## Temporal correlation of photons following frequency up-conversion |

Optics Express, Vol. 19, Issue 11, pp. 10501-10510 (2011)

http://dx.doi.org/10.1364/OE.19.010501

Acrobat PDF (1213 KB)

### Abstract

We demonstrate an approach to measure temporal correlations of photons in the near infrared range using frequency up-conversion. In this approach, the near infrared signal photons are converted into the visible range, in which highly efficient silicon avalanche photodiodes are used to perform the temporal correlation measurements. A coherent light source and a pseudo-thermal light source were used in the experiment. The results are in agreement with theoretical values and those obtained from measurements directly made using superconducting nanowire single photon detectors. We conclude that the temporal correlation (up to 4th order) of photons was preserved in the frequency up-conversion process. We further theoretically and experimentally studied the influence of the dark counts on the measurement. The setup uses commercially available components and achieves high total detection efficiency (~26%).

© 2011 OSA

## 1. Introduction

5. H. Qian and E. L. Elson, “Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states,” Proc. Natl. Acad. Sci. U.S.A. **101**(9), 2828–2833 (2004). [PubMed]

8. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science **298**(5591), 199–202 (2002). [PubMed]

9. J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature **460**(7252), 245–249 (2009). [PubMed]

10. M. Assmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science **325**(5938), 297–300 (2009). [PubMed]

11. A. G. Palmer 3rd and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. **52**(2), 257–270 (1987). [PubMed]

*t*and the

*τ*’s are time delays.

_{i}13. M. J. Stevens, B. Baek, E. A. Dauler, A. J. Kerman, R. J. Molnar, S. A. Hamilton, K. K. Berggren, R. P. Mirin, and S. W. Nam, “High-order temporal coherences of chaotic and laser light,” Opt. Express **18**(2), 1430–1437 (2010). [PubMed]

14. K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express **14**(2), 527–534 (2006). [PubMed]

22. Q. Zhang, C. Langrock, M. M. Fejer, and Y. Yamamoto, “Waveguide-based single-pixel up-conversion infrared spectrometer,” Opt. Express **16**(24), 19557–19561 (2008). [PubMed]

23. L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express **17**(16), 14395–14404 (2009). [PubMed]

24. P. Kumar, “Quantum frequency conversion,” Opt. Lett. **15**(24), 1476–1478 (1990). [PubMed]

25. J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. **68**(14), 2153–2156 (1992). [PubMed]

13. M. J. Stevens, B. Baek, E. A. Dauler, A. J. Kerman, R. J. Molnar, S. A. Hamilton, K. K. Berggren, R. P. Mirin, and S. W. Nam, “High-order temporal coherences of chaotic and laser light,” Opt. Express **18**(2), 1430–1437 (2010). [PubMed]

*i.e.*, the original photon statistical characteristics are preserved in the up-conversion process. If the photon statistics are preserved through up-conversion, then one can use this approach to study the statistics of the original NIR photons. We also further theoretically and experimentally study the influence of the dark counts on the temporal correlation measurements. The setup uses commercially available components and the total detection efficiency is about 26%.

## 2. Experimental configuration

20. H. Xu, L. Ma, A. Mink, B. Hershman, and X. Tang, “1310-nm quantum key distribution system with up-conversion pump wavelength at 1550 nm,” Opt. Express **15**(12), 7247–7260 (2007). [PubMed]

30. J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters,” Opt. Lett. **35**(16), 2804–2806 (2010). [PubMed]

^{5}Hz) [12], but it is significantly higher than that of SNSPDs (~100 Hz) [13

13. M. J. Stevens, B. Baek, E. A. Dauler, A. J. Kerman, R. J. Molnar, S. A. Hamilton, K. K. Berggren, R. P. Mirin, and S. W. Nam, “High-order temporal coherences of chaotic and laser light,” Opt. Express **18**(2), 1430–1437 (2010). [PubMed]

