## Observation of quantum interference between a single-photon state and a thermal state generated in optical fibers

Optics Express, Vol. 16, Issue 17, pp. 12505-12510 (2008)

http://dx.doi.org/10.1364/OE.16.012505

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### Abstract

We experimentally demonstrate a Hong-Ou-Mandel type of two-photon interference effect with a heralded single-photon state and a thermal state. The light sources in the 1550 nm telecom band are generated from two independent dispersion-shifted fibers via four-wave mixing process. The observed visibility is (82±11)%. This type of interference between independent sources is crucial in quantum information process with independent qubits.

© 2008 Optical Society of America

1. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature **409**, 46–52 (2001). [CrossRef] [PubMed]

2. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. **59**, 2044–2047 (1987). [CrossRef] [PubMed]

3. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature **390**, 575–579 (1997). [CrossRef]

4. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. **80**, 3891–3894 (1998). [CrossRef]

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

3. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature **390**, 575–579 (1997). [CrossRef]

4. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. **80**, 3891–3894 (1998). [CrossRef]

6. X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

7. J. Fan, A. Dogariu, and L. J Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. **30**, 1530–1532 (2005). [CrossRef] [PubMed]

8. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, “Generation of Nonclassical Photon Pairs for Scalable Quantum Communication with Atomic Ensembles,” Nature **423**, 731–734 (2003). [CrossRef] [PubMed]

10. H. Takesue, “1.5-um band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers,” Appl. Phys. Lett. **90**, 204,101 (2007). [CrossRef]

11. J. Fulconis, O. Alibart, J. L. O’brien, W. J. Wadsworth, and J. G. Rarity, “Nonclassical Interference and Entanglement Generation Using a Photonic Crystal Fiber Pair Photon Source,” Phys. Rev. Lett. **99**, 120,501 (2007). [CrossRef]

13. T. B. Pittman and J. D. Franson, “Violation of Bell’s Inequality with Photons from Independent Sources,” Phys. Rev. Lett. **90**, 240,401 (2003). [CrossRef]

14. B. Hessmo, P. Usachev, H. Heydari, and G. Bjork, “Experimental Demonstration of Single Photon Nonlocality,” Phys. Rev. Lett. **92**, 180,401 (2004). [CrossRef]

15. Z. Y. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A **37**, 1607–1619 (1988). [CrossRef] [PubMed]

2. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. **59**, 2044–2047 (1987). [CrossRef] [PubMed]

15. Z. Y. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A **37**, 1607–1619 (1988). [CrossRef] [PubMed]

16. Z. Y. Ou and L. Mandel, “Further evidence of nonclassical behavior in optical interference,” Phys. Rev. Lett. **62**, 2941–2944 (1989). [CrossRef] [PubMed]

17. S. M. Tan, D. F Walls, and M. J. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. **66**, 252–255 (1991). [CrossRef] [PubMed]

18. J. G. Rarity and P. R. Tapster, “Three-particle entanglement from entangled photon pairs and a weak coherent state,” Phys. Rev. A **59**, R35–R38 (1999). [CrossRef]

13. T. B. Pittman and J. D. Franson, “Violation of Bell’s Inequality with Photons from Independent Sources,” Phys. Rev. Lett. **90**, 240,401 (2003). [CrossRef]

17. S. M. Tan, D. F Walls, and M. J. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. **66**, 252–255 (1991). [CrossRef] [PubMed]

19. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, (IEEE, New York) pp. 175–179 (1984). [PubMed]

15. Z. Y. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A **37**, 1607–1619 (1988). [CrossRef] [PubMed]

20. X. Li, L. Yang, L. Cui, Z. Y. Ou, and D. Yu, “Fiber-based source of photon pairs at telecom band with high temporal coherence and brightness for quantum information processing,” Opt. Lett. **33**, 593–595 (2008). [CrossRef] [PubMed]

20. X. Li, L. Yang, L. Cui, Z. Y. Ou, and D. Yu, “Fiber-based source of photon pairs at telecom band with high temporal coherence and brightness for quantum information processing,” Opt. Lett. **33**, 593–595 (2008). [CrossRef] [PubMed]

*µ*s. The quantum efficiency of SPD1, SPD2, and SPD3 is 7%, 10%, and 20%, respectively. The total detection efficiency for signal1 (signal2) and idler2 is 0.6% (0.7%) and 3%, respectively, when the efficiencies of the other transmission components, such as the DSF, PBS, and filter F, are included.

