## Second order coherence of broadband down-converted light on ultrashort time scale determined by two photon absorption in semiconductor |

Optics Express, Vol. 18, Issue 19, pp. 20401-20408 (2010)

http://dx.doi.org/10.1364/OE.18.020401

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### Abstract

We study the photon correlation properties of broadband parametric down-converted light. The measurement of the photon correlation is carried out thanks to a modified Hanbury Brown-Twiss interferometer based on two photon absorption in GaAs detector. Since this method is not affected by the phase matching conditions of the detecting apparatus (so called “final state post-selection”), the detection bandwidth can be extremely large. This is illustrated by studying, with the same apparatus, the degree of second order coherence of parametric light in both degenerate and non-degenerate cases. We show that our experiment is able to determine the coherent as well as the incoherent contributions to the degree of second order coherence of parametric light with a time resolution in the fs range scale.

© 2010 OSA

2. Y. Tanaka, N. Sako, T. Kurokawa, H. Tsuda, and M. Takeda, “Profilometry based on two-photon absorption in a silicon avalanche photodiode,” Opt. Lett. **28**(6), 402–404 (2003). [CrossRef] [PubMed]

4. R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature **177**(4497), 27–29 (1956). [CrossRef]

5. S. Friberg, C. K. Hong, and L. Mandel, “Measurement of time delays in the parametric production of photon pairs,” Phys. Rev. Lett. **54**(18), 2011–2013 (1985). [CrossRef] [PubMed]

6. M. Beck, “Comparing measurements of g^{(2)}(0) performed with different coincidence detection techniques,” J. Opt. Soc. Am. B **24**(12), 2972–2978 (2007). [CrossRef]

7. D. B. Scarl, “Measurements of photon correlations in partially coherent light,” Phys. Rev. **175**(5), 1661–1668 (1968). [CrossRef]

*et al.*measured these time correlations by sum frequency generation of the two delayed sub-beams in a nonlinear crystal [8

8. I. Abram I, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct observation of the second-order coherence of parametrically generated light,” Phys. Rev. Lett. **57**(20), 2516–2519 (1986). [CrossRef] [PubMed]

*et al.*[9

9. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” Phys. Rev. Lett. **94**(4), 043602 (2005). [CrossRef] [PubMed]

10. F. Zäh, M. Halder, and T. Feurer, “Amplitude and phase modulation of time-energy entangled two-photon states,” Opt. Express **16**(21), 16452–16458 (2008). [CrossRef] [PubMed]

11. K. A. O’Donnell and A. B. U’Ren, “Time-resolved up-conversion of entangled photon pairs,” Phys. Rev. Lett. **103**(12), 123602 (2009). [CrossRef] [PubMed]

12. B. Dayan, “Theory of two-photon interactions with broadband down-converted light and entangles photons,” Phys. Rev. A **76**(4), 043813 (2007). [CrossRef]

13. O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. **101**(15), 153602 (2008). [CrossRef] [PubMed]

*et al.*[14

14. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two photon absorption in semiconductors,” Nat. Phys. **5**(4), 267–270 (2009). [CrossRef]

15. J. M. Roth, T. E. Murphy, and C. Xu, “Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube,” Opt. Lett. **27**(23), 2076–2078 (2002). [CrossRef]

*i.e.*0.7 eV [16]. It has been shown that the two photon counting rate measures the degree of second order coherence (DSOC)

17. R. Glauber, “Photon correlations,” Phys. Rev. Lett. **10**(3), 84–86 (1963). [CrossRef]

*τ*is the delay between the two beams,

8. I. Abram I, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct observation of the second-order coherence of parametrically generated light,” Phys. Rev. Lett. **57**(20), 2516–2519 (1986). [CrossRef] [PubMed]

9. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” Phys. Rev. Lett. **94**(4), 043602 (2005). [CrossRef] [PubMed]

15. J. M. Roth, T. E. Murphy, and C. Xu, “Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube,” Opt. Lett. **27**(23), 2076–2078 (2002). [CrossRef]

