Photon bunching in parametric down-conversion with continuous-wave excitation

Direct measurement of photon bunching ($g_{\left(2\right)}$ correlation function) in one output arm of a spontaneous-parametric-down-conversion source operated with a continuous pump laser in the single-photon regime is demonstrated. The result is in agreement with the statistics of a thermal field of the same coherence length and shows the feasibility of investigating photon statistics with compact continuous-wave-pumped sources. Implications for entanglement-based quantum cryptography are discussed.

Figure 1

(Color online) The experimental setup consists of a SPDC source of photon pairs, a balanced beam splitter, and two single-photon silicon detectors combined in a Hanbury Brown and Twiss [7] configuration.

Figure 2

(Color online) Second-order correlation function between the idler and signal arms of an auxiliary degenerate SPDC source at 810 nm $\left(405\text{nm}\to 810\text{nm}+810\text{nm}\right)$ rescaled to unity. Since the time correlation between photons of the same pair is tight (subpicoseconds), the FWHM (approximately 640 ps) is essentially an estimate of the combined jitter of the two silicon detectors and the time-tagging unit.

Figure 3

(Color online) $g_{\left(1\right)}$ of the 810 nm arm of the SPDC source as measured in a Michelson interferometer vs optical path difference. $g_{\left(1\right)}$ was calculated from the fringe visibility of the interferogram. The experimental visibility at zero optical path difference is slightly less than 1. When the maximum of the visibility is rescaled to one, the total area under the squared envelope is $\sim 2.2\text{ps}$. The inset shows the visibility fringes around the central part of the interferogram.

Figure 4

(Color online) Second-order correlation function (signal-signal $g_{\left(2\right)}$) of the 810 nm arm of a SPDC source normalized over a measured plateau of $N$ counts in a bin. The solid line represents the washed-out bunching peak (original height of 2) obtained from the jitter plot rescaled to an area of 2.17 ps. Error bars, representing statistical fluctuations of the measured data, are set to $\sqrt{N}$. The shaded gray area, only visible at the very top of the peak, represents the uncertainty in the model prediction. The inset shows an enlarged section of the plateau.