Abstract

Avalanche diodes (ADs) are widely used to count photons in quantum interferometry. In reality they do not count photons, but click once when a bunch of photons arrives in a light pulse. We model this behavior in typical quantum optical interferometers like the Hong–Ou–Mandel beam splitter and the Mach–Zehnder interferometer, and compare it with the behavior of the photon-number-resolving (PNR) detector and the Hanbury-Brown–Twiss detector in these measuring devices. Our results show that quantum interferometric measurements with biphotons could be performed with single ADs, if the noise of the diodes could be reduced. Even a single PNR detector can be used in these interferometers, if the variance of the measurement is determined, since it reveals information about biphoton interference in contrast to the single detector counting rate.

© 2012 Optical Society of America

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References

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  1. M. Ghioni and G. Ripamonti, “Improving the performance of commercially available Geiger-mode avalanche photodiodes,” Rev. Sci. Instrum. 62, 163–167 (1991).
    [CrossRef]
  2. I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
    [CrossRef]
  3. M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
    [CrossRef]
  4. D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
    [CrossRef]
  5. D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
    [CrossRef]
  6. M. Fujiwara and M. Sasaki, “Photon-number-resolving detection at a telecommunications wavelength with a charge-integrating photo detector,” Opt. Lett. 31, 691–693(2006).
    [CrossRef]
  7. D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).
  8. L. Jiang, E. Dauler, and J. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75, 062325 (2007).
    [CrossRef]
  9. D. Marcuse, Principles of Quantum Electronics (Academic, 1980).
  10. O. Keller, “On the theory of spatial localization of photons,” Phys. Rep. 411, 1–232 (2005).
    [CrossRef]
  11. C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef]
  12. A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
    [CrossRef]
  13. R. Glauber, “Coherence and quantum detection,” in Proceedings of the International School Enrico Fermi “Quantum Optics” (Academic, 1969), Vol. XLII, pp. 15–56.
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  15. A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).
  16. Y. Shih, “Entangled biphoton source property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
    [CrossRef]
  17. R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part I,” Proc. R. Soc. Lond. Ser. A 242, 300–324 (1957).
    [CrossRef]
  18. R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part II,” Proc. R. Soc. Lond. Ser. A 243, 291–319 (1958).
    [CrossRef]
  19. K. Siebert, H. Schmitzer, and W. Dultz, “Measurement of the helicity of photon pairs using the optical Berry phase,” Phys. Lett. A 300, 341–347 (2002).
    [CrossRef]
  20. K. Schmid, H. Becker, W. Dultz, W. Martienssen, M. Kempe, and H. Schmitzer, “Interferometric optical path measurements of a glass wedge with single photons and biphotons,” Opt. Lett. 32, 2257–2259 (2007).
    [CrossRef]

2009

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

2008

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

2007

K. Schmid, H. Becker, W. Dultz, W. Martienssen, M. Kempe, and H. Schmitzer, “Interferometric optical path measurements of a glass wedge with single photons and biphotons,” Opt. Lett. 32, 2257–2259 (2007).
[CrossRef]

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

L. Jiang, E. Dauler, and J. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75, 062325 (2007).
[CrossRef]

2006

I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[CrossRef]

M. Fujiwara and M. Sasaki, “Photon-number-resolving detection at a telecommunications wavelength with a charge-integrating photo detector,” Opt. Lett. 31, 691–693(2006).
[CrossRef]

2005

D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
[CrossRef]

O. Keller, “On the theory of spatial localization of photons,” Phys. Rep. 411, 1–232 (2005).
[CrossRef]

2004

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

2003

Y. Shih, “Entangled biphoton source property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
[CrossRef]

2002

K. Siebert, H. Schmitzer, and W. Dultz, “Measurement of the helicity of photon pairs using the optical Berry phase,” Phys. Lett. A 300, 341–347 (2002).
[CrossRef]

1991

M. Ghioni and G. Ripamonti, “Improving the performance of commercially available Geiger-mode avalanche photodiodes,” Rev. Sci. Instrum. 62, 163–167 (1991).
[CrossRef]

1987

C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

1982

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[CrossRef]

1958

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part II,” Proc. R. Soc. Lond. Ser. A 243, 291–319 (1958).
[CrossRef]

1957

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part I,” Proc. R. Soc. Lond. Ser. A 242, 300–324 (1957).
[CrossRef]

Achilles, D.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Aspect, A.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[CrossRef]

Banaszek, K.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Becker, H.

Chang, J.

L. Jiang, E. Dauler, and J. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75, 062325 (2007).
[CrossRef]

Coldenstrod-Ronge, H.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

Cov, S.

I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[CrossRef]

Cova, S.

