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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 15336–15346
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Experimental investigation in transmission performance of polarization-entangled photon-pairs generated by cascaded χ(2) processes over standard single-mode optical fibers

Shin Arahira and Hitoshi Murai  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 15336-15346 (2012)
http://dx.doi.org/10.1364/OE.20.015336


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Abstract

In this paper we report experimental investigation in transmission performance over standard single-mode optical fibers (SMFs) of polarization-entangled photon-pairs in a 1.5-μm band generated by cascaded second-harmonic generation and spontaneous parametric down conversion (c-SHG/SPDC) from a periodically poled LiNbO3 (PPLN) ridge-waveguide device. Clear two-photon interference fringes were observed even after the transmission over 140 km of the SMF spools, remaining small degradation in the visibilities of less than 3%. The performance was also investigated by using optical attenuators, instead of the SMF spools, to study the maximum reach of the distribution of the entanglement in terms of loss penalty. The results show that the quantum entanglement could be distributed even with 50 dB of the transmission loss with violation of Bell inequality by using the c-SHG/SPDC-based photon-pair source.

© 2012 OSA

1. Introduction

Quantum entanglement is not explained by the laws of classical physics and peculiar to quantum mechanics. The quantum entangled particles can make two distant observers share the results with nonlocal correlations. One of the promising and attractive applications using the quantum entanglement is quantum key distribution (QKD) for confidential communications with unconditionally security based on the laws of the quantum mechanics.

To our knowledge, the best value in terms of transmission distance of the quantum-entanglement distribution reported so far is 200 km, or 42 dB of the total transmission loss, over the dispersion-shifted optical fibers (DSFs) by using a periodically poled LiNbO3 (PPLN) device and InGaAs avalanche photodiodes (APDs) in a self-differencing mode [7

7. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]

].

The maximum reach of the distribution of the quantum entanglement is mainly determined by the following parameters: optical loss in the transmission media (typically 0.2 dB/km at 1.5-μm band in optical fibers), dark counts and detection efficiencies of single photon detectors (SPDs), optical loss in the entangled photon-pair source, the probability of the multi-photon-pair generation, and the probability of the noise photons mainly due to the Raman scattering generated from the photon-pair source itself and also from the transmission lines.

Among them, the photon-pair source and the single photon detector are vital components which give actual limit to expand the distribution distance. They should be highly pure with, at the least from the point of the views of practical uses, negligible noise photons and dark counts. Simultaneously they should be as practical as possible in terms of the cost, the reliability, and the compatibility with the existing systems. The results in Ref [7

7. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]

]. indicate that inexpensive InGaAs APDs are usable as the practical SPDs for distribution distance of 200 km if they are managed in a suitable design.

As for the photon-pair source, the photon-pair source based on spontaneous parametric down conversion (SPDC) is almost noise-photon-free because the Raman-induced photons are generated in the wavelength band far away from the photon-pairs and they can be easily eliminated. Mainly for this reason, the SPDC-based sources are used in most of the experimental demonstration of the long-distance distribution of the quantum entanglement. While the SPDC process is a powerful and usable tool, it often requires a complicated optical coupling system. This is because the photons at quite different wavelengths (short-wavelength pump photon and long-wavelength photon-pair) should be simultaneously managed.

In contrast, optical fiber-based photon-pair source often has serious impairments due to considerable Raman-induced photons [11

11. H. Takesue and K. Inoue, “1.5-microm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13(20), 7832–7839 (2005). [CrossRef] [PubMed]

, 12

12. K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008). [CrossRef] [PubMed]

], even though it has a merit that the source can entirely consist of the telecom-compatible optical resources.

