, 董瑞芳, 刘涛, 张首刚. 基于波长到时间映射快速测量纠缠光子相位匹配波长的实验方法[J]. 中国激光, 2021, 48(3): 0312001. Baihong Li, Zhiguang Xia, Xiao Xiang, Yaqing Jin, Run'ai Quan, Ruifang Dong, Tao Liu, Shougang Zhang. Experimental Method for Fast Measuring the Phase-matched Wavelengths of Entangled Photons by Wavelength-to-Time Mapping[J]. Chinese Journal of Lasers, 2021, 48(3): 0312001.

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