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.