Recently a new type of the quantum-entangled photon-pair source by using cascaded χ(2) processes, the second harmonic generation (SHG) and the following SPDC (c-SHG/SPDC process), was reported by some research groups including us [13

13. M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, and M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO3 waveguide,” Opt. Lett. 35(8), 1239–1241 (2010). [CrossRef] [PubMed]

15

15. S. Arahira, N. Namekata, T. Kishimoto, and S. Inoue, “Experimental studies in generation of high-purity photon-pairs using cascaded χ2 processes in a periodically poled LiNbO3 ridge-waveguide device,” J. Opt. Soc. Am. B 29(3), 434–442 (2012). [CrossRef]

]. We revealed that this photon-pair source using a periodically poled LiNbO3 (PPLN) ridge-waveguide device had very low contribution of the Raman noise photons, even though the pump photon, the Raman photon, and the photon-pairs are in the same wavelength-band [14

14. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]

, 15

15. S. Arahira, N. Namekata, T. Kishimoto, and S. Inoue, “Experimental studies in generation of high-purity photon-pairs using cascaded χ2 processes in a periodically poled LiNbO3 ridge-waveguide device,” J. Opt. Soc. Am. B 29(3), 434–442 (2012). [CrossRef]

]. The photon-pair source can also consist of the optical resources used in the standard telecom fields. This leads to the realization of low-cost and reliable photon-pair source. But detailed investigation in transmission performance of the quantum entanglement using this photon-pair source has not been reported to date.

In this paper we report the experimental studies in transmission performance of the polarization-entangled photon-pairs generated by the c-SHG/SPDC in a PPLN ridge-waveguide device over the standard single-mode optical fibers (SMFs). We observed clear two-photon interference fringes even after the transmission over 140 km of the SMF spools. The degradation in the visibility was less than 3% (approximately from 91% to 88%) even after the fiber transmission. This value agreed well with theoretical assumption. The results indicate that the QKD systems with the c-SHG/SPDC-based entangled photon-pair source can fully cover metro/access networks in which the standard SMFs are used without dispersion management. We also tested the performance by using optical attenuators, instead of the SMF spools, to study the maximum reach of the distribution in terms of loss penalty. The results revealed that the visibility exceeding 70.7% could be obtained even with 25 dB of the single channel loss, indicating that the quantum entanglement with the violation of the Bell inequality could be retained even at 50 dB of the transmission loss by using the c-SHG/SPDC-based entangled photon-pair source with proper dispersion management.

2. Experimental setup

Figure 1
Fig. 1 Experimental setup. PBSC: polarization beam splitter/combiner. OPBC: optical phase-bias compensator. PC: polarization controller. Pol.: rotatable fiber polarizer.
schematically draws the experimental setup. Setup of the polarization-entangled photon-pair source was detailed in our preceding work [14

14. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]

]. The home-made PPLN device with a ridge-waveguide structure was used in this work. It showed approximately 700%/W of the SHG conversion efficiency under the QPM condition at 1548.6 nm of the pump wavelength. The PPLN device was then packaged in a fiber-pigtailed optical module with a thermistor, a thermoelectric cooler, and two polarization-maintaining optical fibers (PMFs) for standard telecommunication uses. The insertion loss of the module was estimated to be approximately 3.0 dB at the 1.5-μm band.

The pump pulses were generated using a wavelength-tunable external-cavity laser diode and a LiNbO3 intensity modulator. The pulse repetition rate, the pulse width, and the center wavelength of the pump pulses were 240 MHz, 120 ps, and 1548.66 nm (corresponding to the QPM wavelength), respectively. After amplification by a polarization-maintaining erbium-doped fiber amplifier (PM-EDFA), residual amplified spontaneous emission (ASE) was eliminated by using a narrow-band optical bandpass filter (OBF#1). The 45 ° -polarized pump pulses then passed a WDM filter (WDM#1) and a polarization beam splitter/combiner (PBSC), and finally excited the PPLN module bidirectionally.

