## Long-distance distribution of time-bin entanglement generated in a cooled fiber

Optics Express, Vol. 14, Issue 8, pp. 3453-3460 (2006)

http://dx.doi.org/10.1364/OE.14.003453

Acrobat PDF (447 KB)

### Abstract

This paper reports the first demonstration of the generation and distribution of time-bin entangled photon pairs in the 1.5-*μ*m band using spontaneous four-wave mixing in a cooled fiber. Noise photons induced by spontaneous Raman scattering were suppressed by cooling a dispersion shifted fiber with liquid nitrogen, which resulted in a significant improvement in the visibility of two-photon interference. By using this scheme, time-bin entangled qubits were successfully distributed over 60 km of optical fiber with a visibility of 76%, which was obtained without removing accidental coincidences.

© 2006 Optical Society of America

## 1. Introduction

*μ*m band, namely the existence of noise photons generated by spontaneous Raman scattering [8

8. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical fiber-source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053601 (2005). [CrossRef] [PubMed]

9. H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , **70**, 031802(R) (2004). [CrossRef]

10. H. Takesue and K. Inoue, “Generation of 1.5-*μ*m band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041804(R) (2005). [CrossRef]

14. X. Li, J. Chen, P. 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]

15. K. Inoue and K. Shimizu, “Generation of quantum-correlated photon pairs in optical fiber: influence of spontaneous Raman scattering,” Jpn. J. Appl. Phys. **43**, 8048–8052 (2004). [CrossRef]

8. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical fiber-source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053601 (2005). [CrossRef] [PubMed]

9. H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , **70**, 031802(R) (2004). [CrossRef]

10. H. Takesue and K. Inoue, “Generation of 1.5-*μ*m band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041804(R) (2005). [CrossRef]

11. X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, “Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber,” Opt. Lett. **30**, 1201–1203 (2005). [CrossRef] [PubMed]

18. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. **82**, 2594–2597 (1999). [CrossRef]

19. I. Marcikic, H. de Reidmatten, W. Tittel, H. Zbinden, M. Legre, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. **93**, 180502 (2004). [CrossRef] [PubMed]

## 2. Suppression of spontaneous Raman scattering by cooling fiber

20. M. G. Raymer and I. A. Walmsley, “The quantum coherence properties of stimulated Raman scattering,” Progress in Optics **28**, 181–270 (1990). [CrossRef]

*n*, and anti-Stokes photons,

_{s}*n*as a function of temperature

_{as}*T*are expressed as [16

16. H. Takesue and K. Inoue, “1.5-*μ*m band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express **13**, 7832–7839 (2005). [CrossRef] [PubMed]

## 3. Experiments

*k*〉

_{x}represents a state in which there is a photon in a time slot

*k*in a mode

*x*, signal (

*s*) or idler (

*i*).

*ϕ*is a relative phase term that is equal to 2

*ϕ*, where

_{p}*ϕ*is the phase difference between two pump pulses, and is stably fixed because of the long coherent time of the laser output. The output light from the DSF is input into a fiber Bragg grating (FBG) to suppress pump photons, and launched into an arrayed waveguide grating (AWG) to separate the signal and idler channels. AWG output ports with peak frequencies of +400 and -400 GHz from the pump photon frequency are used for the signal and idler, respectively. The 3-dB bandwidths of the signal and idler channels are both 25 GHz (≃0.2 nm). Then the signal and idler photons are launched into optical bandpass filters to further suppress the pump photons.

_{p}23. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. **29**, 2797–2799 (2004). [CrossRef] [PubMed]

10. H. Takesue and K. Inoue, “Generation of 1.5-*μ*m band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041804(R) (2005). [CrossRef]

*k*〉

_{x}is converted as follows by the interferometer.

*a*and

*b*denote two output ports of the interferometer.

*θ*is the phase difference between the two paths of the interferometer for channel

_{x}*x*, and can be tuned by changing the temperature. As a result, the time-bin entangled state ∣Ψ〉 is converted to

*θ*=

*θ*+

_{s}*θ*and 16 non-coincident terms in the parentheses are not shown because they are not observed in a coincidence measurement. We can observe a two-photon interference fringe by changing

_{i}*θ*and measuring the coincidence counts in the second time slot.

*a*of each interferometer is connected to a photon counter based on an InGaAs avalanche photodiode operated in a gated mode with a 4-MHz gate frequency. The electric signals from the photon counter for the signal and the idler are input into a time interval analyzer as a start and stop pulse, respectively. The losses of the signal and idler channels including the excess losses of the interferometers are both approximately 8 dB. The quantum efficiencies and dark count rate per gate are 8% and 4 × 10

^{-5}for the signal, and 7% and 5 × 10

^{-5}for the idler, respectively.