**18**(2), 1430–1437 (2010). [PubMed]

## 3. Experimental results

**18**(2), 1430–1437 (2010). [PubMed]

## 4. Discussion on the dark counts and their influence

20. H. Xu, L. Ma, A. Mink, B. Hershman, and X. Tang, “1310-nm quantum key distribution system with up-conversion pump wavelength at 1550 nm,” Opt. Express **15**(12), 7247–7260 (2007). [PubMed]

31. M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A **32**(1), 332–344 (1985). [PubMed]

*n*signal counts in one time slot, given the BED with mean count number

*n*dark counts in a time slot, given the Possonian distribution with mean count number

*n*photons is the summation of all probabilities that the number of total photons generated from the both sources equal to

*n*. The mixed signal probability density function can expressed as:where

*n*-count probability in one time slot for mixed of signal counts obeying the BED (

## 5. Conclusion

## Acknowledgments

## References and links

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

2. | M. Fox, |

3. | Y. Zhou, J. Liu, and Y. Shih, “Third order temporal correlation function of pseudo-thermal light,” arXiv: 0909.3512v1 [quant-ph] (2009). |

4. | R. E. Meyers and K. S. Deacon, “Quantum ghost imaging experiments,” Proc. SPIE |

5. | H. Qian and E. L. Elson, “Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states,” Proc. Natl. Acad. Sci. U.S.A. |

6. | P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering processes by using |

7. | E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, correlations, and collisions: what one learns about Bose-Einstein condensates from their decay,” Phys. Rev. Lett. |

8. | H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science |

9. | J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature |

10. | M. Assmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science |

11. | A. G. Palmer 3rd and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. |

12. | R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics |

13. | M. J. Stevens, B. Baek, E. A. Dauler, A. J. Kerman, R. J. Molnar, S. A. Hamilton, K. K. Berggren, R. P. Mirin, and S. W. Nam, “High-order temporal coherences of chaotic and laser light,” Opt. Express |

14. | K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express |

15. | A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt. |

16. | M. A. Albota and F. N. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett. |

17. | C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. |

18. | E. Diamanti, H. Takesue, T. Honjo, K. Inoue, and Y. Yamamoto, “Performance of various quantum-key-distribution systems using 1.55-μm up-conversion single-photon detectors,” Phys. Rev. A |

19. | R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” N. J. Phys. |

20. | H. Xu, L. Ma, A. Mink, B. Hershman, and X. Tang, “1310-nm quantum key distribution system with up-conversion pump wavelength at 1550 nm,” Opt. Express |

21. | H. Dong, H. Pan, Y. Li, E. Wu, and H. Zeng, “Efficient single-phton frequency upconversion at 1.06 μm with ultralow background counts,” Appl. Phys. Lett. |

22. | Q. Zhang, C. Langrock, M. M. Fejer, and Y. Yamamoto, “Waveguide-based single-pixel up-conversion infrared spectrometer,” Opt. Express |

23. | L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express |

24. | P. Kumar, “Quantum frequency conversion,” Opt. Lett. |

25. | J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. |

26. | M. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics |

27. | L. Mandel and E. Wolf, |

28. | M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. |

29. | Datasheet of Perkin Elmer Single Photon Counting Module SPCM-AQR Series. |

30. | J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters,” Opt. Lett. |

31. | M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A |

32. | P. Voss, Y. Su, P. Kumar, and M. Vasilyev, “Photon statistics of a single mode of spontaneous Raman scattering in a distributed Raman amplifier,” Optical Fiber Communication Conference (IEEE, 2001), paper WDD23. |

33. | Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A |

34. | R. H. Hadfield, M. J. Stevens, R. P. Mirin, and S. W. Nam, “Single-photon source characterization with twin infrared-sensitive superconducting single-photon detectors,” J. Appl. Phys. |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(230.7370) Optical devices : Waveguides

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 20, 2011

Revised Manuscript: May 9, 2011

Manuscript Accepted: May 9, 2011

Published: May 12, 2011

**Citation**

Lijun Ma, Matthew T. Rakher, Martin J. Stevens, Oliver Slattery, Kartik Srinivasan, and Xiao Tang, "Temporal correlation of photons following frequency up-conversion," Opt. Express **19**, 10501-10510 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10501

