## Narrowband polarization-entangled photon pairs distributed over a WDM link for qubit networks

Optics Express, Vol. 15, Issue 11, pp. 6926-6933 (2007)

http://dx.doi.org/10.1364/OE.15.006926

Acrobat PDF (921 KB)

### Abstract

We present a bright, narrowband, portable, quasi-phase-matched two-crystal source generating polarization-entangled photon pairs at 809 nm and 1555 nm at a maximum rate of 1.2 × 10^{6} s^{-1} THz^{-1} mW^{-1} after coupling to single-mode fiber. The quantum channel at 1555 nm and the synchronization signal gating the single photon detector are multiplexed in the same optical fiber of length 27 km by means of wavelength division multiplexers (WDM) having 100 GHz (0.8 nm) spacing between channels. This implementation makes quantum communication applications compatible with current high-speed optical networks.

© 2007 Optical Society of America

## 1. Introduction

5. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. **75**, 4337–4340 (1995). [CrossRef] [PubMed]

6. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically-poled KTiOPO_{4} parametric downconverter,” Phys. Rev. A **69**, 013807 (2004). [CrossRef]

7. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using a periodically poled lithium niobate waveguide,” Electron. Lett. **37**, 26–28 (2001). [CrossRef]

8. M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, “Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP,” Opt. Express **12**, 3573–3580 (2004). [CrossRef] [PubMed]

9. D. Ljunggren, M. Tengner, P. Marsden, and M. Pelton, “Theory and experiment of entanglement in a quasi-phase-matched two-crystal source,” Phys. Rev. A **73**, 032326 (2006). [CrossRef]

10. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A **72**, 062301 (2005). [CrossRef]

*L*

^{1/2}and 1/

*L*, respectively, where

*L*is the length of each crystal. Assuming optimal focusing, we can therefore only see advantages using long crystals. To our knowledge, this is the first time that such long crystals are used in this configuration.

## 2. The source

_{p}) such that each photon has an equal probability of down-converting either in the first or in the second crystal, respectively generating vertically (V) or horizontally (H) polarized photon pairs. The source has collinear emission at the non degenerate wavelengths of λ

_{s}= 809 nm for the signal (remaining at Alice) and λ

_{i}= 1555 nm for the idler (sent to Bob), allowing efficient single-photon detection and low attenuation in fibers at telecom wavelength, respectively (wavelength tuning can be achieved by varying the temperature of the brass ovens heating the crystals at around 100 °C).

*w*

_{0}= 150 μm, giving a Rayleigh range

*z*

_{0}= π

*w*

_{0}

^{2}/λ of about 72 mm in PPLN:MgO, hence a

*z*

_{0}/

*L*ratio of 1.44. For the signal and idler beams, we measured a beam divergence 2θ of ca. 9 mrad and 15 mrad respectively, leading to beam waists

*w*

_{0}= λ/πθ of 110 μm at 809 nm and 130 μm at 1555 nm, which gives an average value of 120 μm.

_{s}, L

_{i}), filtered from residual pump light by means of long-pass filters (LPF) and eventually focused into single-mode fiber (SMF) at Alice’s side. Due to the difference in beam divergences at 809 nm and 1555 nm after generation in the two crystals, we selected for each arm a collimating lens with a specific focal length (f

_{s}= 200 mm, f

_{i}= 150 mm) such that each collimated beam gets coupled with a focusing angle matching the numerical aperture of the fibers (NA

_{s}= 0.12, NA

_{i}= 0.13).

_{p}, ω

_{s}and ω

_{i}are the pump, signal and idler frequencies respectively and φ is the total phase difference of the two polarization components.

*and*(H) crystal, signal and idler (V) have a difference in group delays 11 ps larger than the one between signal and idler (H). Since the estimated coherence time of idler (V or H) is about 16 ps, the 11 ps delay between idler (V) and idler (H) leads to 75% lower visibility in the D/A basis than in the H/V basis. In order to restore indistinguishability, we slow down idler (V) with respect to idler (H) by transmitting them through a 25 mm long piece of birefringent calcite crystal (CLC). It introduces ca. 15 ps group delay difference between idler (H) and (V). We complemented CLC by a 3 meter-long piece of polarization maintaining fiber (PMF), which introduces a group delay difference between idler (H) and (V) of -4 ps (slow axis of PMF is aligned with fast axis of CLC). The reason to use PMF is to fine-tune the phase difference φ of the two polarization components. This is achieved by applying a (local) mechanical strain on the fiber.