Since strong pump light remains at the center of the SPDC spectra in the c-SHG/SPDC based system, the pump light should be sufficiently reduced and the generated photon-pairs should be wavelength non-degenerate in the c-SHG/SPDC based system. The signal and the idler photons by the c-SHG/SPDC from the fiber loop passed the optical filtering system consisting of an optical low pass filter (LPF) and three-step WDM filters (WDM#1, #2, and #3). The LPF, the WDM#1, and the WDM#2 were mainly used to eliminate the pump light and the SHG light. Then the signal/idler photons were spatially separated by WDM#3 and two optical bandpass filters (OBF#2 and OBF#3). In this work we set the center wavelengths of the signal photons and the idler photons to 1538.8 nm and 1558.66 nm, respectively. Wavelength detuning from the pump wavelength was approximately 10 nm. The peak transmittance was −9.4 dB for the signal photons and −7.9 dB for the idler photons, respectively, including the insertion losses of the polarization controllers (PCs) and the rotatable polarizers to evaluate the two-photon interference fringes. The 3-dB bandwidth of the transmittance window was approximately 0.6 nm for the signal photons and 0.67 nm for the idler photons, respectively.

The photon-pairs were then launched into two individual transmission lines. In this work, we used two types of the transmission lines (Fig. 2
Fig. 2 Transmission lines used in this study. (A) transmission over SMF reel. (B) transmission with variable optical attenuator.
). One was two standard SMF reels combined with optical circulators (OCRs) and Faraday rotator mirrors (FRMs) (Fig. 2 (a)), and another was variable optical attenuators (Fig. 2 (b)).

In this work we used the standard SMFs as the transmission lines, while dispersion-shifted fibers (DSFs) or non-zero dispersion shifted fibers (NZ-DSF) has been commonly used in the long-distance QKD experiments [2

2. T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors,” Opt. Express 15(21), 13957–13964 (2007). [CrossRef] [PubMed]

8

8. A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Lorünser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys. 11(4), 045013 (2009). [CrossRef]

] to avoid or reduce the pulse broadening due to the chromatic dispersion (CD). But such fibers are actually used in backbone (core) networks for very long-distance transmission (>1000 km) in the existing optical telecommunication infrastructure. Considering the present technical status of the QKD system, a realistic target at the first step of the QKD system should be the realization of the QKD networks over metro/access networks in which the standard SMFs are commonly installed without dispersion management. For this purpose the evaluation in the transmission performance over the standard SMF infrastructure is strongly desired.

Different from the time-bin entanglement protocol [2

2. T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors,” Opt. Express 15(21), 13957–13964 (2007). [CrossRef] [PubMed]

, 4

4. Q. Zhang, H. Takesue, S. W. Nam, C. Langrock, X. Xie, B. Baek, M. M. Fejer, and Y. Yamamoto, “Distribution of time-energy entanglement over 100 km fiber using superconducting single-photon detectors,” Opt. Express 16(8), 5776–5781 (2008). [CrossRef] [PubMed]

, 5

5. T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over optical fiber,” Opt. Express 16(23), 19118–19126 (2008). [CrossRef] [PubMed]

, 7

7. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]

], the performance of the polarization entanglement is strongly dependent on the state-of-polarization (SOP) of the photon-pairs after the distribution. The SOP of the photon-pairs after the fiber transmission is in general remarkably fluctuated, therefore any polarization control scheme is necessary for actual long-distance distribution [3

3. H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorünser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express 15(12), 7853–7862 (2007). [CrossRef] [PubMed]

, 8

8. A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Lorünser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys. 11(4), 045013 (2009). [CrossRef]

]. In the setup of Fig. 2(a), the change of the SOP in the long SMF reel was almost compensated due to polarization-exchange by the FRM located at the center of the transmission line. This setup quite resembles “Plug-and-Play” system for BB84 protocol [16

16. G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, “Automated plug & play quantum key distribution,” Electron. Lett. 34(22), 2116–2117 (1998). [CrossRef]

], but is maybe not suitable to actual system of the distribution of the quantum entanglement. This is because in this setup the photons should roundtrip between two distant observers and doubled transmission loss will seriously degrade the transmission performance. Consequently this setup is used only in laboratory for the experimental convenience, but is effective and usable to estimate the performance in the long-distance distribution over the true transmission line. The insertion loss of the OCR and the FRM was approximately 2.2 dB in this study. The transmission loss of the SMF reel was typically 0.21 dB/km.

