Home

Direct measurement of the dependence of the photon-number distribution on the number of modes in parametric down-conversion


  Liat Dovrat [1]  ,  Michael Bakstein [1]  ,  Daniel Istrati [1]  ,  Assaf Shaham [1]  ,  Hagai Eisenberg [1]  
 [1] Racah Institute of Physics, Hebrew University of Jerusalem, Israel

For more than two decades, the optical process of parametric down-conversion (PDC) has been the primary photon source in quantum optics experiments.  The statistical nature of this process is a subject of great interest and has practical implications on state preparation schemes.  The photon-number distribution of a PDC source can range between a thermal distribution, when a single down-converted mode is collected, and a Poisson distribution when an infinitely large number of modes (multimode) is collected [1]. In this work, we use a photon-number resolving detector in order to directly measure the photon statistics of the signal and idler photons collected from a controlled number of spatial and spectral modes, allowing us to observe the range of distributions between the single-mode and the multimode extremes.

We have built a detection setup, which incorporates a Silicon Photomultiplier (SiPM) [2] as a photon-number resolving detector. Measurements were conducted on a single polarization mode of a type-II collinear PDC process. The photon states were produced using amplified 150 fs pulses which pump a type-II collinear β−BaB2O4 (BBO) nonlinear crystal. The number of collected spatial and spectral modes was controlled by spatially and spectrally filtering the photons using optical fibers with different core diameters and numerical apertures [3] and filters of different bandwidths, respectively.

Our setup enables good photon-number discrimination for as many as 20 photons. The high photon-number resolution of our system enables the  differentiation between distributions collected from a different number of spectral and spatial modes. The results show how the photon-number distribution is determined by the number of collected modes. Furthermore,we show the dependence of the average number of photons on the number of collected
modes, and the stimulated nature of parametric down-conversion. Our experimental data is interpreted using a novel analytical model for the optical crosstalk effect in SiPM detectors, which we also present.

[1] L. Mandel, Proceedings of the Physical Society 74 , 233 (1959).
[2] G. Bondarenko, B. Dolgoshein, V. Golovin, A. Ilyin, R. Klanner, and E. Popova, Nucl. Phys. B. (Proc. Suppl) 61 , 347 (1998).
[3] A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1991).