*α*and

_{s}*α*denote transmittances for the signal and idler channels including the quantum efficiency of the photon counters, respectively. On the other hand, the accidental coincidence rate

_{i}*R*is given by

_{acc}*μ*and

_{x}*d*denote the average number of photons per pulse and the dark count rate of the detector for channel

_{x}*x*with

*x*=

*s*,

*i*, respectively. If the average number of noise photons per pulse for channel

*x*is given by

*μ*,

_{nx}*μ*is expressed as

_{x}*R*+

_{c}*R*and

_{acc}*R*is observed at the maximum and minimum points of a two-photon interference fringe. Therefore, the visibility

_{acc}*V*is expressed as

*μ*and

_{s}*μ*were again set at around 0.05 and 0.06, respectively. Squares show the coincidence rate per start pulse and

_{i}*x*symbols show the idler count rate as a function of interferometer temperature. The average count rate for the signal was ~430 Hz. The average coincidence rate at the peak of the fringe was as low as ~0.3 Hz, which resulted in a long measurement time (the measurement shown in Fig. 3 took more than three hours to complete). The visibility of the fringe was 75.8%, which was obtained without removing accidental coincidences. Thus, time-bin entangled photon pairs were successfully distributed over 60 km (30 km × 2) of fiber.

*μ*m band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041804(R) (2005). [CrossRef]

## 4. Discussions

*μ*m zero dispersion wavelength were not available. According to the following calculation, the photons generated from this source are expected to be transmitted over 60 km of SMF, thanks to the narrow bandwidth of the signal/idler photons. Let us assume that the dispersion in the cooled fiber and the optical filters is negligible and the transmittance spectra of signal and idler channels are both Gaussian. Then, the temporal shapes of the signal and idler photons are approximated as transform-limited Gaussian pulses. The half-width at the 1/

*e*-intensity point

*T*

_{0}is expressed as √ln2/(

*π*Δ

*f*), where Δ

*f*is the full width at half maximum of the signal/idler spectrum. After transmission over an optical fiber with length

*z*, the half width at the 1/

*e*-intensity point of the output pulse

*T*

_{1}is expressed as [22]

*β*

_{2}denotes second derivative of the propagation constant in optical fiber. With

*z*= 30 km, Δ

*f*= 25 GHz and

*β*

_{2}= -20 ps

^{2}/km,

*T*

_{1}is calculated to be ~60 ps, which is small compared with the 1-ns pulse interval. Thus, chromatic dispersion does not seem to result in serious degradation of the visibility even when two 30-km SMF spools are used. Nevertheless, it will be important to demonstrate long-distance distribution over SMF experimentally in the future.

25. A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: production, characterization and utilization,” Phys. Rev. Lett. **83**, 3103–3107 (1999). [CrossRef]

26. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A **64**, 052312 (2001). [CrossRef]

27. P. G. Kwiat, A. M. Steinberg, and R. Y. Chao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A **47**, R2472 (1993). [CrossRef]

## 5. Conclusion

*μ*m band entanglement source based on a cooled fiber is a promising technology for realizing advanced quantum information systems over optical fiber networks.

## Acknowledgments

## References and links

1. | A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. |

2. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

3. | C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. |

4. | C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. |

5. | H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. |

6. | P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. |

7. | P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A |

8. | X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical fiber-source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. |

9. | H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , |

10. | H. Takesue and K. Inoue, “Generation of 1.5- |

11. | X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, “Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber,” Opt. Lett. |

12. | J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. St. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express |

13. | J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. |

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

15. | K. Inoue and K. Shimizu, “Generation of quantum-correlated photon pairs in optical fiber: influence of spontaneous Raman scattering,” Jpn. J. Appl. Phys. |

16. | H. Takesue and K. Inoue, “1.5- |

17. | K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “High-purity telecom-band entangled photon-pairs via four-wave mixing in dispersion-shifted fiber,” postdeadline paper presented at the Frontiers in Optics 2005-the 89th OSA Annual Meeting, Tucson, AZ, October 16-20, 2005;paper PDP-A4. |

18. | J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. |

19. | I. Marcikic, H. de Reidmatten, W. Tittel, H. Zbinden, M. Legre, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. |

20. | M. G. Raymer and I. A. Walmsley, “The quantum coherence properties of stimulated Raman scattering,” Progress in Optics |

21. |
The unit of n is determined by that of the pump photon number: for example, if the pump photon number is defined per pulse, _{as}n and _{s}n denote the number of Stokes and anti-Stokes photons per pump pulse._{as} |