The setup using the variable optical attenuators is usable to estimate the maximum reach of the distribution when the transmission performance is simply dominated by the optical losses. This setup also almost corresponds to the case of the distribution over the DSFs.

Monitor light coupled to the Sagnac loop of the photon-pair source via a 1:9 coupler was used to monitor the polarization rotation during the fiber transmission and to compensate it by the polarization controllers (PCs).

The signal/idler photons were finally detected by using InGaAs-APD based single photon detectors (Princeton lightwave benchtop receiver PGA-600HSU) (D1, D2). Periodical gate voltages applied to the two APDs were synchronized to the pump pulses. The gate frequency was 40 MHz. The detection efficiencies of both the APDs were estimated to be approximately 20%. The gate width was 1 ns. The dark count rates were approximately 2x10−6 per pulse for both detectors.

3. Experimental entanglement distribution

3.1Distribution over the SMF reels

We investigated the performance of the long-distance distributions by measuring two-photon interference fringes. In these measurements, we fixed the polarizer angle of the signal polarizer (θs), and measured the coincidence counts while rotating the polarizer angle of the idler polarizer (θi). The averaged pump power (Pave) was approximately −2.1 dBm per end facet of the PPLN module (totally + 0.9 dBm for both facets). The pulse peak power was estimated to be + 12.9 dBm from the experimental conditions. This value almost corresponded to the condition in which the mean number of the photon-pair per pulse (μc) was 0.1. While the optimal value of the μc which maximizes the final secure key rate after distillation is slightly changed depending on security scenario, 0.1 of the μc almost corresponds to the optimal value in most cases [17

17. B. Miquel and H. Takesue, “Observation of 1.5μm band entanglement using single photon detectors based on sinusoidally gated InGaAs/InP avalanche photodiodes,” New J. Phys. 11(4), 045006 (2009). [CrossRef]

]. A smaller μc will increase the visibility, and therefore decrease the quantum error rate, in our setup.

The optical phase difference in the optical phase bias compensator (OPBC) [14

14. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]

] of the photon-pair source was adjusted so that the coincidence counts were minimized when θs = + 45° and θi = −45°. This implies that the quantum state used here was adjusted to be 1/2(|Hs|Hi+|Vs|Vi)state. The setting value of the OPBC remained constant during each measurement of the two-photon interference fringe. This value was slightly adjusted again when the SMF reels was changed, because of the residual birefringence of the SMF reels. All the data were raw data without subtracting the accidental counts. We undertook several runs of the measurements at specific conditions in which the coincidence counts were maximized and minimized, i. e., θs = 0° and θi = 0° and 90° in the H/V basis; θs = + 45° and θi = + 45° and −45° in the diagonal basis, to estimate standard deviation and error bars of the measurements.

Figure 3
Fig. 3 Two-photon interference fringes after (a) 0 km (back-to-back), (b) 40 km, and (c) 140 km transmission over the SMF fiber reels. Black closed circles: results of the H/V basis. Red closed circles: results of the diagonal basis. Polarizer angle of the signal polarizer (θs) were 0° (H/V basis) and + 45° (diagonal basis), respectively. The solid curves in the figures are fitting curves assumingcos2(θsθi).
show the coincidence counts as a function of θi at the H/V basis and the diagonal basis (θs = 0° and + 45°, respectively) after the distribution over the SMF reels. Before the fiber transmission (Fig. 3(a)), the visibilities of the fitted curves were estimated to be 91.4 ± 0.5% in the H/V basis (θs = 0°) and 91.2 ± 2.1% in the diagonal basis (θs = + 45°). The peak coincidence counts were approximately 4000 counts/15 seconds for both the H/V basis and the diagonal basis. The single count rate was approximately 5.1x10−4 per pulse and 6.3x10−4 per pulse for the signal photons and the idler photons, respectively.

The ratio between the coincidence count rate and the single count rate for the signal (idler) photons gives the channel loss for the idler (signal) before transmission (see [14

14. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]

] for details). The μc can be also estimated from the single count rate and the channel loss.