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### References

- R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
- M. Fox, Quantum Optics, An Introduction (Oxford University Press, 2006).
- Y. Zhou, J. Liu, and Y. Shih, “Third order temporal correlation function of pseudo-thermal light,” arXiv: 0909.3512v1 [quant-ph] (2009).
- R. E. Meyers and K. S. Deacon, “Quantum ghost imaging experiments,” Proc. SPIE 7465, 746508 (2009).
- H. Qian and E. L. Elson, “Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states,” Proc. Natl. Acad. Sci. U.S.A. 101(9), 2828–2833 (2004). [PubMed]
- P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A 16(7), 1651–1664 (1999).
- E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, “Coherence, correlations, and collisions: what one learns about Bose-Einstein condensates from their decay,” Phys. Rev. Lett. 79(3), 337–340 (1997).
- H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002). [PubMed]
- J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460(7252), 245–249 (2009). [PubMed]
- M. Assmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325(5938), 297–300 (2009). [PubMed]
- A. G. Palmer and N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52(2), 257–270 (1987). [PubMed]
- R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009).
- M. J. Stevens, B. Baek, E. A. Dauler, A. J. Kerman, R. J. Molnar, S. A. Hamilton, K. K. Berggren, R. P. Mirin, and S. W. Nam, “High-order temporal coherences of chaotic and laser light,” Opt. Express 18(2), 1430–1437 (2010). [PubMed]
- K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006). [PubMed]
- A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt. 51, 1433–1445 (2004).
- M. A. Albota and F. N. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett. 29(13), 1449–1451 (2004). [PubMed]
- C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30(13), 1725–1727 (2005). [PubMed]
- E. Diamanti, H. Takesue, T. Honjo, K. Inoue, and Y. Yamamoto, “Performance of various quantum-key-distribution systems using 1.55-μm up-conversion single-photon detectors,” Phys. Rev. A 72(5), 052311 (2005).
- R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” N. J. Phys. 8(3), 32 (2006).
- H. Xu, L. Ma, A. Mink, B. Hershman, and X. Tang, “1310-nm quantum key distribution system with up-conversion pump wavelength at 1550 nm,” Opt. Express 15(12), 7247–7260 (2007). [PubMed]
- H. Dong, H. Pan, Y. Li, E. Wu, and H. Zeng, “Efficient single-phton frequency upconversion at 1.06 μm with ultralow background counts,” Appl. Phys. Lett. 93(7), 071101 (2008).
- Q. Zhang, C. Langrock, M. M. Fejer, and Y. Yamamoto, “Waveguide-based single-pixel up-conversion infrared spectrometer,” Opt. Express 16(24), 19557–19561 (2008). [PubMed]
- L. Ma, O. Slattery, and X. Tang, “Experimental study of high sensitivity infrared spectrometer with waveguide-based up-conversion detector(1),” Opt. Express 17(16), 14395–14404 (2009). [PubMed]
- P. Kumar, “Quantum frequency conversion,” Opt. Lett. 15(24), 1476–1478 (1990). [PubMed]
- J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992). [PubMed]
- M. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
- Datasheet of Perkin Elmer Single Photon Counting Module SPCM-AQR Series.
- J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters,” Opt. Lett. 35(16), 2804–2806 (2010). [PubMed]
- M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32(1), 332–344 (1985). [PubMed]
- P. Voss, Y. Su, P. Kumar, and M. Vasilyev, “Photon statistics of a single mode of spontaneous Raman scattering in a distributed Raman amplifier,” Optical Fiber Communication Conference (IEEE, 2001), paper WDD23.
- Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75(2), 023803 (2007).
- R. H. Hadfield, M. J. Stevens, R. P. Mirin, and S. W. Nam, “Single-photon source characterization with twin infrared-sensitive superconducting single-photon detectors,” J. Appl. Phys. 101(10), 103104 (2007).

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