22. | G. P. Agrawal, |

23. | T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. |

24. |
Exactly speaking, μ for the cooled fiber was slightly smaller than that for the uncooled fiber. This is because, according to Eqs. (1) and (2), the difference between Raman gain coefficients for the Stokes and anti-Stokes processes increases slightly as the fiber is cooled._{s} |

25. | A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: production, characterization and utilization,” Phys. Rev. Lett. |

26. | D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A |

27. | P. G. Kwiat, A. M. Steinberg, and R. Y. Chao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: February 10, 2006

Revised Manuscript: April 6, 2006

Manuscript Accepted: April 11, 2006

Published: April 17, 2006

**Citation**

Hiroki Takesue, "Long-distance distribution of time-bin entanglement generated in a cooled fiber," Opt. Express **14**, 3453-3460 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3453

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### References

- A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777-780 (1935). [CrossRef]
- A. K. Ekert, "Quantum cryptography based on Bell’s theorem," Phys. Rev. Lett. 67, 661-663 (1991). [CrossRef] [PubMed]
- C. H. Bennett, G. Brassard, and N. D. Mermin, "Quantum cryptography without Bell’s theorem," Phys. Rev. Lett. 68, 557-559 (1992). [CrossRef] [PubMed]
- C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993). [CrossRef] [PubMed]
- H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, "Quantum repeaters: the role of imperfect local operations in quantum communication," Phys. Rev. Lett. 81, 5932-5935 (1998). [CrossRef]
- P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995). [CrossRef] [PubMed]
- P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773-776 (1999). [CrossRef]
- X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber-source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005). [CrossRef] [PubMed]
- H. Takesue and K. Inoue, "Generation of polarization entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in fiber loop," Phys. Rev. A, 70, 031802(R) (2004). [CrossRef]
- H. Takesue and K. Inoue, "Generation of 1.5- μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers," Phys. Rev. A 72, 041804(R) (2005). [CrossRef]
- X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, "Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber," Opt. Lett. 30, 1201-1203 (2005). [CrossRef] [PubMed]
- J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth and P. St. J. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005). [CrossRef] [PubMed]
- J. Fan, A. Migdall and L. J. Wang, "Efficient generation of correlated photon pairs in a microstructure fiber," Opt. Lett. 30, 3368-3370 (2005). [CrossRef]
- X. Li, J. Chen, P. 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]
- K. Inoue and K. Shimizu, "Generation of quantum-correlated photon pairs in optical fiber: influence of spontaneous Raman scattering," Jpn. J. Appl. Phys. 43, 8048-8052 (2004). [CrossRef]
- H. Takesue and K. Inoue, "1.5- μm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber," Opt. Express 13, 7832-7839 (2005). [CrossRef] [PubMed]
- K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, "High-purity telecom-band entangled photonpairs via four-wave mixing in dispersion-shifted fiber," postdeadline paper presented at the Frontiers in Optics 2005-the 89th OSA Annual Meeting, Tucson, AZ, October 16-20, 2005;paper PDP-A4.
- J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, "Pulsed energy-time entangled twin-photon source for quantum communication," Phys. Rev. Lett. 82, 2594-2597 (1999). [CrossRef]
- I. Marcikic, H. de Reidmatten,W. Tittel, H. Zbinden,M. Legre, and N. Gisin, "Distribution of time-bin entangled qubits over 50 km of optical fiber," Phys. Rev. Lett. 93, 180502 (2004). [CrossRef] [PubMed]
- M. G. Raymer and I. A. Walmsley, "The quantum coherence properties of stimulated Raman scattering," Prog. Opt. 28, 181-270 (1990). [CrossRef]
- The unit of ns and nas is determined by that of the pump photon number: for example, if the pump photon number is defined per pulse, ns and nas denote the number of Stokes and anti-Stokes photons per pump pulse.
- G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995).
- T. Honjo, K. Inoue, and H. Takahashi, "Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer," Opt. Lett. 29, 2797-2799 (2004). [CrossRef] [PubMed]
- Exactly speaking, μi was set at the same value in both cases, and μs for the cooled fiber was slightly smaller than that for the uncooled fiber. This is because, according to Eqs. (1) and (2), the difference between Raman gain coefficients for the Stokes and anti-Stokes processes increases slightly as the fiber is cooled.
- A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999). [CrossRef]
- D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001). [CrossRef]
- P. G. Kwiat, A. M. Steinberg, and R. Y. Chao, "High-visibility interference in a Bell-inequality experiment for energy and time," Phys. Rev. A 47, R2472 (1993). [CrossRef]

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