From experimental values above, we estimated the channel loss before the transmission to be 19.8 dB (αs) and 18.8 dB (αi), respectively, for the signal photons and the idler photons. These values included the detection efficiencies of the SPDs and the insertion losses of the polarization controllers and the fiber polarizers as well as the transmission losses of the optical filters. Also from these values, the μc was experimentally determined to be 0.096. This value agreed well with the visibilities in the two-photon interferences. The pump rate of the photon-pair source, hence the μc, remained the same during all the distribution experiments hereafter.

Figure 3(b) and 3(c) show the results after the fiber transmission. The visibilities in the two-photon interferences exhibited no significant changes when the distribution length was less than 100 km (50 km x 2), even though the coincidence count rate was decreased corresponding to the increase of the loss. After the 140-km transmission (70 km x 2) (Fig. 3(c)), the visibilities were estimated to be 88.7 ± 4.7% in the H/V basis (θs = 0°) and 88.2 ± 3.9% in the diagonal basis (θs = 45°). The decreases in the visibilities agreed well with the theoretical assumption, as is discussed in detail in Section 3.3. These results indicate that the QKD system consisting of the c-SHG/SPDC-based photon-pair source and the inexpensive InGaAs-APD-based detectors can fully cover the SMF-based metro/access networks, at least in terms of the security of the confidential communications.

In this work, further expanding of the distribution distance was limited by the temporal broadening of the wave packet of the photon-pairs due to the CD. The CD of the SMF in the 1.5-μm band is typically 18 ps/km/nm. The pulse width after the fiber transmission is approximately given by CDΔλL, where Δλ is the spectral bandwidth of the signal/idler photons and L is the SMF length. Since the Δλ was approximately 0.65 nm in this work, the pulse width was broadened to approximately 1.2 ns after the transmission over 100 km of the SMF. This value was comparable to the gate width of the SPD in this work (1 ns), and showed remarkable influence on the performance of the distribution, especially on the coincidence counts. This was discussed in more detail in Section 3.3.

3.2 Distribution over the optical attenuators

Experiments with the variable optical attenuators, instead of the SMF reels, are usable to estimate the final performance of the long-distance distribution if the transmission performance is only limited by the transmission loss without the other transmission impairments such as the CD, the PMD, and the SOP fluctuations.

Figure 4
Fig. 4 Two-photon interference fringes when additional losses were given by the optical attenuators. (a) −8 dB/channel. (b) −18 dB/channel. (c) −25 dB/channel. Black closed circles: results of the H/V basis. Red closed circles: results of the diagonal basis. Polarizer angle of the signal polarizer (θs) were 0° (H/V basis) and + 45° (diagonal basis), respectively. The solid curves in the figures are fitting curves assuming cos2(θsθi).
show the results of the two-photon interference fringes, as a function of single channel loss for the signal/idler photons. We observed clear two-photon interference even after giving 25 dB of the single channel loss (total loss was 50 dB). The visibilities were estimated to be 79.9 ± 7.9% in the H/V basis and 79.4 ± 7.7% in the diagonal basis at 22.5 dB of the single channel loss, whereas they were 74.0 ± 10.7% in the H/V basis and 74.2 ± 9.5%, respectively at 25 dB of the single channel loss. The results indicate that the Bell inequality might be violated by a standard deviation in the case of 22.5 dB of the single channel loss. They also strongly suggest that the violation of the Bell inequality was still retained even with 25 dB of the single channel loss. This indicates that our simple setup consisting of the telecom-compatible optical resources can distribute the quantum entanglement over 250 km of the optical fibers.

3.3 Discussion on the experimental results

Figure 5
Fig. 5 Dependence of the visibilities in the two-photon interference fringes on the single channel loss. Circles: experimental results with the SMF fiber reels. Triangles: experimental results with the optical attenuators. Black solid curve: calculation results using Eq. (1). Black dashed curve: calculation including the pulse broadening due to the CD. Results in Ref [7]. were also shown as gray squares for comparison.
shows the summary of the visibilities in the two-photon interference fringes as a function of the single channel loss. The results using the SMF reels are shown as open circles, whereas those using the optical attenuators are shown as open triangles.

