## Polarization insensitive phase modulator for quantum cryptosystems

Optics Express, Vol. 14, Issue 10, pp. 4264-4269 (2006)

http://dx.doi.org/10.1364/OE.14.004264

Acrobat PDF (102 KB)

### Abstract

In this paper, we propose a polarization-insensitive phase modulation scheme based on frequency modulation of light waves using either one or a pair of acousto-optic modulators. A stable Sagnac quantum key distribution (QKD) system employing this technique is also proposed. The interference visibility for a 40km and a 10km fiber loop is 96% and 99% respectively, at single-photon level. We ran standard BB84 QKD protocol in a simplified Sagnac setup (40km fiber loop) continuously for one hour and the measured quantum bit error rate stayed within 2%–5% range.

© 2006 Optical Society of America

## 1. Introduction

2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

4. Z. Yuan and A. Shields, “Continuous operation of a one-way quantum key distribution system over installed telecom fibre,” Opt. Express **13**, 660–665 (2005). [CrossRef] [PubMed]

4. Z. Yuan and A. Shields, “Continuous operation of a one-way quantum key distribution system over installed telecom fibre,” Opt. Express **13**, 660–665 (2005). [CrossRef] [PubMed]

5. A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, “Plug and play” systems for quantum cryptography,” Appl. Phys. Lett. **70**, 793–795 (1997). [CrossRef]

6. T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, “Circular type” quantum key distribution,” IEEE Photon. Technol. Lett. **14**, 576–578 (2002). [CrossRef]

9. P. D. Kumavor, A. C. Beal, S. Yelin, E. Donkor, and B. C. Wang, “Comparison of four multi-user quantum key distribution schemes over passive optical networks,” J. Lightwave Technol. **23**, 268–276 (2005). [CrossRef]

8. C. Y. Zhou, G. Wu, L. E. Ding, and H. P. Zeng, “Single-photon routing by time-division phase modulation in a Sagnac interferometer,” Appl. Phys. Lett. **83**, 15–17 (2003). [CrossRef]

## 2. Phase modulation with frequency shifters

*L*.

*f*(due to the Doppler effect). The phase of the diffracted light is also shifted by an amount of-

*ϕ*(

*t*), which is the phase of acoustic wave at the time of diffraction [10

10. A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, “Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters,” Phys. Rev. A **67**, 042115 (2003). [CrossRef]

*S*and

_{1}*S*, are in phase and are sent to the phase modulator at the same time from opposite directions as shown in Fig. 1(a). They will reach the AOM at different times with a time difference

_{2}*n*is effective index of fiber and

*c*is the speed of light in vacuum. The phase difference between

*S*and

_{1}*S*after they go through the phase modulator will be

_{2}*f*, the relative phase between

*S*and

_{1}*S*can be modulated. This is the basic mechanism of our AOM-based phase modulator. We remark that the frequency of light will be up-shifted by this phase modulator by an amount

_{2}*f*. To remove this “side-effect”, we can add another frequency down shifter at the other end of the fiber, as shown in Fig. 1(b). In Fig. 1(b), the two AOMs, which are driven by the same driver, will shift the frequency of light by the same amount but with different signs. So the net frequency shift will be zero. Since a down-shift AOM will shift the phase of the diffracted light by an amount of -

*ϕ*(

*t*), the resulting phase difference between

*S*and

_{2}*S*after they go through the phase modulator can be derived as

_{1}*LiNbO*

_{3}waveguide-based phase modulator, this phase modulator is insensitive to the polarization state of the input light, and the phase delay can be controlled precisely by the acoustic frequency

*f*.

## 3. QKD based on fiber Sagnac interferometer

*1550nm*laser (L) is modulated by an amplitude modulator (AM) to generate 500ps laser pulses. Each laser pulse is split into

*S*and

_{1}*S*at a symmetric fiber coupler, which go through a long fiber loop (

_{2}*L*+

_{1}*L*~40km) in the clockwise and counterclockwise directions, respectively. The interference patterns at Ch1 and Ch2 are measured by two InGaAs single photon detectors (SPD, Id Quantique, id200), which work in gated mode. For a 5ns gating window, the overall detection efficiency is ~10% and the dark count probability is 5×10

_{2}^{-5}per gating window. A fiber-pigtailed AOM (Brimrose inc.) is placed inside the fiber loop asymmetrically (