_{s}= 60 %, and a homebuilt InGaAs-APD (Epitaxx) module for the idler side (1555 nm), having η

_{i}= 18 % quantum efficiency. The latter is gated with 2.5 ns-long pulses, and to avoid after-pulsing effects it is used together with a hold-off circuit, which discards any trigger pulse arriving within 10 μs after the detector has been gated, corresponding to the mean lifetime of the trapped carriers in the semi-conductor photo-diode. In order to limit the noise of the InGaAs detector, we reduced its gate time artificially to discriminate between true counts (well localized in time) and dark ones (which occur with a higher probability as the time during which the detector is gated is increased). For that purpose, we built a time-discriminator circuit (TDC), which registers a count if the two TTL pulses output by the two APD upon (coincident) detection overlap. The TDC provides a gain of a few percents in the visibility when the overlap between the two TTL pulses is adjusted to be τ ≈ 1.5 ns (corresponding to the new effective gate time of the APD). When using TDC, about 20% of coincidence events also get discarded so we increase the pump power in order to reach the same coincidence rate as when TDC is not used, this time with a higher visibility. As a result, the single count rate at 809 nm is increased from 0.8 × 10

^{6}s

^{-1}to 1.1 × 10

^{6}s

^{-1}when TDC is used.

## 3. Experimental results

_{i}of the 1555 nm photons is 0.5 nm FWHM before coupling to the WDM filters (those have 0.2 nm flat-top bandwidth and 0.5 nm FWHM). Assuming a chromatic dispersion (

*CD*) of 18 ps/nm/km for standard single-mode fiber, one could transmit 1555 nm photons over a distance

*d*≈ 150 km while keeping a chromatic dispersion-induced time spread of the photon τ

_{CD}=

*CD*× Δλ

_{i}×

*d*below the gate time τ ≈ 1.5 ns of the InGaAs-APD. The signal at 809 nm has an expected bandwidth Δλ

_{s}below 0.15 nm, as derived from the conversion factor between signal and idler bandwidths Δλ

_{i}= (λ

_{i}/λ

_{s})

^{2}× Δλ

_{s}≈ 3.7 × Δλ

_{s}(this formula can be obtained by writing that both signal and idler have the same coherence length, which is proportional to λ

^{2}/Δλ).

*R*= 25 × 10

_{c}^{3}s

^{-1}when pumping one crystal only (V) at a power

*P*of around 3 mW. The single count rate at 809 nm was

*R*= 0.8 × 10

_{s}^{6}s

^{-1}, yielding a conditional detection probability

*R*/

_{c}*R*of about 3 % (TDC was not used in this particular case as it would lead to bias down our estimate of

_{s}*R*/

_{c}*R*). Taking into account the quantum efficiency η

_{s}_{i}= 18 % of the InGaAs APD, we reach a corrected conditional detection probability of 16 %. The difference to an optimal value of around 90 % for single-crystal [10

10. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A **72**, 062301 (2005). [CrossRef]

*R*= 0.9 × 10

_{a}^{3}s

^{-1}, leading to a raw visibility VV = (

*R*-

_{c}*R*)/(

_{a}*R*+

_{c}*R*) = 93 % at maximum coincidence count rate. Taking into account the quantum efficiency η

_{a}_{s}= 60 % and η

_{i}= 18 % of the two APD, we estimate that fibers carry photon pairs at a maximum rate

*R*≈

_{f}*R*/(η

_{c}_{s}η

_{i}) × 1/

*P*× 1/(

*k*Δλ

_{i}) ≈ 1.2 × 10

^{6}s

^{-1}THz

^{-1}mW

^{-1}, where

*k*= 0.125 THz nm

^{-1}is the conversion factor between nm and THz.

^{6}s

^{-1}at 809 nm and only one WDM used with a bandwidth of 0.5 nm for 1555 nm photons. In comparison to (i), the coincidences rate Rc dropped by a factor of about three, due to WDM coupling/filtering losses and insertion loss into the free-space analyzer used at Bob’s side. Raw visibilities for each of the four polarization states (H/V and D/A) of the signal were V

_{H}= 94 %, V

_{V}= 90 %, V

_{D}= 87 % and V

_{A}= 89 %, respectively. The drop in the visibility (from 93 % to 90 % for V

_{V}) despite the use of TDC is mainly due to non-ideal polarization alignment. Random fluctuations of the polarization after 100 m of fiber also affect how stable the visibility remains over time. The quantum bit error rate (QBER), given by the averaged ratio

*R*/

_{a}*R*over all four bases, amounts to about 5 %.