Assuming Poisson distribution as photon-number statics, the visibility in the two-photon interference of the polarization entanglement, V, is given by [18

18. H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express 16(8), 5721–5727 (2008). [CrossRef] [PubMed]

],
V=μcαsαiηsηi2μcαsαiηsηi2+2(μcαsηs2+sns+ds)(μcαiηi2+sni+di)
(1)
where μc, αx, ηx, and dx are the mean number of photon-pairs per pulse, the transmittance for channel x before the transmission, the transmission loss for channel x, and the dark count rate for channel x, with x = s (signal) or i (idler), respectively. snx (x = s, i) expresses the noise photons such as the Raman scattering, except for multi-photon pair-generation inherent to the SPDC. If the noise photons simply originate from the photon-pair source, the snx is simply given in a form of μnxαxηx.

Solid curve in Fig. 5 shows the calculation from Eq. (1) using the experimental parameters given in the earlier sections. Here the snx was ignored. The experimental results agreed well with theoretical values. This implies that in the c-SHG/SPDC-based photon-pair source the noise photons such as the Raman scattering showed negligible influence on the performance of the long-distance distribution and that the theoretically expected performance was well realized.

The results imply both theoretically and experimentally that the quantum entanglement in this work could violate the Bell inequality (V>70.7%) even when the single channel loss was 25 dB. In terms of the secure communication, theoretical assumption indicates that the final distilled secret keys can be obtained if the quantum error rate is below approximately 11.4% [17

17. B. Miquel and H. Takesue, “Observation of 1.5μm band entanglement using single photon detectors based on sinusoidally gated InGaAs/InP avalanche photodiodes,” New J. Phys. 11(4), 045006 (2009). [CrossRef]

]. The error rate corresponds to approximately 77.2% of the visibility. Our results also show that the secure communication is possible over 225 km of the SMF transmission lines (22.5 dB in the single channel loss).

In Fig. 5, the results in Ref [7

7. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]

] are also shown as gray squares for comparison. Our results exhibited better values than those in Ref [7

7. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]

] both theoretically and experimentally. While the differences of course reflected the differences in the experimental setup (detection efficiencies, losses, and etc.), we can point out that they also originate from the fundamental predominance of the polarization-entanglement over the time-bin entanglement.

In the time-bin entanglement, the “true” coincidence count rate becomes half of that of the polarization-entanglement in principle, while the accidental count rate is the same, if the μc is the same. This implies that the visibility is worse in the time-bin entanglement than in the polarization entanglement.

Figure 6
Fig. 6 Dependence of the coincidence count rates on the single channel loss. Black closed circles: experimental results with the SMF fiber reels. Red closed circles: experimental results with the optical attenuators. Solid curve: calculation results only considering optical losses. Dashed curve: calculation results considering both the optical losses and the pulse broadening due to the chromatic dispersion (CD) of the SMF.
shows the summary of the coincidence count rates at the matched time slot. The coincidence count rate at the matched time slot is given by,
μcαsαiηsηi2+(μcαsηs2+ds)(μcαiηi2+di)
(2)
when neglecting the noise photons (snx).

The results using the optical attenuators agreed well with the theoretical curve shown as the black thin curve. In contrast the results using the SMF reels showed smaller coincidence count rates as the loss per channel, therefore the transmission distance, increased.

Taking into account the pulse broadening due to the CD after the fiber transmission, the channel loss ηx should be expressed as,
ηx=η(0)xptr(t)g(t)dtptr(t)dt
(3)
where η(0),x is transmission loss of the optical fibers, ptr(t) is the pulse waveform after the fiber transmission, and g(t) is the gate waveform of the SPD. When the pulse width after the fiber transmission is much shorter than the gate width of the SPD, ptr(t)g(t)dtptr(t)dt and the channel loss is simply given by the transmission loss, η(0),x.

