Abstract

I present measurements of the degree of second-order coherence g(2)(0) for spontaneous parametric downconversion fields and discuss the differences between two-detector (unconditional) and three-detector (conditional) measurements of g(2)(0). An emphasis is placed on comparing measurements made using time-to-amplitude converters (TACs) to those made using a logic circuit, illustrating how the TAC measurements are adversely influenced by dead time effects. Finally, I show how the detrimental effects of dead time when using TACs can be mitigated by renormalizing the measurement results.

© 2007 Optical Society of America

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References

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  1. R. Hanbury Brown and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature (London) 177, 27-29 (1956).
    [CrossRef]
  2. R. Q. Twiss, A. G. Little, and R. Hanbury Brown, "Correlation between photons in coherent beams of light, detected by a coincidence counting technique," Nature (London) 180, 324-326 (1957).
    [CrossRef]
  3. H. J. Kimble, M. Dagenais, and L. Mandel, "Photon antibunching in resonance fluorescence," Phys. Rev. Lett. 39, 691-695 (1977).
    [CrossRef]
  4. Some references use the normalized intensity correlation function λ(τ) in place of the degree of second-order coherence; they are related by g(2)(τ)=1+λ(τ).
  5. P. Grangier, G. Roger, and A. Aspect, "Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences," Europhys. Lett. 1, 173-179 (1986).
    [CrossRef]
  6. P. G. Kwiat and R. Y. Chiao, "Observation of a nonclassical Berry phase for the photon," Phys. Rev. Lett. 66, 588-591 (1991).
    [CrossRef] [PubMed]
  7. S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, "High-quality asynchronous heralded single-photon source at telecom wavelength," New J. Phys. 6, 163 (2004).
    [CrossRef]
  8. C. W. Chou, S. V. Polyakov, A. Kuzmich, and H. J. Kimble, "Single-photon generation from stored excitation in an atomic ensemble," Phys. Rev. Lett. 92, 213601 (2004).
    [CrossRef] [PubMed]
  9. T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, "Storage and retrieval of single photons transmitted between remote quantum memories," Nature (London) 438, 833-836 (2005).
    [CrossRef]
  10. A. B. U'Ren, C. Silberhorn, J. L. Ball, K. Banaszek, and I. A. Walmsley, "Characterization of the nonclassical nature of conditionally prepared single photons," Phys. Rev. A 72, 021802(R) (2005).
    [CrossRef]
  11. C. Santori, S. Gotzinger, Y. Yamamoto, S. Kako, K. Hoshino, and Y. Arakawa, "Photon correlation studies of single GaN quantum dots," Appl. Phys. Lett. 87, 051916 (2005).
    [CrossRef]
  12. E. Wu, V. Jacques, H. P. Zeng, P. Grangier, F. Treussart, and J. F. Roch, "Narrow-band single-photon emission in the near infrared for quantum key distribution," Opt. Express 14, 1296-1303 (2006).
    [CrossRef] [PubMed]
  13. R. Loudon, The Quantum Theory of Light, 3rd ed. (Clarendon, 2000).
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  15. J. J. Thorn, M. S. Neal, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, "Observing the quantum behavior of light in an undergraduate laboratory," Am. J. Phys. 72, 1210-1219 (2004).
    [CrossRef]
  16. C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
    [CrossRef] [PubMed]
  17. I am not alone in associating α and g(2)(0); see also the text by Loudon . It is reasonable for one to think of the three-detector g(2)(0) as being a third-order intensity correlation. However, I prefer to follow Loudon's lead and consider it a conditional g(2)(0).
  18. M. Beck, "Modern quantum mechanics experiments," http://www.whitman.edu/~beckmk/QM/.
  19. F. T. Arecchi, E. Gatti, and A. Sona, "Time distribution of photons from coherent and Gaussian sources," Phys. Lett. 20, 27-29 (1966).
    [CrossRef]

2006 (1)

2005 (3)

T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, "Storage and retrieval of single photons transmitted between remote quantum memories," Nature (London) 438, 833-836 (2005).
[CrossRef]

A. B. U'Ren, C. Silberhorn, J. L. Ball, K. Banaszek, and I. A. Walmsley, "Characterization of the nonclassical nature of conditionally prepared single photons," Phys. Rev. A 72, 021802(R) (2005).
[CrossRef]

