Experimental Reconstruction of Photon Statistics without Photon Counting

Experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams are reported. Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood estimation and does not involve photon counting. Reconstructions of the distribution for both semiclassical and quantum states of light are reported for single-mode as well as for multimode beams.

Figure 1

Reconstruction of the photon distribution for a weak coherent state (gray) and for the heralded single-photon state produced in type II PDC (black). Inset: experimental frequencies $f_{\nu }$ of no-click events as a function of the quantum efficiency ${\eta }_{\nu }$ for a weak coherent state (upper curve) and for PDC heralded photon state (lower curve) compared with the theoretical curves, $p_{\nu }\simeq 1-{\eta }_{\nu }|\alpha {|}^2$ and $p_{\nu }=1-{\eta }_{\nu }$, respectively.

Figure 2

Reconstructed photon distribution (black bars) and best theoretical fit (gray bars) for three different states in the pulsed regime: (a) laser pulse, (b) diffused laser pulse, (c) multimode state produced in type I PDC. Insets: experimental frequency $f_{\nu }$ data in function of the quantum efficiency ${\eta }_{\nu }$ and theoretical model for each one of the states.