Dashed curves in Fig. 6 show the calculation results including the effect of the pulse broadening. The calculation results agreed well with the experimental ones in the SMF reels.

In the true transmission lines in the fields, the polarization-mode dispersion (PMD) of the optical fibers should be another vital parameter that determines the maximum reach of the distribution. The PMD induces remarkable decoherence and would give the final limit of the possible distribution distance, even when the CD, the SOP fluctuation, and the other transmission impairments are perfectly controlled. The effect of the PMD has been discussed in some preceding papers including Ref [3

3. H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorünser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express 15(12), 7853–7862 (2007). [CrossRef] [PubMed]

, 8

8. A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Lorünser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys. 11(4), 045013 (2009). [CrossRef]

]. The PMD value is known to range 0.2 ps/km to 1 ps/km for installed old fibers and is improved to less than 0.1 ps/km in recent fibers. Considering this, to speak properly, the PMD effect might affect to some degrees the performance of the entanglement distribution, especially for the 140-km transmission, over “true” transmission lines, since the coherent time of the photon-pairs was estimated to be approximately 6 ps from the filter bandwidth (0.6 nm) in this work. A simple and promising way to relax the PMD issue is narrowing the bandwidth of the optical filters to extract the photon-pairs, as is the case of the relaxation of the pulse broadening due to the CD. Typical bandwidth of the arrayed waveguide filter (AWG) commonly used in WDM systems in classical communications is 0.2 nm, and use of this will improve the tolerance to the PMD issue, by three times in comparison with the setup in this paper.

4. Conclusion

In summary we have reported experimental investigation in the transmission performance over standard SMFs of the polarization-entangled photon-pairs generated by the c-SHG/SPDC in a PPLN ridge-waveguide device. Clear two-photon interference fringes have been observed after the distribution of 140 km of the SMF fiber spools with approximately 88% of the visibilities. The degradation in the visibility was less than 3% even after the fiber transmission. This revealed that the QKD systems with this entangled photon-pair source could fully cover metro/access networks consisting of the standard SMFs without dispersion management. Demonstration using the optical attenuators revealed that the quantum entanglement could remain even at 50 dB of the transmission loss with the violation of the Bell inequality and also that secure communication was possible even at 45 dB of the transmission loss. These results indicate that the c-SHG/SPDC-based photon-pair source can offer the long-distance QKD networks over the preinstalled telecom infrastructure using the SMFs.

References and links

1.

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,” post deadline paper, Optical Fiber Communications Conference (OFC’2006), paper PDP35.

2.

T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors,” Opt. Express 15(21), 13957–13964 (2007). [CrossRef] [PubMed]

3.

H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorünser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express 15(12), 7853–7862 (2007). [CrossRef] [PubMed]

4.

Q. Zhang, H. Takesue, S. W. Nam, C. Langrock, X. Xie, B. Baek, M. M. Fejer, and Y. Yamamoto, “Distribution of time-energy entanglement over 100 km fiber using superconducting single-photon detectors,” Opt. Express 16(8), 5776–5781 (2008). [CrossRef] [PubMed]

5.

T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over optical fiber,” Opt. Express 16(23), 19118–19126 (2008). [CrossRef] [PubMed]

6.

H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Distribution of polarization-entangled photon pairs produced via spontaneous parametric down-conversion within a local-area fiber network: Theoretical model and experiment,” Opt. Express 16(19), 14512–14523 (2008). [CrossRef] [PubMed]

7.

J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]

8.

A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Lorünser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys. 11(4), 045013 (2009). [CrossRef]

9.

K. J. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city, free-space quantum channel,” Opt. Express 13(1), 202–209 (2005). [CrossRef] [PubMed]

10.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 (2007). [CrossRef]

11.

H. Takesue and K. Inoue, “1.5-microm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13(20), 7832–7839 (2005). [CrossRef] [PubMed]

12.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008). [CrossRef] [PubMed]

13.

M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, and M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO3 waveguide,” Opt. Lett. 35(8), 1239–1241 (2010). [CrossRef] [PubMed]

14.