*â*

_{1}and

*â*

_{2}are the field operators for the thermal state and single-photon state, respectively. The two-photon coincidence probability

*P*

_{2}is proportional to [15

**37**, 1607–1619 (1988). [CrossRef] [PubMed]

*n̅*is the average photon number of the thermal field, and

*I*

_{12}=〈

*a*

^{†}

_{2}(

*t*)

*a*

^{†}

_{1}(

*t*′)

*a*

_{2}(

*t*′)

*a*

_{1}(

*t*)〉/

*n̅*is the interference term, that leads to two-photon interference and depends on the overlap between signal1 and signal2 fields at the 50/50 beam splitter. When

*t*=

*t*′,

*I*

_{12}=1 corresponding to the bottom of the dip in figure 2 but when

*t*and

*t*′ are very different,

*I*

_{12}=0 corresponding to the wings in figure 2. From Eqs (1)–(2), we have

*V*approaches to 1 or 100% visibility if the average photon number of the thermal state

*n ̅*≪1.

*n̄*from measured efficiencies of detectors and single counts and obtain

*n̄*=0.26±0.035 and

*n̄*=0.38±0.05, which leads to

*V*=0.79±0.03 and

_{theory}*V*=0.72±0.03. These values are consistent with the results in Fig. 2.

_{theory}6. X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

20. X. Li, L. Yang, L. Cui, Z. Y. Ou, and D. Yu, “Fiber-based source of photon pairs at telecom band with high temporal coherence and brightness for quantum information processing,” Opt. Lett. **33**, 593–595 (2008). [CrossRef] [PubMed]

10. H. Takesue, “1.5-um band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers,” Appl. Phys. Lett. **90**, 204,101 (2007). [CrossRef]

**33**, 593–595 (2008). [CrossRef] [PubMed]

11. J. Fulconis, O. Alibart, J. L. O’brien, W. J. Wadsworth, and J. G. Rarity, “Nonclassical Interference and Entanglement Generation Using a Photonic Crystal Fiber Pair Photon Source,” Phys. Rev. Lett. **99**, 120,501 (2007). [CrossRef]

## Acknowledgment

## References and links

1. | E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

2. | C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. |

3. | D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature |

4. | J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. |

5. | C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. |

6. | X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express |

7. | J. Fan, A. Dogariu, and L. J Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. |

8. | A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, “Generation of Nonclassical Photon Pairs for Scalable Quantum Communication with Atomic Ensembles,” Nature |

9. | X. Li, C. Liang, K. F. Lee, J. Chen, P. L. Voss, and P. Kumar, “Integrable optical-fiber source of polarization-entangled photon pairs in the telecom band,” Phys. Rev. A |

10. | H. Takesue, “1.5-um band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers,” Appl. Phys. Lett. |

11. | J. Fulconis, O. Alibart, J. L. O’brien, W. J. Wadsworth, and J. G. Rarity, “Nonclassical Interference and Entanglement Generation Using a Photonic Crystal Fiber Pair Photon Source,” Phys. Rev. Lett. |

12. | J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” arXiv |

13. | T. B. Pittman and J. D. Franson, “Violation of Bell’s Inequality with Photons from Independent Sources,” Phys. Rev. Lett. |

14. | B. Hessmo, P. Usachev, H. Heydari, and G. Bjork, “Experimental Demonstration of Single Photon Nonlocality,” Phys. Rev. Lett. |

15. | Z. Y. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A |

16. | Z. Y. Ou and L. Mandel, “Further evidence of nonclassical behavior in optical interference,” Phys. Rev. Lett. |

17. | S. M. Tan, D. F Walls, and M. J. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. |

18. | J. G. Rarity and P. R. Tapster, “Three-particle entanglement from entangled photon pairs and a weak coherent state,” Phys. Rev. A |

19. | C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, (IEEE, New York) pp. 175–179 (1984). [PubMed] |

