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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 6 — Mar. 15, 2010
  • pp: 5957–5963
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Bragg-grating-enhanced narrowband spontaneous parametric downconversion

Li Yan, Lijun Ma, and Xiao Tang  »View Author Affiliations


Optics Express, Vol. 18, Issue 6, pp. 5957-5963 (2010)
http://dx.doi.org/10.1364/OE.18.005957


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Abstract

We propose a new method to narrow the line width of entangled photons generated from spontaneous parametric downconversion (SPDC). The single structure device incorporates an internal Bragg grating onto a nonlinear optical waveguide. We study theoretically the spectral characteristics of SPDC under two Bragg grating structures. We show that using the Bragg grating with a midway π-phase shifter, it is a promising way to generate narrow-line (~GHz to sub-GHz) entangled photons.

© 2010 OSA

1. Introduction

Quantum information science and technology open up a fascinating future for the research, development and application in information technologies. Quantum communication is one of its most important and practical applications. Entangled photon pair sources are necessary for quantum communication systems, such as quantum key distribution [1

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

], quantum teleportation [2

2. D. Bouwmeester, J. W. Pan, K. Mattele, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997). [CrossRef]

4

4. J. Yang, X. Bao, H. Zhang, S. Chen, C. Peng, Z. Chen, and J. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80(4), 042321 (2009). [CrossRef]

], entanglement swapping [5

5. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental nonlocality proof of quantum teleportation and entanglement swapping,” Phys. Rev. Lett. 88, 017903 (1998).

9

9. P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “ High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801(R) (2010). [CrossRef]

], and quantum repeater [10

10. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef] [PubMed]

]. In an entanglement-based quantum communication system, a photon source with broad line width limits the fiber transmission distance due to the dispersion effect in the fiber. In the case of time-bin entanglement, the impurity of the entanglement is greatly degraded, which becomes a limitation for high data rate. Thus an entangled photon source with narrow line width is crucial for high-speed long-distance quantum communication systems [11

11. G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15(20), 12769–12776 (2007). [CrossRef] [PubMed]

13

13. T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide,” Opt. Express 17(14), 12019–12030 (2009). [CrossRef] [PubMed]

].

For distance longer than ~100 km, it is necessary to use quantum repeaters, which are formed mainly by an entangled photon source for teleporting long distance and a quantum memory for storing of quantum information. With regard to quantum memory, an atomic ensembles or rare earth ions in solids are used to store quantum information carried by single photons. In this approach, non-degenerate entangled photon pairs are needed to fulfill the purpose: one wavelength is in the communication band for long distance transmission, and the other matches the transition line of the quantum memory. The line width of the photon sources should be comparable to the transition line width of the memory, which was a few MHz in early studies [10

10. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef] [PubMed]

]. Recently, this requirement is relaxed to the GHz range by using atomic frequency combs [14

14. H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008). [CrossRef] [PubMed]

] or Raman type approach [15

15. K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, I. A. Walmsley, and P. Road, “Towards high-speed optical quantum memories,” arXiv:0912.2970v1, 15 Dec (2009).

].

The current mainstream method to generate entangled photons is through a nonlinear optical process called spontaneous parametric down conversion (SPDC) [16

16. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995). [CrossRef] [PubMed]

]. For easy system integration with a low power pump laser, the nonlinear optical crystal is made into a waveguide, and crystal’s polarity is spatially periodically poled, resulting in quasi-phase matching. However, the entangled photons generated by single-pass SPDC from such a nonlinear optical waveguide have relatively broad line width, typically several hundred GHz (or a few nm at communication wavelengths). This kind of entangled photon source is not suitable to be used in above mentioned applications which need a narrow bandwidth. Therefore, reduction of the bandwidth of entangled photons generated by SPDC is important for quantum communication systems. A straight forward way of narrowing the SPDC bandwidth is through passive filtering [17

17. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15(23), 15377–15386 (2007). [CrossRef] [PubMed]

,18

18. O. Kuzucu and F. N. C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77(3), 032314 (2008). [CrossRef]

]. This approach suffers the disadvantage of additional loss of the desired signal and idler photons. Below-threshold optical parametric oscillator is another approach [19

19. Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999). [CrossRef]

25

25. F. Wolfgramm, X. Xing, A. Cerè, A. Predojević, A. M. Steinberg, and M. W. Mitchell, “Bright filter-free source of indistinguishable photon pairs,” Opt. Express 16(22), 18145–18151 (2008). [CrossRef] [PubMed]

]. Although spectral width at specific signal or idler wavelength can be quite narrow, because of the closeness of the resonator longitudinal modes, multiple signal and idler lines exist, and it has bulky and complex configuration.