S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]

15.

S. Arahira, N. Namekata, T. Kishimoto, and S. Inoue, “Experimental studies in generation of high-purity photon-pairs using cascaded χ2 processes in a periodically poled LiNbO3 ridge-waveguide device,” J. Opt. Soc. Am. B 29(3), 434–442 (2012). [CrossRef]

16.

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, “Automated plug & play quantum key distribution,” Electron. Lett. 34(22), 2116–2117 (1998). [CrossRef]

17.

B. Miquel and H. Takesue, “Observation of 1.5μm band entanglement using single photon detectors based on sinusoidally gated InGaAs/InP avalanche photodiodes,” New J. Phys. 11(4), 045006 (2009). [CrossRef]

18.

H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express 16(8), 5721–5727 (2008). [CrossRef] [PubMed]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(270.4180) Quantum optics : Multiphoton processes
(270.5565) Quantum optics : Quantum communications

ToC Category:
Quantum Optics

History
Original Manuscript: May 8, 2012
Revised Manuscript: June 7, 2012
Manuscript Accepted: June 7, 2012
Published: June 22, 2012

Citation
Shin Arahira and Hitoshi Murai, "Experimental investigation in transmission performance of polarization-entangled photon-pairs generated by cascaded χ(2) processes over standard single-mode optical fibers," Opt. Express 20, 15336-15346 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15336


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References

  1. 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,” post deadline paper, Optical Fiber Communications Conference (OFC’2006), paper PDP35.
  2. T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors,” Opt. Express15(21), 13957–13964 (2007). [CrossRef] [PubMed]
  3. H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorünser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express15(12), 7853–7862 (2007). [CrossRef] [PubMed]
  4. Q. Zhang, H. Takesue, S. W. Nam, C. Langrock, X. Xie, B. Baek, M. M. Fejer, and Y. Yamamoto, “Distribution of time-energy entanglement over 100 km fiber using superconducting single-photon detectors,” Opt. Express16(8), 5776–5781 (2008). [CrossRef] [PubMed]
  5. T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over optical fiber,” Opt. Express16(23), 19118–19126 (2008). [CrossRef] [PubMed]
  6. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Distribution of polarization-entangled photon pairs produced via spontaneous parametric down-conversion within a local-area fiber network: Theoretical model and experiment,” Opt. Express16(19), 14512–14523 (2008). [CrossRef] [PubMed]
  7. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express17(14), 11440–11449 (2009). [CrossRef] [PubMed]
  8. A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Lorünser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys.11(4), 045013 (2009). [CrossRef]
  9. K. J. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city, free-space quantum channel,” Opt. Express13(1), 202–209 (2005). [CrossRef] [PubMed]
  10. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3(7), 481–486 (2007). [CrossRef]
  11. H. Takesue and K. Inoue, “1.5-microm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express13(20), 7832–7839 (2005). [CrossRef] [PubMed]
  12. K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express16(25), 20368–20373 (2008). [CrossRef] [PubMed]
  13. M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, and M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO3 waveguide,” Opt. Lett.35(8), 1239–1241 (2010). [CrossRef] [PubMed]
  14. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express19(17), 16032–16043 (2011). [CrossRef] [PubMed]
  15. S. Arahira, N. Namekata, T. Kishimoto, and S. Inoue, “Experimental studies in generation of high-purity photon-pairs using cascaded χ2 processes in a periodically poled LiNbO3 ridge-waveguide device,” J. Opt. Soc. Am. B29(3), 434–442 (2012). [CrossRef]
  16. G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, “Automated plug & play quantum key distribution,” Electron. Lett.34(22), 2116–2117 (1998). [CrossRef]
  17. B. Miquel and H. Takesue, “Observation of 1.5μm band entanglement using single photon detectors based on sinusoidally gated InGaAs/InP avalanche photodiodes,” New J. Phys.11(4), 045006 (2009). [CrossRef]
  18. H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express16(8), 5721–5727 (2008). [CrossRef] [PubMed]

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