*L*–

_{1}*L*is about 700m, which is the length difference of two 20km fiber loop. There is no specific requirement for the length difference). Due to this asymmetry, phase modulation between

_{2}*S*and

_{1}*S*can be achieved by modulating AOM’s driving frequency, similar to the phase modulator shown in Fig. 1(a). Because of the birefringence in the fiber loop, the polarization states of S1 and S2 could be different after they go through the fiber loop [12

_{2}12. D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

## 4. Experimental results

13. Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. **96**, 070502 (2006). [CrossRef] [PubMed]

^{5}Hz (for 700m fiber length difference), which is much smaller than the spectral width of a nanosecond pulse (~10

^{9}Hz). It’s impossible for an eavesdropper (Eve) to decode the phase information by measuring the spectrum of a single photon pulse. On the other hand, Eve could explore this imperfection and launch a “phase remapping attack” [14

14. C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum key distribution systems,” arXiv:quant-ph/0601115 (2006) http://xxx.lanl.gov/abs/quant-ph/0601115

## 5. Conclusion

## Acknowledgments

## References and links

1. | C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in |

2. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

3. | R. J. Hughes, G. L. Morgan, and C. G. Peterson, “Quantum key distribution over a 48 km optical fiber network,” J. of Mod. Opt. |

4. | Z. Yuan and A. Shields, “Continuous operation of a one-way quantum key distribution system over installed telecom fibre,” Opt. Express |

5. | A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, “Plug and play” systems for quantum cryptography,” Appl. Phys. Lett. |

6. | T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, “Circular type” quantum key distribution,” IEEE Photon. Technol. Lett. |

7. | C. Y. Zhou and H. P. Zeng, “Time-division single-photon Sagnac interferometer for quantum key distribution,” Appl. Phys. Lett. |

8. | C. Y. Zhou, G. Wu, L. E. Ding, and H. P. Zeng, “Single-photon routing by time-division phase modulation in a Sagnac interferometer,” Appl. Phys. Lett. |

9. | P. D. Kumavor, A. C. Beal, S. Yelin, E. Donkor, and B. C. Wang, “Comparison of four multi-user quantum key distribution schemes over passive optical networks,” J. Lightwave Technol. |

10. | A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, “Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters,” Phys. Rev. A |

11. | E.-B. Li, J.-Q. Yao, D.-Y. Yu, J.-T. Xi, and J. Chicharo, “Optical phase shifting with acousto-optic devices,” Opt. Lett. |

12. | D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol. |

13. | Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. |

14. | C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum key distribution systems,” arXiv:quant-ph/0601115 (2006) http://xxx.lanl.gov/abs/quant-ph/0601115 |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.5060) Fiber optics and optical communications : Phase modulation

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 22, 2006

Manuscript Accepted: April 25, 2006

Published: May 15, 2006

**Citation**

Bing Qi, Lei-Lei Huang, Hoi-Kwong Lo, and Li Qian, "Polarization insensitive phase modulator for quantum cryptosystems," Opt. Express **14**, 4264-4269 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4264

Sort: Year | Journal | Reset

### References

- C. H. Bennett and G. Brassard, "Quantum cryptography: public key distribution and coin tossing," in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984), pp.175-179.
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).
- Z. Yuan and A. Shields, "Continuous operation of a one-way quantum key distribution system over installed telecom fibre," Opt. Express 13, 660-665 (2005). [CrossRef] [PubMed]
- A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997). [CrossRef]
- T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002). [CrossRef]
- C. Y. Zhou and H. P. Zeng, "Time-division single-photon Sagnac interferometer for quantum key distribution," Appl. Phys. Lett. 82, 832-834 (2003). [CrossRef]
- C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003). [CrossRef]
- P. D. Kumavor, A. C. Beal, S. Yelin, E. Donkor, B. C. Wang, "Comparison of four multi-user quantum key distribution schemes over passive optical networks," J. Lightwave Technol. 23, 268-276 (2005). [CrossRef]
- A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003). [CrossRef]
- E.-B. Li, J.-Q. Yao, D.-Y. Yu, J.-T. Xi, and J. Chicharo, "Optical phase shifting with acousto-optic devices," Opt. Lett. 30, 189-191 (2005). [CrossRef] [PubMed]
- D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988). [CrossRef]
- Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006). [CrossRef] [PubMed]
- C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, "Phase-remapping attack in practical quantum key distribution systems," arXiv:quant-ph/0601115 (2006) http://xxx.lanl.gov/abs/quant-ph/0601115

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.