## High-efficiency, ultra low-noise all-fiber photon-pair source

Optics Express, Vol. 16, Issue 13, pp. 9966-9977 (2008)

http://dx.doi.org/10.1364/OE.16.009966

Acrobat PDF (283 KB)

### Abstract

We demonstrate an all-fiber photon-pair source with the highest coincidence-to-accidental ratio (CAR) reported to date in the fiber-optic telecom C-band. We achieve this through careful optimization of pair-production efficiency as well as careful characterization and minimization of all sources of background photons, including Raman generation in the nonlinear fiber, Raman generation in the single-mode fiber, and leakage of pump photons. We cool the nonlinear fiber to 4 K to eliminate most of the Raman scattering, and we reduce other noise photon counts through careful system design. This yields a CAR of 1300 at a pair generation rate of 2 kHz. This CAR is a factor of 12 higher than previously reported results in the C-band. Measured data agree well with theoretical predictions.

© 2008 Optical Society of America

## 1. Introduction

1. Y. Shih, “Entangled biphoton source - property and preparation,” Rep. Prog. Phys. **66**, 1009–1044 (2003). [CrossRef]

2. 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]

3. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. **31**, 1905–1907 (2006). [CrossRef] [PubMed]

6. 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]

7. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. **57**, 691–694 (1986). [CrossRef] [PubMed]

8. 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]

10. J. Fan and A. Migdall, “A broadband high spectral brightness fiber-based two-photon source,” Opt. Express **15**, 2915–2920 (2007). [CrossRef] [PubMed]

13. 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**, 023803 (2007). [CrossRef]

13. 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**, 023803 (2007). [CrossRef]

13. 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**, 023803 (2007). [CrossRef]

## 2. Nonlinear fiber characterization using stimulated four wave mixing

*ω*and

_{p}*ω*are the frequencies of the pump and probe lasers, respectively, and

_{s}*ω*is the frequency of the generated idler photons. We measure the ratio of the intensity of the four-wave mixing component to the intensity of the probe on the OSA. Under the undepleted pump approximation, that ratio, which is called the FWM efficiency, is estimated by [14]

_{i}*L*is the length of the nonlinear fiber,

*P*is the power of the generated photons at the idler wavelength,

_{i}*g*is the parametric gain, and

*P*is the power at the probe laser wavelength, which we assume is large compared with

_{s}*P*for all

_{i}*L*, i.e., the power from the probe laser is much stronger than the power generated through FWM. We are also assuming perfect alignment of the polarization states of the pump and probe lasers. The effective phase mismatch

*κ*is given by

*β*is the group-velocity parameter (equal to

_{2}*d*, where

^{2}β/dω^{2}*β*is the fiber propagation constant) and Ω

_{s}is the radial frequency difference between the pump and the signal or idler. We approximate the group velocity parameter

*β*as a linear function:

_{2}*β*≈

_{2}*mΔλ*, where

_{ZD}*m*is the slope and

*Δλ*is the difference between the pump wavelength and the zero-dispersion wavelength (

_{ZD}*Δλ*=

_{ZD}*λ*-

_{p}*ZDW*). Note that this linear approximation will not work well with specialty fiber such as dispersion flattened fiber; in that case we would approximate

*β*as a quadratic or even cubic function of

_{2}*Δλ*, but for DSF and assuming a small

_{ZD}*Δλ*, a linear approximation is sufficient.