*TPA*(

_{LPF}*τ*)): it is shown in Ref [18

18. K. Mogi, K. Naganuma, and H. Yamada, “A novel real-time measurement method for ultrashort optical pulses,” Jpn. J. Appl. Phys. **27**(Part 1, No. 11), 2078–2081 (1988). [CrossRef]

14. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two photon absorption in semiconductors,” Nat. Phys. **5**(4), 267–270 (2009). [CrossRef]

*TPA*(

_{LPF}*τ*) (see Eq. (2), we can estimate a coherence time of about 140 fs which is again in compliance with the OPG bandwidth of 50 nm. Once again, we measure

*g*

^{(2)}(0) ≈2 in both cases.

*et al*. [20

20. B. Huttner, S. Serulnik, and Y. Ben-Aryeh, “Quantum analysis of light propagation in a parametric amplifier,” Phys. Rev. A **42**(9), 5594–5600 (1990). [CrossRef] [PubMed]

_{d}can be straightforwardly connected to the one at the crystal output according to the following expression:where

*ω*at the output port of the Michelson interferometer. The TPC signal

*S*

_{TPC}is then proportional to [19]:

10. F. Zäh, M. Halder, and T. Feurer, “Amplitude and phase modulation of time-energy entangled two-photon states,” Opt. Express **16**(21), 16452–16458 (2008). [CrossRef] [PubMed]

12. B. Dayan, “Theory of two-photon interactions with broadband down-converted light and entangles photons,” Phys. Rev. A **76**(4), 043813 (2007). [CrossRef]

*et al.*[21

21. A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. **94**(7), 073601 (2005). [CrossRef] [PubMed]

*Δ*is the spectral width of the parametric light and

*et al*[11

11. K. A. O’Donnell and A. B. U’Ren, “Time-resolved up-conversion of entangled photon pairs,” Phys. Rev. Lett. **103**(12), 123602 (2009). [CrossRef] [PubMed]

14. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two photon absorption in semiconductors,” Nat. Phys. **5**(4), 267–270 (2009). [CrossRef]

9. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” Phys. Rev. Lett. **94**(4), 043602 (2005). [CrossRef] [PubMed]

## References and links

1. | H. Z. Cummins, and E. R. Pike, |

2. | Y. Tanaka, N. Sako, T. Kurokawa, H. Tsuda, and M. Takeda, “Profilometry based on two-photon absorption in a silicon avalanche photodiode,” Opt. Lett. |

3. | D. Bouwmeester, A. Ekert, and A. E. Zeilinger, |

4. | R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature |

5. | S. Friberg, C. K. Hong, and L. Mandel, “Measurement of time delays in the parametric production of photon pairs,” Phys. Rev. Lett. |

6. | M. Beck, “Comparing measurements of g |

7. | D. B. Scarl, “Measurements of photon correlations in partially coherent light,” Phys. Rev. |

8. | I. Abram I, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct observation of the second-order coherence of parametrically generated light,” Phys. Rev. Lett. |

9. | B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” Phys. Rev. Lett. |

10. | F. Zäh, M. Halder, and T. Feurer, “Amplitude and phase modulation of time-energy entangled two-photon states,” Opt. Express |

11. | K. A. O’Donnell and A. B. U’Ren, “Time-resolved up-conversion of entangled photon pairs,” Phys. Rev. Lett. |

12. | B. Dayan, “Theory of two-photon interactions with broadband down-converted light and entangles photons,” Phys. Rev. A |

13. | O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. |

14. | F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two photon absorption in semiconductors,” Nat. Phys. |

15. | J. M. Roth, T. E. Murphy, and C. Xu, “Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube,” Opt. Lett. |

16. | C. Cohen-Tannoudji, B. Diu, and F. Laloe, |

17. | R. Glauber, “Photon correlations,” Phys. Rev. Lett. |

18. | K. Mogi, K. Naganuma, and H. Yamada, “A novel real-time measurement method for ultrashort optical pulses,” Jpn. J. Appl. Phys. |