20. | X. Li, L. Yang, L. Cui, Z. Y. Ou, and D. Yu, “Fiber-based source of photon pairs at telecom band with high temporal coherence and brightness for quantum information processing,” Opt. Lett. |

21. | B. Yurke and M. Potasek, “Obtainment of thermal noise from a pure quantum state,” Phys. Rev. A |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: June 9, 2008

Revised Manuscript: July 18, 2008

Manuscript Accepted: July 23, 2008

Published: August 4, 2008

**Citation**

Xiaoying Li, Lei Yang, Liang Cui, Zhe Yu Ou, and Daoyin Yu, "Observation of quantum interference between a single-photon state and a
thermal state generated in optical fibers," Opt. Express **16**, 12505-12510 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-12505

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### References

- E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409,46-52 (2001). [CrossRef] [PubMed]
- C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2047 (1987). [CrossRef] [PubMed]
- D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997). [CrossRef]
- J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, "Experimental entanglement swapping: entangling photons that never interacted," Phys. Rev. Lett. 80, 3891-3894 (1998). [CrossRef]
- C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986). [CrossRef] [PubMed]
- X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications: Improved generation of correlated photons," Opt. Express 12, 3737-3744 (2004). [CrossRef] [PubMed]
- J. Fan, A. Dogariu, and L. J. Wang, "Generation of correlated photon pairs in a microstructure fiber," Opt. Lett. 30, 1530-1532 (2005). [CrossRef] [PubMed]
- A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of Nonclassical Photon Pairs for Scalable Quantum Communication with Atomic Ensembles," Nature 423, 731-734 (2003). [CrossRef] [PubMed]
- X. Li, C. Liang, K. F. Lee, J. Chen, P. L. Voss, and P. Kumar, "Integrable optical-fiber source of polarizationentangled photon pairs in the telecom band," Phys. Rev. A 73, 052,301 (2006).
- H. Takesue, "1.5-um band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers," Appl. Phys. Lett. 90, 204,101 (2007). [CrossRef]
- J. Fulconis, O. Alibart, J. L. O�??brien, W. J. Wadsworth, and J. G. Rarity, "Nonclassical Interference and Entanglement Generation Using a Photonic Crystal Fiber Pair Photon Source," Phys. Rev. Lett. 99, 120,501 (2007). [CrossRef]
- J. G. Rarity, P. R. Tapster, and R. Loudon, "Non-classical interference between independent sources," arXiv quant-ph, 9702,032 (1997).
- T. B. Pittman and J. D. Franson, "Violation of Bell�??s Inequality with Photons from Independent Sources," Phys. Rev. Lett. 90, 240,401 (2003). [CrossRef]
- B. Hessmo, P. Usachev, H. Heydari, and G. Bjork, "Experimental Demonstration of Single Photon Nonlocality," Phys. Rev. Lett. 92, 180,401 (2004). [CrossRef]
- Z. Y. Ou, "Quantum theory of fourth-order interference," Phys. Rev. A 37, 1607-1619 (1988). [CrossRef] [PubMed]
- Z. Y. Ou and L. Mandel, "Further evidence of nonclassical behavior in optical interference," Phys. Rev. Lett. 62, 2941-2944 (1989). [CrossRef] [PubMed]
- S. M. Tan, D. F. Walls, and M. J. Collett, "Nonlocality of a single photon," Phys. Rev. Lett. 66, 252-255 (1991). [CrossRef] [PubMed]
- J. G. Rarity and P. R. Tapster, "Three-particle entanglement from entangled photon pairs and a weak coherent state," Phys. Rev. A 59, R35-R38 (1999). [CrossRef]
- C. H. Bennett and G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, (IEEE, New York) pp. 175-179 (1984). [PubMed]
- X. Li, L. Yang, L. Cui, Z. Y. Ou, and D. Yu, "Fiber-based source of photon pairs at telecom band with high temporal coherence and brightness for quantum information processing," Opt. Lett. 33, 593-595 (2008). [CrossRef] [PubMed]
- B. Yurke and M. Potasek, "Obtainment of thermal noise from a pure quantum state," Phys. Rev. A 36, 3464-3466 (1987). [CrossRef] [PubMed]

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