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Thermal photon statistics in spontaneous parametric downconversion

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Abstract

We investigate photon statistics in the signal beam generated by frequency nondegenerate parametric downconversion both with and without a seed field along the idler direction. The experiments are performed on the signal generated in β-barium borate by a traveling-wave pump pulse that is the frequency-tripled output of an amplified Nd:YLF picosecond laser. The high powers obtained allow us to measure the number of photons with a simple detection technique. When both signal and idler fields are initially in their vacuum states, the generated fields are mixtures of equally occupied modes with thermal photon-number statistics.

©2004 Optical Society of America

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Supplementary Material (1)

Media 1: GIF (2233 KB)     

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Figures (4)

Fig. 1.
Fig. 1. Layout of the experimental setup. The outputs (fundamental, ω ; second-harmonic, 2ω ; third-harmonic, 3ω) of the picosecond amplified Nd:YLF laser serve as: pump (3ω); an idler seed when necessary (ω); synchronous trigger (2ω) for the measuring apparatus via the photodiode, PD. BBO I is a nonlinear crystal with type I interaction. Lens LB focuses the signal cone reflected by BBO I onto the S monitor (photodiode monitoring the signal-cone energy). The blank at the LB center is actually a small mirror reflecting the pump reflected by BBO I onto the P monitor (photodiode monitoring the pump-pulse energy). The animation shows photographs of the signal cones striking the wall of the laboratory (see text for details). [Media 1]
Fig. 2.
Fig. 2. Photon detection probability distributions as a function of channel number x for different ND filters on the signal at 2ω [optical-density (OD) values of the ND filters are indicated]. Experimental data, solid curves; numerical fits, vide infra. The inset shows the mean channel number, X, of the experimental distributions as a function of ND-filter transmittance, i.e., 10-OD; straight line, least-squares fit. For conversion to photon numbers: n=(Δq η)x, with Δq=78125 electrons/channel; see text.
Fig. 3.
Fig. 3. Photon detection probability distributions in the signal at 2ω as a function of channel number x for spontaneous downconversion (open circles) and for downconversion with a seed idler pulse (filled circles). Square symbols, distribution for X=0. Inset, logarithmic plot of the data for spontaneous downconversion and best-fitting Gaussian with a fixed mean value corresponding to the experimental X value. For conversion to photon numbers see Fig. 2 with Δq=34393 electrons/channel.
Fig. 4.
Fig. 4. Calculated FWHM bandwidth, ΔωS (left-hand scale), of the signal gain at 2ω for a nondepleted pump of intensity IP . Right-hand scale, number of modes calculated as m=TP ΔωS , where the pump-pulse duration, TP , is assumed to be 4.45 ps (FWHM value).

Equations (3)

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P ( n ) = 1 n exp ( n n ) .
P m ( n ) = exp ( n N m ) ( N m ) m × n m 1 ( m 1 ) ! ,
P m ( x ) = exp ( x X m ) ( X m ) m × x m 1 ( m 1 ) ! ,
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