19. | R. Loudon, |

20. | B. Huttner, S. Serulnik, and Y. Ben-Aryeh, “Quantum analysis of light propagation in a parametric amplifier,” Phys. Rev. A |

21. | A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. |

**OCIS Codes**

(270.4180) Quantum optics : Multiphoton processes

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 7, 2010

Revised Manuscript: June 7, 2010

Manuscript Accepted: June 25, 2010

Published: September 10, 2010

**Citation**

Fabien Boitier, Antoine Godard, Aleksandr Ryasnyanskiy, Nicolas Dubreuil, Philippe Delaye, Claude Fabre, and Emmanuel Rosencher, "Second order coherence of broadband down-converted light on ultrashort time scale determined by two photon absorption in semiconductor," Opt. Express **18**, 20401-20408 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20401

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### References

- H. Z. Cummins, and E. R. Pike, Photon correlation spectroscopy and light beating spectroscopy (Plenum Press, New York, 1974).
- Y. Tanaka, N. Sako, T. Kurokawa, H. Tsuda, and M. Takeda, “Profilometry based on two-photon absorption in a silicon avalanche photodiode,” Opt. Lett. 28(6), 402–404 (2003). [CrossRef] [PubMed]
- D. Bouwmeester, A. Ekert, and A. E. Zeilinger, The Physics of Quantum Information (Springer-Verlag, New York, 2000).
- R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956). [CrossRef]
- S. Friberg, C. K. Hong, and L. Mandel, “Measurement of time delays in the parametric production of photon pairs,” Phys. Rev. Lett. 54(18), 2011–2013 (1985). [CrossRef] [PubMed]
- M. Beck, “Comparing measurements of g(2)(0) performed with different coincidence detection techniques,” J. Opt. Soc. Am. B 24(12), 2972–2978 (2007). [CrossRef]
- D. B. Scarl, “Measurements of photon correlations in partially coherent light,” Phys. Rev. 175(5), 1661–1668 (1968). [CrossRef]
- I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct observation of the second-order coherence of parametrically generated light,” Phys. Rev. Lett. 57(20), 2516–2519 (1986). [CrossRef] [PubMed]
- B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” Phys. Rev. Lett. 94(4), 043602 (2005). [CrossRef] [PubMed]
- F. Zäh, M. Halder, and T. Feurer, “Amplitude and phase modulation of time-energy entangled two-photon states,” Opt. Express 16(21), 16452–16458 (2008). [CrossRef] [PubMed]
- K. A. O’Donnell and A. B. U’Ren, “Time-resolved up-conversion of entangled photon pairs,” Phys. Rev. Lett. 103(12), 123602 (2009). [CrossRef] [PubMed]
- B. Dayan, “Theory of two-photon interactions with broadband down-converted light and entangles photons,” Phys. Rev. A 76(4), 043813 (2007). [CrossRef]
- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008). [CrossRef] [PubMed]
- F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009). [CrossRef]
- J. M. Roth, T. E. Murphy, and C. Xu, “Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube,” Opt. Lett. 27(23), 2076–2078 (2002). [CrossRef]
- C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Hermann, Paris, 1977).
- R. Glauber, “Photon correlations,” Phys. Rev. Lett. 10(3), 84–86 (1963). [CrossRef]
- K. Mogi, K. Naganuma, and H. Yamada, “A novel real-time measurement method for ultrashort optical pulses,” Jpn. J. Appl. Phys. 27(Part 1, No. 11), 2078–2081 (1988). [CrossRef]
- R. Loudon, The Quantum Theory of Light (Oxford Univ. Press., Oxford, 2000).
- B. Huttner, S. Serulnik, and Y. Ben-Aryeh, “Quantum analysis of light propagation in a parametric amplifier,” Phys. Rev. A 42(9), 5594–5600 (1990). [CrossRef] [PubMed]
- A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005). [CrossRef] [PubMed]

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