Statistics of multiphoton events in spontaneous parametric down-conversion

We present an experimental characterization of the statistics of multiple photon pairs produced by spontaneous parametric down-conversion realized in a nonlinear medium pumped by high-energy ultrashort pulses from a regenerative amplifier. The photon-number-resolved measurement has been implemented with the help of a fiber loop detector. We introduce an effective theoretical description of the observed statistics based on parameters that can be assigned direct physical interpretation. These parameters, determined for our source from the collected experimental data, characterize the usefulness of down-conversion sources in multiphoton interference schemes that underlie protocols for quantum-information processing and communication.

Figure 1

(Color online) Schematic of a spontaneous parametric down-conversion source. The nonlinear crystal $X$ is pumped with a laser beam $p$. The generated photons are highly correlated, and useful modes $a$ and $b$ are typically selected by narrow spatial and frequency filters $f$.

Figure 2

Contour plots of the contamination parameters for single photon pairs ${\epsilon }_2$ (upper plot) and double photon pairs ${\epsilon }_4$ (lower plot) as a function of the overall efficiency $\eta$ and the corresponding production rates $p_{1,1}$ and $p_{2,2}$. The calculations have been carried out in the regime of single selected modes when $\mathcal{M}=1$.

Figure 3

(Color online) Experimental setup. RegA, Regenerative amplifier; FL, IL, lenses; XSH, second harmonic crystal; DM, dichroic mirrors; BG, blue glass filter; ND, neutral density filter; HWP, half-wave plate; X, down-conversion crystal; RG, red glass filters; FC, fiber coupling stages; IF, interference filter; D1, D2, avalanche photodiodes; CE, coincidence electronics. Thin solid lines indicate single mode fibers, dashed lines, multimode fibers.

Figure 4

(Color online) An exemplary joint photon number distribution measured without spectral filters. The average photon numbers in the two arms are $⟨n⟩=0.15$ and $⟨n^{\prime }⟩=0.18$.

Figure 5

Equivalent number of modes $\mathcal{M}$ in a single arm as a function of the average photon number $⟨n⟩$, for measurements carried out without interference filters (circles), with 10 (squares) and $5\mathrm{nm}$ FWHM filters (crosses).

Figure 6

Equivalent detection efficiency $\eta$ as a function of the total average photon number $⟨n⟩$, measured without interference filters (circles), with 10 (squares) and $5\mathrm{nm}$ FWHM filters (crosses).

Figure 7

(Color online) Contamination parameter ${\epsilon }_2$ for single photon pairs as a function of the pair production rate, measured without interference filters (circles) and with 10 (squares) and $5\mathrm{nm}$ FWHM filters (crosses). The parameters of the fitted theoretical curves are $\mathcal{M}=16.6$ and $\eta =4.5\%$ (solid line), $\mathcal{M}=3.1$ and $\eta =4.2\%$ (dashed line), and $\mathcal{M}=1.5$ and $\eta =2.6\%$ (dash-dotted line).

Figure 8

(Color online) Contamination coefficient ${\epsilon }_4$ for double photon pairs as a function of the production rate, measured without interference filters (dots). The parameters of the fitted theoretical curve are $\mathcal{M}=16$ and $\eta =4.9\%$ (dashed line). Measurements with interference filters did not provide statistically significant data.