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

Dalibard, J.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[CrossRef]

Damayanthi, R.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Dauler, E.

L. Jiang, E. Dauler, and J. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75, 062325 (2007).
[CrossRef]

Dultz, W.

K. Schmid, H. Becker, W. Dultz, W. Martienssen, M. Kempe, and H. Schmitzer, “Interferometric optical path measurements of a glass wedge with single photons and biphotons,” Opt. Lett. 32, 2257–2259 (2007).
[CrossRef]

K. Siebert, H. Schmitzer, and W. Dultz, “Measurement of the helicity of photon pairs using the optical Berry phase,” Phys. Lett. A 300, 341–347 (2002).
[CrossRef]

Eisert, J.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

Feito, A.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

Fitch, M.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Franson, J.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Fujii, G.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Fujiwara, M.

Fukuda, D.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Ghioni, M.

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[CrossRef]

M. Ghioni and G. Ripamonti, “Improving the performance of commercially available Geiger-mode avalanche photodiodes,” Rev. Sci. Instrum. 62, 163–167 (1991).
[CrossRef]

Glauber, R.

R. Glauber, “Coherence and quantum detection,” in Proceedings of the International School Enrico Fermi “Quantum Optics” (Academic, 1969), Vol. XLII, pp. 15–56.

Gulinatti, A.

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part II,” Proc. R. Soc. Lond. Ser. A 243, 291–319 (1958).
[CrossRef]

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part I,” Proc. R. Soc. Lond. Ser. A 242, 300–324 (1957).
[CrossRef]

Hong, C.

C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Inoue, S.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Jacobs, B.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Jiang, L.

L. Jiang, E. Dauler, and J. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75, 062325 (2007).
[CrossRef]

Keller, O.

O. Keller, “On the theory of spatial localization of photons,” Phys. Rep. 411, 1–232 (2005).
[CrossRef]

Kempe, M.

Labanca, I.

I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[CrossRef]

Lita, A.

D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
[CrossRef]

Lundeen, J.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

Mandel, L.

C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marcuse, D.

D. Marcuse, Principles of Quantum Electronics (Academic, 1980).

Martienssen, W.

Miller, A.

D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
[CrossRef]

Nam, S.

D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
[CrossRef]

Ohkubo, M.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Ou, Z.

C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Pittman, T.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Plenio, M.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

Rech, I.

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[CrossRef]

Ripamonti, G.

M. Ghioni and G. Ripamonti, “Improving the performance of commercially available Geiger-mode avalanche photodiodes,” Rev. Sci. Instrum. 62, 163–167 (1991).
[CrossRef]

Roger, G.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[CrossRef]

Rosenberg, D.

D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
[CrossRef]

Sasaki, M.

Schmid, K.

Schmitzer, H.

K. Schmid, H. Becker, W. Dultz, W. Martienssen, M. Kempe, and H. Schmitzer, “Interferometric optical path measurements of a glass wedge with single photons and biphotons,” Opt. Lett. 32, 2257–2259 (2007).
[CrossRef]

K. Siebert, H. Schmitzer, and W. Dultz, “Measurement of the helicity of photon pairs using the optical Berry phase,” Phys. Lett. A 300, 341–347 (2002).
[CrossRef]

Shih, Y.

Y. Shih, “Entangled biphoton source property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
[CrossRef]

Siebert, K.

K. Siebert, H. Schmitzer, and W. Dultz, “Measurement of the helicity of photon pairs using the optical Berry phase,” Phys. Lett. A 300, 341–347 (2002).
[CrossRef]

Silberhorn, C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Sliwa, C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Takahashi, H.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Tsuchida, H.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part II,” Proc. R. Soc. Lond. Ser. A 243, 291–319 (1958).
[CrossRef]

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part I,” Proc. R. Soc. Lond. Ser. A 242, 300–324 (1957).
[CrossRef]

Walmsley, I.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Yoshizawa, A.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

Zappa, F.

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Ghioni, A. Gulinatti, I. Rech, F. Zappa, and S. Cova, “Progress in silicon single-photon avalanche diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 852–862 (2007).
[CrossRef]

J. Low Temp. Phys.

D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, R. Damayanthi, H. Takahashi, S. Inoue, and M. Ohkubo, “High speed photon number resolving detectors with titanium transition edge sensor,” J. Low Temp. Phys. 151, 100–105 (2008).
[CrossRef]

J. Mod. Opt.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. Walmsley, M. Fitch, B. Jacobs, T. Pittman, and J. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 15, 1499–1515 (2004).

New J. Phys.

A. Feito, J. Lundeen, H. Coldenstrod-Ronge, J. Eisert, M. Plenio, and I. Walmsley, “Measuring measurements: theory and practice,” New J. Phys. 11, 093038 (2009).

