Spectral correlation control in down-converted photon pairs

Sources of photon pairs based on the spontaneous parametric down-conversion process are commonly used for long-distance quantum communication and quantum information processing. The key feature for improving the range of transmission is engineering their spectral properties. Our analysis shows the way for full control of spectral correlation within a fiber-coupled photon pair. The result of extensive numerical simulations allows us to specify the settings for the generation of pairs featuring positive-energy correlation, which can potentially improve the signal-to-noise ratio in practical implementation of quantum communication protocols. We analytically and numerically analyze the characteristics of a source based on a $\beta$-barium borate crystal cut for type-II phase matching at the degenerated frequencies $755\mathrm{nm} \to 1550\mathrm{nm}+1550\mathrm{nm}$. The presented framework is general and can be applied to other crystals.

Figure 1

A single-photon source is based on a $\beta$-barium borate (BBO) nonlinear crystal of thickness $L$ cut for type II phase matching at frequencies $755\mathrm{nm} \to 1550\mathrm{nm}+1550\mathrm{nm}$ and half cone opening angle 3 deg. A pump pulse of ${\tau }_p$ duration is centered around $775\mathrm{nm}$ and its transverse spatial mode is assumed to be a Gaussian function with a characteristic diameter $2w_p$. The photon pairs are coupled into single mode fibers (SMF), which together with coupling stages (C1,C2) define collected transverse spatial modes, which are assumed to be Gaussian functions of diameters $2w_f$.

Figure 2

(a,c) The effective phase-matching function $\mathrm{\Theta }({\omega }_s,{\omega }_i)$ and (b,d) the biphoton wave function $\mathrm{\Psi }({\omega }_s,{\omega }_i)$ for two exemplary crystal lengths (a,b) $L=1$ mm and (c,d) $L=7.5$ mm are depicted with contours. The functions are real and the contours refer to five equidistant values of the respective functions. Green solid (dashed) lines represent pump pulse central frequency (spectral width). The simulations were performed for ${\tau }_p^{\text{FWHM}}=50$ fs, $2w_p=100\mu \mathrm{m}, 2w_f=440\mu \mathrm{m}$. The origin of the negative spectral correlation, panel (b), can be understand as an overlap of a broad EPMF (thin crystal, large ${\sigma }_{+}$) with a pump pulse spectral amplitude. On the other hand, a thin EPMF (long crystal, small ${\sigma }_{+}$) can result in positive spectral correlation as seen in panel (d).

Figure 3

The SMF coupling efficiency $\eta$ (surface plot), SMF coupled pair production rate $R_c$ (color scaling), and correlation parameter $r$ (contours) as a function of pump $2w_p$ and collected $2w_f$ spatial mode diameters.