_{c}^{6}s

^{-1}at 809 nm and all four WDM filters inserted. The coincidences rate dropped to 1.1 × 10

^{3}s

^{-1}, mainly due to the attenuation by the 27 km fiber link added (-6 dB) and insertion losses into the 3 other WDM (-3 dB). Raw visibilities decreased down to V

_{H}= 85 %, V

_{V}= 85 %, V

_{D}= 83 % and V

_{A}= 85 %, respectively, mainly due to a residual leak of the trigger laser into the quantum channel, which could be reduced by using larger channel spacing. The moderate drop in the visibility also suggests that polarization fluctuations do not increase significantly with longer fiber links. This is supported by [12

12. H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization entangled qubits over 100 km of telecom fibers,” Opt. Express **15**, 7853 (2007). [CrossRef] [PubMed]

13. P.W. Shor and J. Preskill, “Simple proof of security of the BB84 Quantum key distribution protocol,” Phys. Rev. Lett. **85**, 441–444 (2000). [CrossRef] [PubMed]

## 4. Conclusions

^{3}s

^{-1}photon pairs with a raw visibility of 85 % in all measurement bases after transmission over 27 km of single mode fiber. With the current isolation of about 100 dB achieved between adjacent channels, we expect that the quantum channel could also be multiplexed with a classical data channel [14]. Investigation is under way.

15. M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A **69**, 041801 (2004). [CrossRef]

## Acknowledgments

## References and links

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

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

3. | I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, “Long-distance teleportation of qubits at telecommunication wavelengths,” Nature |

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

5. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. |

6. | C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically-poled KTiOPO |

7. | S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using a periodically poled lithium niobate waveguide,” Electron. Lett. |

8. | M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, “Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP,” Opt. Express |

9. | D. Ljunggren, M. Tengner, P. Marsden, and M. Pelton, “Theory and experiment of entanglement in a quasi-phase-matched two-crystal source,” Phys. Rev. A |

10. | D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A |

11. | C. Liang, K. F. Lee, J. Chen, and P. Kumar, “Distribution of fiber-generated polarization entangled photon-pairs over 100 km of standard fiber in OC-192 WDM environment,” postdeadline paper, Optical Fiber Communications Conference (OFC’2006), paper PDP35. |

12. | H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization entangled qubits over 100 km of telecom fibers,” Opt. Express |

13. | P.W. Shor and J. Preskill, “Simple proof of security of the BB84 Quantum key distribution protocol,” Phys. Rev. Lett. |

14. | J. J. Xia, D. Z. Chen, G. Wellbrock, A. Zavriyev, A. C. Beal, and K. M. Lee, “In-band quantum key distribution (QKD) on fiber populated by high-speed classical data channels,” Optical Fiber Communications Conference (OFC’2006), paper OTuJ7. |

15. | M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 26, 2007

Revised Manuscript: May 16, 2007

Manuscript Accepted: May 16, 2007

Published: May 21, 2007

**Citation**

S. Sauge, M. Swillo, S. Albert-Seifried, G. B. Xavier, J. Waldebäck, M. Tengner, D. Ljunggren, and A. Karlsson, "Narrowband polarization-entangled photon pairs distributed over a WDM link for qubit networks," Opt. Express **15**, 6926-6933 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-11-6926

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### References

- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2001). [CrossRef]
- A.K. Ekert, "Quantum cryptography based on Bell’s theorem," Phys. Rev. Lett. 67, 661 (1991). [CrossRef] [PubMed]
- I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, "Long-distance teleportation of qubits at telecommunication wavelengths," Nature 421, 509-513 (2003). [CrossRef] [PubMed]
- H. Briegel, W. Dür, 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, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4340 (1995). [CrossRef] [PubMed]
- C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarization entangled photons from a periodically-poled KTiOPO4 parametric downconverter," Phys. Rev. A 69, 013807 (2004). [CrossRef]
- S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using a periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001). [CrossRef]
- M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, "Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP," Opt. Express 12, 3573-3580 (2004). [CrossRef] [PubMed]
- D. Ljunggren, M. Tengner, P. Marsden, and M. Pelton, "Theory and experiment of entanglement in a quasi-phase-matched two-crystal source," Phys. Rev. A 73, 032326 (2006). [CrossRef]
- D. Ljunggren and M. Tengner, "Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers," Phys. Rev. A 72, 062301 (2005). [CrossRef]
- C. Liang, K. F. Lee, J. Chen, and P. Kumar, "Distribution of fiber-generated polarization entangled photon-pairs over 100 km of standard fiber in OC-192 WDM environment," postdeadline paper, Optical Fiber Communications Conference (OFC’2006), paper PDP35.
- H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, A. Poppe, and A. Zeilinger, "High-fidelity transmission of polarization entangled qubits over 100 km of telecom fibers," Opt. Express 15, 7853-7862 (2007). [CrossRef] [PubMed]
- P.W. Shor and J. Preskill, "Simple proof of security of the BB84 Quantum key distribution protocol," Phys. Rev. Lett. 85, 441-444 (2000). [CrossRef] [PubMed]
- J. J. Xia, D. Z. Chen, G. Wellbrock, A. Zavriyev, A. C. Beal, and K. M. Lee, "In-band quantum key distribution (QKD) on fiber populated by high-speed classical data channels," Optical Fiber Communications Conference (OFC’2006), paper OTuJ7.
- M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, "Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints," Phys. Rev. A 69, 041801 (2004). [CrossRef]

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