Opt. Lett.

Phys. Lett. A

K. Siebert, H. Schmitzer, and W. Dultz, “Measurement of the helicity of photon pairs using the optical Berry phase,” Phys. Lett. A 300, 341–347 (2002).
[CrossRef]

Phys. Rep.

O. Keller, “On the theory of spatial localization of photons,” Phys. Rep. 411, 1–232 (2005).
[CrossRef]

Phys. Rev. A

L. Jiang, E. Dauler, and J. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A 75, 062325 (2007).
[CrossRef]

D. Rosenberg, A. Lita, A. Miller, and S. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803 (2005).
[CrossRef]

Phys. Rev. Lett.

C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[CrossRef]

Proc. R. Soc. Lond. Ser. A

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part I,” Proc. R. Soc. Lond. Ser. A 242, 300–324 (1957).
[CrossRef]

R. Hanbury Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations of light, Part II,” Proc. R. Soc. Lond. Ser. A 243, 291–319 (1958).
[CrossRef]

Rep. Prog. Phys.

Y. Shih, “Entangled biphoton source property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
[CrossRef]

Rev. Sci. Instrum.

M. Ghioni and G. Ripamonti, “Improving the performance of commercially available Geiger-mode avalanche photodiodes,” Rev. Sci. Instrum. 62, 163–167 (1991).
[CrossRef]

I. Rech, I. Labanca, M. Ghioni, and S. Cov, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[CrossRef]

Other

D. Marcuse, Principles of Quantum Electronics (Academic, 1980).

R. Glauber, “Coherence and quantum detection,” in Proceedings of the International School Enrico Fermi “Quantum Optics” (Academic, 1969), Vol. XLII, pp. 15–56.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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Figures (2)

Fig. 1.
Fig. 1.

Quantum optical interference devices discussed in text.

Fig. 2.
Fig. 2.

Hong-Ou-Mandel interference with a 1:1 beam splitter and different detectors. For the HBT detector the polarization of the photons is varied instead of the delay.

Tables (1)

Tables Icon

Table 1. Comparison of the Counting Rates of Different Photon Detectors

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

C(n)=ψ|n^|ψ,
C^(n^)|n=1·|nfornNandC^(n^)|0=0·|0forn=0,
C^(n^,2)=3/2n^1/2n^2C^(n^,3)=11/6n^n^2+1/6n^3.
C^=1|00|.
C^(η)=1n=0(1η)n|nn|.
ψE|C^3C^4|ψE=ψE|(13|030|3)(14|040|4)|ψE,
|ψI=n=0cn(a^1)nn!|01|02BS|ψE=n=0cn1n!(ta^3+ira^4)n|03|04,
a4=ira1+ta2a^1=ta^3ira^4a3=ta1+ira2a^2=ira^3+ta^4,
|ψE=n=0cnn!(12)nk=0n(i)k(nk)!k!|nk3|k4.
|ψE=c0|03|04+c112(|13|04+i|03|14)+c212(|23|04+i2|13|14|03|24).
ψE|C^3C^4|ψE=ψE|n^3n^4|ψE=12|c2|2.
|ψI=a^1+a^2+|01|02BS|ψE=(ta^3++ia^4+)(ira^3++ta^4+)|03|04=(t2r2)|13|14+i2rt(|23|04+|03|24).
ψE|n^3|ψE=n3=(t2r2)2+4r2t2=1,|ψI=|11|12,
n=02npn=0·r2t2+1·(t4+r4)+2·r2t2=1,
ψE|(13|030|3)|ψE=12r2t2;|ψI=|11|12.
Ccl=n=02npn=0·r2t2+1·(t4+r4)+1·r2t2=1r2t2.
ψE|{1n=02(1η)n|nn|}|ψE=12r2t2(t2r2)(1η)2r2t2(1η)2=η(112η)forr=t=12.
Ccl=(t4+r4)η+r2t2{η+η(1η)}=η(114η)forr=t=12,
|ψI=12{exp(i2φ)|21|02+|01|22}.
|ψIBS|ψE=14{2(exp(i2φ)1)|23|04+2i(exp(i2φ)+1)|13|142(exp(i2φ)1)|03|24}
ψE|(13|030|3)|ψE=112sin2φ.
ψ|O^|ψ=νoν|oν|ψ|2.
V=ψ|(O^)2|ψ(ψ|O^|ψ)2.
V=ψE|(Δn^3)2|ψE=ψE|(n^3)2|ψE(ψE|n^3|ψE)2=sin2φ.
V=ψE|n^32|ψE(ψE|n^3|ψE)2=1.
Vc=n=02n2pn(n=02npn)2=0/4+1/2+4/4(0/4+1/2+2/4)2=1/2.

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