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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Nature (London) (1)

D. Boumeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, ???Experimental quantum teleportation,??? Nature (London) 390, 575-579 (1997), <a href="http://www.nature.com/cgitaf/ DynaPage.taf?file=/nature/journal/v390/n6660/full/390575a0_fs.html&content_filetype=PDF.">http://www.nature.com/cgitaf/ DynaPage.taf?file=/nature/journal/v390/n6660/full/390575a0_fs.html&content_filetype=PDF</a>
[CrossRef]

Opt. Lett. (4)

Phys. Rev A (1)

M. M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, ???Photon-number statistics from the phase-averaged quadrature-field distribution: theory and ultrafast measurement,??? Phys. Rev A 52, R924- R927 (1995), <a href="http://link.aps.org/abstract/PRA/v52/pR924.">http://link.aps.org/abstract/PRA/v52/pR924</a>
[CrossRef] [PubMed]

Phys. Rev. (1)

B. R. Mollow and R. J. Glauber, ???Quantum theory of parametric amplification. II,??? Phys. Rev. 160, 1097- 1108 (1967), <a href="http://prola.aps.org/pdf/PR/v160/i5/p1097_1.">http://prola.aps.org/pdf/PR/v160/i5/p1097_1.</a>
[CrossRef]

Phys. Rev. A (4)

M. S. Kim, J.Y. Lee, D. Ahn, and P. L. Knight, ???Entanglement induced by a single-mode heat environment,??? Phys. Rev. A 65, 040-101(R) (2002), <a href="http://link.aps.org/abstract/PRA/v65/e040101">http://link.aps.org/abstract/PRA/v65/e040101</a>
[CrossRef]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, ???Photon-number resolution using time-multiplexed single-photon detectors,??? Phys. Rev. A 68, 043814 (2003), <a href="http://link.aps.org/abstract/PRA/v68/e043814.">http://link.aps.org/abstract/PRA/v68/e043814<a/>
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, ???Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,??? Phys. Rev. A 69, 023802 (2004), <a href="http://link.aps.org/abstract/PRA/v69/e023802">http://link.aps.org/abstract/PRA/v69/e023802</a>
[CrossRef]

A. Beržanskis, W. Chinaglia, L. A. Lugiato, K.-K. Feller, and P. Di Trapani, ???Spatial structures in optical parametric amplification,??? Phys. Rev. A 60, 1626-1635 (1999), <a href="http://prola.aps.org/pdf/PRA/v60/i2/p1626_1.">http://prola.aps.org/pdf/PRA/v60/i2/p1626_1.</a>
[CrossRef]

Phys. Rev. Lett. (5)

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, ???Measurement of the Wigner distribution of the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,??? Phys. Rev. Lett. 70, 1244-1247 (1993), <a href="http://prola.aps.org/abstract/PRL/v70/i9/p1244_1.">http://prola.aps.org/abstract/PRL/v70/i9/p1244_1.</a>
[CrossRef] [PubMed]

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, ??? Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein???Podolsky???Rosen channels,??? Phys. Rev. Lett. 80, 1121-1125 (1998), <a href="http://prola.aps.org/pdf/PRL/v80/i6/p1121_1.">http://prola.aps.org/pdf/PRL/v80/i6/p1121_1.<a/>
[CrossRef]

Z. Y. Ou and L. Mandel, ???Violation of Bell's inequality and classical probability in a two-photon correlation experiment,??? Phys. Rev. Lett. 61, 50-53 (1988), <a href="http://prola.aps.org/pdf/PRL/v61/i1/p50_1.">http://prola.aps.org/pdf/PRL/v61/i1/p50_1.</a>
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, ???New type of Einstein???Podolsky???Rosen??? Bohm experiment using pairs of light quanta produced by optical parametric down conversion,??? Phys. Rev. Lett. 61, 2921-2924 (1988), <a href="http://prola.aps.org/pdf/PRL/v61/i26/p2921_1.">http://prola.aps.org/pdf/PRL/v61/i26/p2921_1.</a>
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, ??? New high-intensity source of polarization-entangled photon pairs,??? Phys. Rev. Lett. 75, 4337-4341 (1995), <a href="http://prola.aps.org/pdf/PRL/v75/i24/p4337_1.">http://prola.aps.org/pdf/PRL/v75/i24/p4337_1.</a>
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

G. Zambra, M. Bondani, A. S. Spinelli, F. Paleari, and A. Andreoni, ???Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,??? Rev. Sci. Instrum. (to be published).

Science (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, ???Unconditional quantum teleportation,??? Science 282, 706-709 (1998), <a href="http://www.sciencemag.org/cgi/content/abstract/282/5389/706 .">http://www.sciencemag.org/cgi/content/abstract/282/5389/706 .</a>
[CrossRef] [PubMed]

Other (2)

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, Oxford, 2000).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Chap. 14.

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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