C. Santori, S. Gotzinger, Y. Yamamoto, S. Kako, K. Hoshino, and Y. Arakawa, "Photon correlation studies of single GaN quantum dots," Appl. Phys. Lett. 87, 051916 (2005).
[CrossRef]

2004 (3)

J. J. Thorn, M. S. Neal, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, "Observing the quantum behavior of light in an undergraduate laboratory," Am. J. Phys. 72, 1210-1219 (2004).
[CrossRef]

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, "High-quality asynchronous heralded single-photon source at telecom wavelength," New J. Phys. 6, 163 (2004).
[CrossRef]

C. W. Chou, S. V. Polyakov, A. Kuzmich, and H. J. Kimble, "Single-photon generation from stored excitation in an atomic ensemble," Phys. Rev. Lett. 92, 213601 (2004).
[CrossRef] [PubMed]

1991 (1)

P. G. Kwiat and R. Y. Chiao, "Observation of a nonclassical Berry phase for the photon," Phys. Rev. Lett. 66, 588-591 (1991).
[CrossRef] [PubMed]

1986 (2)

C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

P. Grangier, G. Roger, and A. Aspect, "Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences," Europhys. Lett. 1, 173-179 (1986).
[CrossRef]

1977 (1)

H. J. Kimble, M. Dagenais, and L. Mandel, "Photon antibunching in resonance fluorescence," Phys. Rev. Lett. 39, 691-695 (1977).
[CrossRef]

1966 (1)

F. T. Arecchi, E. Gatti, and A. Sona, "Time distribution of photons from coherent and Gaussian sources," Phys. Lett. 20, 27-29 (1966).
[CrossRef]

1957 (1)

R. Q. Twiss, A. G. Little, and R. Hanbury Brown, "Correlation between photons in coherent beams of light, detected by a coincidence counting technique," Nature (London) 180, 324-326 (1957).
[CrossRef]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature (London) 177, 27-29 (1956).
[CrossRef]

Am. J. Phys. (1)

J. J. Thorn, M. S. Neal, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, "Observing the quantum behavior of light in an undergraduate laboratory," Am. J. Phys. 72, 1210-1219 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

C. Santori, S. Gotzinger, Y. Yamamoto, S. Kako, K. Hoshino, and Y. Arakawa, "Photon correlation studies of single GaN quantum dots," Appl. Phys. Lett. 87, 051916 (2005).
[CrossRef]

Europhys. Lett. (1)

P. Grangier, G. Roger, and A. Aspect, "Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences," Europhys. Lett. 1, 173-179 (1986).
[CrossRef]

Nature (London) (3)

R. Hanbury Brown and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature (London) 177, 27-29 (1956).
[CrossRef]

R. Q. Twiss, A. G. Little, and R. Hanbury Brown, "Correlation between photons in coherent beams of light, detected by a coincidence counting technique," Nature (London) 180, 324-326 (1957).
[CrossRef]

T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, "Storage and retrieval of single photons transmitted between remote quantum memories," Nature (London) 438, 833-836 (2005).
[CrossRef]

New J. Phys. (1)

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, "High-quality asynchronous heralded single-photon source at telecom wavelength," New J. Phys. 6, 163 (2004).
[CrossRef]

Opt. Express (1)

Phys. Lett. (1)

F. T. Arecchi, E. Gatti, and A. Sona, "Time distribution of photons from coherent and Gaussian sources," Phys. Lett. 20, 27-29 (1966).
[CrossRef]

Phys. Rev. A (1)

A. B. U'Ren, C. Silberhorn, J. L. Ball, K. Banaszek, and I. A. Walmsley, "Characterization of the nonclassical nature of conditionally prepared single photons," Phys. Rev. A 72, 021802(R) (2005).
[CrossRef]

Phys. Rev. Lett. (4)

C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

C. W. Chou, S. V. Polyakov, A. Kuzmich, and H. J. Kimble, "Single-photon generation from stored excitation in an atomic ensemble," Phys. Rev. Lett. 92, 213601 (2004).
[CrossRef] [PubMed]

P. G. Kwiat and R. Y. Chiao, "Observation of a nonclassical Berry phase for the photon," Phys. Rev. Lett. 66, 588-591 (1991).
[CrossRef] [PubMed]

H. J. Kimble, M. Dagenais, and L. Mandel, "Photon antibunching in resonance fluorescence," Phys. Rev. Lett. 39, 691-695 (1977).
[CrossRef]

Other (5)

Some references use the normalized intensity correlation function λ(τ) in place of the degree of second-order coherence; they are related by g(2)(τ)=1+λ(τ).

