Universal relation between the conditional auto-correlation function and the cross-correlation function of biphotons.

We systematically studied the relation between the conditional auto-correlation function (CACF) and cross-correlation function (CCF) of biphotons or pairs of single photons. The biphotons were generated from a heated atomic vapor via the spontaneous four-wave mixing (SFWM) process. In practical usage, one single photon of a pair is utilized as the heralding photon, and another is employed as the heralded photon. Motivated by the data of CACF of the heralded photons versus CCF, we proposed a universal formula to predict the CACF. The derived formula was based on general theory and is also valid for the biphoton generation process of spontaneous parametric down-conversion (SPDC). With the formula, we utilized the experimentally determined parameters to predict CACFs, which can well agree with the measured CACFs. The proposed formula enables one to quantitatively know the CACF of heralded single photons without the measurement of Hanbury-Brown-Twiss-type three-fold coincidence count. This study provides a better understanding of biphoton generation using the SFWM or SPDC process. Our work demonstrates a valuable tool for analyzing a vital property of how the heralded photons are close to Fock-state single photons.

Generation of sub-MHz and spectrally-bright biphotons from hot atomic vapors with a phase mismatch-free scheme.

We utilized the all-copropagating scheme, which maintains the phase-match condition, in the spontaneous four-wave mixing (SFWM) process to generate biphotons from a hot atomic vapor. The linewidth and spectral brightness of our biphotons surpass those of the biphotons produced with the hot-atom SFWM in the previous works. Moreover, the generation rate of the sub-MHz biphoton source in this work can also compete with those of the sub-MHz biphoton sources of the cold-atom SFWM or cavity-assisted spontaneous parametric down conversion. Here, the biphoton linewidth is tunable for an order of magnitude. As we tuned the linewidth to 610 kHz, the generation rate per linewidth is 1,500 pairs/(s·MHz) and the maximum two-photon correlation function, gs,as(2), of the biphotons is 42. This gs,as(2) violates the Cauchy-Schwarz inequality for classical light by 440 folds, and demonstrates that the biphotons have a high purity. By increasing the pump power by 16 folds, we further enhanced the generation rate per linewidth to 2.3×104 pairs/(s·MHz), while the maximum gs,as(2) became 6.7. In addition, we are able to tune the linewidth down to 290±20 kHz. This is the narrowest linewidth to date among all single-mode biphoton sources of room-temperature and hot media.