In this paper, we propose a new method to narrow the line width of entangled photons generated by SPDC. A quasi-phase-matched nonlinear optical crystal waveguide is incorporated with an internal distributed Bragg grating. SPDC with a distributed Bragg reflector (DBR) has been studied previously where it was used as one of the reflectors in an external micro-cavity configuration [26

26. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023825 (2005). [CrossRef]

] or to increase the pump acceptance bandwidth for higher efficiency [27

27. K. Thyagarajan, R. Das, O. Alibart, M. d. Micheli, D. B. Ostrowsky, and S. Tanzilli, “Increased pump acceptance bandwidth in spontaneous parametric downconversion process using Bragg reflection waveguides,” Opt. Express 16(6), 3577–3582 (2008). [CrossRef] [PubMed]

]. Our scheme is to use the single nonlinear crystal waveguide with distributed Bragg grating as the entangled photon source with a reduced spectral line width. This approach, when implemented, has only a single longitudinal mode, and its configuration will be much simple, compact, and robust. We study theoretically the spectral characteristics of SPDC incorporated with internal Bragg grating under finite quasi-phase-matching. Two grating structures are considered. We propose to use a Bragg grating with a midway π-phase shifter for the first time to our knowledge, and we show that it is a promising way to generate narrow-line (~GHz to sub-GHz) entangled photons.

2. Model

The schematic structure of the proposed SPDC with internal distributed Bragg grating is shown in Fig. 1
Fig. 1 Periodically poled nonlinear optical crystal waveguide with Bragg grating. (a) Continuous grating; (b) grating with midway π-phase shifter.
. A Bragg grating is written onto a periodically poled nonlinear optical crystal waveguide. We consider two Bragg grating structures. One has a continuous grating modulation. Another has a half grating period of flat spacer at the middle of the full Bragg grating, which is commonly used in semiconductor distributed feed-backed lasers. Note that fabrication of a distributed Bragg grating on a periodically poled nonlinear optical crystal waveguide is technically practical, as similar technology (fabrication of a continuous Bragg grating on a periodically poled LiNbO3) has been demonstrated for distributed feedback optical parametric oscillation [28

28. A. C. Chiang, Y. Y. Lin, T. D. Wang, Y. C. Huang, and J. T. Shy, “Distributed-feedback optical parametric oscillation by use of a photorefractive grating in periodically poled lithium niobate,” Opt. Lett. 27(20), 1815–1817 (2002). [CrossRef]

]. Fabrication of a Bragg grating with a midway phase shifter should be implementable using a proper grating mask.

κg=μεgωsc4ns,
(15)
κd=μωsωiε0nsnidQE˜p(0)4,
(16)
ΔβG=2βsβG,
(17)
ΔβQ=βpβsβiβQ
(18)

ΔβQ=[(nins)/2ns]ΔβG
(19)

When dispersion is neglected, the group indexes can be approximated by the corresponding refractive indexes. For the second Bragg grating structure, it is equivalently to have a π-phase shift at the midpoint of the full sinusoidal Bragg grating
Δε(z)={εgcosβGz0z<L/2εgcosβGzL/2zL,
(20)
corresponding toκg changing a sign in the second half region.

Note that distributed feedback optical parametric amplification (OPA) and oscillation with a continuous Bragg grating have been studied by the classical theory, in which phase matching among pump, signal and idler waves is assumed and for OPA only the signal wave has input [30

30. Y.-C. Huang and Y.-Y. Lin, “Coupled-wave theory for distributed-feedback optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 21(4), 777–790 (2004). [CrossRef]

]. However, the classical calculation in [30

30. Y.-C. Huang and Y.-Y. Lin, “Coupled-wave theory for distributed-feedback optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 21(4), 777–790 (2004). [CrossRef]

] cannot be used directly to describe the SPDC process. With definite input signal and idler fields Eqs. (12)-(14) describe indeed a classical coherent process. The straight-forwardly calculated spectral characteristic of PDC is sensitive to the phases of the input signal and idler and is in general asymmetrical about the phase-matching center wavelength. SPDC is a quantum mechanical process with both signal and idler photons generated from vacuum. There is no first-order correlation between the signal and idler photons generated from SPDC, and the spectral characteristic is symmetrical (in theory) about the phase-matching center wavelength. In order to use the classical theory, as an approximate approach, to calculate the SPDC spectral characteristic, one needs to treat the equivalent input fields of signal and idler as noises indeed. We take equivalent input fields for the forward signal and idler waves with random phases at z=0 and zero input field for the backward signal wave at z=L. The physical SPDC spectral characteristic is obtained from the ensemble-average over random phases of input signal and idler.