I am not alone in associating α and g(2)(0); see also the text by Loudon . It is reasonable for one to think of the three-detector g(2)(0) as being a third-order intensity correlation. However, I prefer to follow Loudon's lead and consider it a conditional g(2)(0).

M. Beck, "Modern quantum mechanics experiments," http://www.whitman.edu/~beckmk/QM/.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Clarendon, 2000).

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

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Figures (5)

Fig. 1
Fig. 1

Coincidence measurement. The incident ( I ) beam is split into transmitted ( T ) and reflected ( R ) beams at a 50 50 beamsplitter. Detections at T and R are examined to see whether they occur simultaneously.

Fig. 2
Fig. 2

Experimental apparatus. Major components include the pump laser; the downconversion crystal (DC); the half-wave plate ( λ 2 ) ; the polarizing beam splitter (PBS); the single-photon counting modules (SPCMs); and gating, transmission-side, and reflection-side collection optics (G, T, and R). Optical fibers direct the light from G, T, and R to their corresponding SPCMs. The coincidence electronics and counting occur after the SPCMs.

Fig. 3
Fig. 3

Rate of VALID STARTs on the gate R G vs is plotted versus STARTs R G . Circles are for a periodic train of STARTs, while triangles are for a random stream of STARTs from the downconversion source.

Fig. 4
Fig. 4

The degree of second-order coherence measured with two detectors g 2 D ( 2 ) ( 0 ) is plotted versus the singles rate on detector T, R T . The sources of error are described in the text. In (a) data taken using the TAC is compared for analysis using Eqs. (7, 11). In (b) data acquired using the TAC and the corrected expression Eq. (11) is compared to data acquired using the logic circuit and the uncorrected expression Eq. (7).

Fig. 5
Fig. 5

The conditional degree of second-order coherence measured with three detectors g 3 D ( 2 ) ( 0 ) is plotted versus the singles rate on detector G, R G . Markers represent data taken using the TAC and analyzed using Eqs. (10, 13) and also data taken using the logic circuit. Error bars (representing the standard deviation of 10 measurements) are smaller than the markers. Lines represent the expected value of g 3 D ( 2 ) ( 0 ) determined using Eq. (14) for two different values of Δ t 3 D .

Equations (15)

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g ( 2 ) ( τ ) = I T ( t + τ ) I R ( t ) I T ( t + τ ) I R ( t ) ,
g ( 2 ) ( τ ) = I I ( t + τ ) I I ( t ) I I ( t + τ ) I I ( t ) .
g ( 2 ) ( 0 ) = I I 2 ( t ) I I ( t ) 2 .
g ( 2 ) ( τ ) = : I ̂ T ( t + τ ) I ̂ R ( t ) : I ̂ T ( t + τ ) I ̂ R ( t ) ,
g 2 D ( 2 ) ( 0 ) = P T R P T P R ,
P T = R T Δ t = ( N T Δ T ) Δ t , P R = R R Δ t = ( N R Δ T ) Δ t ,
P T R = R T R Δ t = ( N T R Δ T ) Δ t .
g 2 D ( 2 ) ( 0 ) = N T R N T N R ( Δ T Δ t ) .
g 3 D ( 2 ) ( 0 ) = P G T R P G T P G R .
P G T R = N G T R N G , P G T = N G T N G , P G R = N G R N G ,
g 3 D ( 2 ) ( 0 ) = N G T R N G N G T N G R .
g 2 D ( 2 ) ( 0 ) = N T R N T vs N R ( Δ T Δ t ) .
P G T = N G T N G vs , P G R = N G R N G vs ,
g 3 D ( 2 ) ( 0 ) = ( N G vs ) 2 N G T R N G N G T N G R .
g 3 D ( 2 ) ( 0 ) = R G Δ t 3 D ( R R R G R + R T R G T ) .

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