_{ZD}*γ*,

*m*, and ZDW by fitting the data of Fig. 2 to Eqs. (3)–(6). We obtain

*γ*=2.2 W

^{-1}·km

^{-1},

*m*=-0.12 ps

^{2}·nm

^{-1}·km

^{-1}, ZDW (T=4 K)=ZDW (T=77 K)=1544.8 nm, and ZDW (T=300 K)=1549 nm. Previously, the temperature coefficient of the ZDW of DSF was reported to be 0.03 nm/K, but that was based on measurements near room temperature [15

15. S. E. Mechels, J. B. Schlager, and D. L. Franzen, “Accurate measurements of the zero-dispersion wavelength in optical fibers,” J. Res. Natl. Inst. Stand. Technol. **102**, 333–347 (1997). [CrossRef]

*m*with temperature was negligible, as predicted by [15

15. S. E. Mechels, J. B. Schlager, and D. L. Franzen, “Accurate measurements of the zero-dispersion wavelength in optical fibers,” J. Res. Natl. Inst. Stand. Technol. **102**, 333–347 (1997). [CrossRef]

## 3. Spontaneous FWM and photon pair generation

**75**, 023803 (2007). [CrossRef]

*η*is the effective detection efficiency, which includes both detector quantum efficiency and the insertion loss of the signal or idler filters,

_{u}*Δν*is the bandwidth of the signal and idler filters (which we model as perfect rect functions with equal bandwidths),

*P*is the peak power, and

_{0}*D*is the duty cycle of the pump laser. The subscript

_{c}*u*is replaced with

*i*for idler photons and

*s*for signal photons. Here we use the undepleted pump approximation, and we neglect the Raman contribution to the nonlinear phase shift (i.e.,

*f*≈0) [13

_{R}**75**, 023803 (2007). [CrossRef]

**75**, 023803 (2007). [CrossRef]

*g*is given by Eq. (5). For low pump powers and small

*Δλ*, the

_{ZD}*gL*term of Eq. (7) is small, and therefore we can make the approximation that sinh(

*gL*)/

*gL*≈1. In that case, Eq. (7) above is consistent with Eq. (22) of [13

**75**, 023803 (2007). [CrossRef]

*g*≈0. This assumption is also valid for low pump powers and large detunings, where

*g*≈i

*Δk*/2. In both of these cases (either

*g*≈0 or

*g*≈iΔk/2), we can approximate the pair generation rate of Eq. (7) as quadratic with pump power.

## 4. Characterizing the Raman contribution

**75**, 023803 (2007). [CrossRef]

*g*is the Raman gain, which is determined by the properties of the fiber as well as from the detuning Ω

_{R}_{s}=

*ω*-

_{s}*ω*=

_{p}*ω*-

_{p}*ω*,

_{i}*μ*is defined as the probability of a Raman count per pulse, and

_{b}*f*is the repetition frequency of the pump laser. The phonon population is predicted by

_{p}*T*. The difference of +1 between the Stokes and anti-Stokes components of the Raman scattering in Eq. (9) reflects the fact that energy can still be transferred to the fiber when it is cooled near absolute zero. This +1 difference between Stokes and anti-Stokes scattering is negligible at room temperature where

*φ*(

*T*,

*Ω*)≈9 (assuming

_{s}*Ω*≈4 THz, corresponding to a 5 nm detuning), but at T=4 K where

_{s}*φ*(

*T*,

*Ω*)≈0.0005, it creates a substantial difference between the Stokes and anti-Stokes scattering.

_{s}_{s}until it peaks near 15 THz, which corresponds to a wavelength detuning of 120 nm at a center wavelength of 1550 nm [13

**75**, 023803 (2007). [CrossRef]

*g*=0.03 W

_{R}^{-1}·km

^{-1}) and the combined length (15 m) of the SMF pigtail of the last pump filter and the SMF pigtail of the first of the signal and idler filters. However, we believe that the actual length of these SMF pigtails is somewhat shorter than this measurement indicates (no longer than 8 m). It is possible that some small percentage of pump photons are leaking through the signal and idler filters and being misidentified as Raman photons generated in the SMF in this measurement.

*g*=0.08 W

_{R}^{-1}·km

^{-1}for the DSF.

## 5. Minimizing other sources of background photons

## 6. Comparison of predicted and measured coincidence-to-accidental ratios

*μ*is defined as the probability of a pair generation per pulse. The probability of detecting an accidental coincidence per pulse is approximated by

*p*is the probability that a dark count will occur in any sampling bin of the histogram, and the subscripts s and i distinguish between the Raman scattering at the signal and idler frequencies. The CAR is then calculated as

_{d}*C*/

*A*.

_{0})

^{1/2}, where N

_{0}is the total number of counts in the zero delay peak. Similarly, we estimate the uncertainty of the accidentals as (ΣN

_{i}-N

_{0})

^{1/2}, where N

_{i}is the number of counts in each histogram peak. The estimated total uncertainty is then calculated from the estimated coincidence and accidental uncertainties through standard error-propagation techniques. The integration times are chosen such that N

_{0}is approximately 100 for each histogram. The histograms at the highest pump power were integrated for 500 s, and we integrate for 10 h at the lowest pump power.

## 7. Summary

3. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. **31**, 1905–1907 (2006). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | Y. Shih, “Entangled biphoton source - property and preparation,” Rep. Prog. Phys. |

2. | 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 |

3. | K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. |

4. | J. Chen, K. F. Lee, C. Liang, and P. Kumar, “Fiber-based telecom-band degenerate-frequency source of entangled photon pairs,” Opt. Lett. |

5. | C. Liang, K. F. Lee, M. Medic, P. Kumar, R. H. Hadfield, and S. W. Nam, “Characterization of fibergenerated entangled photon pairs with superconducting single-photon detectors,” Opt. Express |

6. | 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 |

7. | R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. |

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

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

10. | J. Fan and A. Migdall, “A broadband high spectral brightness fiber-based two-photon source,” Opt. Express |

11. | 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 |

12. | K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U–Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express |

13. | 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 |

14. | G. P. Agrawal, |

15. | S. E. Mechels, J. B. Schlager, and D. L. Franzen, “Accurate measurements of the zero-dispersion wavelength in optical fibers,” J. Res. Natl. Inst. Stand. Technol. |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 28, 2008

Revised Manuscript: June 6, 2008

Manuscript Accepted: June 16, 2008

Published: June 20, 2008

**Citation**

Shellee D. Dyer, Martin J. Stevens, Burm Baek, and Sae Woo Nam, "High-efficiency, ultra low-noise all-fiber photon-pair source," Opt. Express **16**, 9966-9977 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9966

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### References

- Y. Shih, "Entangled biphoton source - property and preparation," Rep. Prog. Phys. 66, 1009-1044 (2003). [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. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, "Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber," Opt. Lett. 31, 1905-1907 (2006). [CrossRef] [PubMed]
- J. Chen, K. F. Lee, C. Liang, and P. Kumar, "Fiber-based telecom-band degenerate-frequency source of entangled photon pairs," Opt. Lett. 31, 2798-2800 (2006). [CrossRef] [PubMed]
- C. Liang, K. F. Lee, M. Medic, P. Kumar, R. H. Hadfield, and S. W. Nam, "Characterization of fiber-generated entangled photon pairs with superconducting single-photon detectors," Opt. Express 15, 1322-1327 (2007). [CrossRef] [PubMed]
- H. Takesue and K. Inoue, "1.5-?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]
- R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, "Broad-band parametric deamplification of quantum noise in an optical fiber," Phys. Rev. Lett. 57, 691-694 (1986). [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]
- 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]
- J. Fan and A. Migdall, "A broadband high spectral brightness fiber-based two-photon source," Opt. Express 15, 2915-2920 (2007). [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]
- K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U???Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, "Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber," Opt. Express 15, 14870-14886 (2007). [CrossRef] [PubMed]
- 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, 023803 (2007). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007), Chap. 10.
- S. E. Mechels, J. B. Schlager, and D. L. Franzen, "Accurate measurements of the zero-dispersion wavelength in optical fibers," J. Res. Natl. Inst. Stand. Technol. 102, 333-347 (1997). [CrossRef]

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