3. Results

As a baseline, Fig. 2
Fig. 2 Transmission and reflection characteristics of two Bragg grating structures. (a) Continuous grating; (b) grating with midway π-phase shifter.
shows the transmission and reflection characteristics of the two Bragg grating structures for the forward and backward signal waves, with grating coupling parameter κgL=3, a reasonable grating coupling strength [30

30. Y.-C. Huang and Y.-Y. Lin, “Coupled-wave theory for distributed-feedback optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 21(4), 777–790 (2004). [CrossRef]

]. The unit of frequency detuning isΔβGL/2. For the continuous Bragg grating, around zero detuning, the signal wave is mostly reflected with a broadband. In contrast, for the Bragg grating structure with a midway π-phase shift, the transmitted signal wave has a sharp peak at zero detuning. The stop-band of the Bragg grating (full widthΔβGL/23π) corresponds to ~20 GHz for a 1-cm LiNbO3 waveguide.

Figure 3
Fig. 3 Signal and idler photon flux densities with and without a Bragg grating. (a) Continuous grating; (b) grating with π-phase shifter.
shows the spectral characteristics of spontaneous optical parametric downconversion with two types of Bragg grating in resonance with the signal wave. As a comparison, the broadband spectral response of parametric downconversion is also shown. For illustration, we take phase-mismatch with a nominal value ΔβQ=0.1ΔβGand pump strength κdL=1.1. The calculated nominal SPDC line width (full widthΔβGL/28π) is about 55 GHz (~0.3 nm at wavelength of 1.3 µm) for a 1-cm nonlinear optical waveguide and refractive index of 2.2 (LiNbO3). The refractive index difference of commonly used nonlinear optical crystals in type-I configuration is about one-order of magnitude smaller, corresponding to an SPDC line width of a few nm for 1-cm length of nonlinear optical waveguide [29

29. L. Ma, O. Slattery, T. Chang, and X. Tang, “Non-degenerated sequential time-bin entanglement generation using periodically poled KTP waveguide,” Opt. Express 17(18), 15799–15807 (2009). [CrossRef] [PubMed]

]. For type-II configuration, the refractive index difference is usually larger than for type-I configuration, and the SPDC line width (with a corresponding larger ΔβQ) is narrower (less than 1 nm).

With an internal continuous Bragg grating (κgL=3, κdL=1.1), within the stop-band of the Bragg grating, most of the signal flux is in the backward direction, while the idler’s flux is also reduced. However, the signal and idler photons are generally still broadband. In contrast, with the Bragg grating structure that has a midway π-phase shift (κgL=3, κdL=0.7), the forward signal and idler waves peak sharply, with comparable high fluxes, at zero detuning. The SPDC line width is about 15 times narrower than the stop-band of the Bragg grating and is less than 1.5 GHz for a 1-cm LiNbO3 waveguide. Note that the reduced SPDC line width is due to the distributed Bragg grating and should be about the same for type-I or type-II nonlinear interactions. With a longer crystal length, the spectral narrowing will be more prominent with line width down into sub-GHz easily.

The narrow-band peak of PDC is reminiscent of spectral resonant characteristics. In the context of quantum nature of SPDC, the resonant characteristics should be understood as a result of the imposition of a constraint on the nonlinear system by the midway π-phase-shifted Bragg grating and consequently forcing the spontaneous parametric downconversion into only a narrow band. As mentioned above, the grating structure with a midway π-phase shift is equivalent to a grating structure that has a midway flat spacer, which can be viewed physically as a micro-cavity of ΛG/2 length and bounded by two Bragg reflectors. The internal-grating-enhanced SPDC contrasts with the external passive filtering in several ways. First, the internal-grating/SPDC is a single structure device, does not suffer loss in principle and result in high spectral density flux for both signal and idler. For passive filtering, besides suffering additional loss, the spectral density of signal or idler does not increase. Furthermore, implementation of narrow-band passive filtering for both signal and idler would need two filters, and matching and maintaining their accurate center wavelengths would be difficult.

4. Summary

We propose a new approach to narrow down the line width of entangled photons, by incorporating a Bragg grating structure with a midway π-phase shifter onto a nonlinear optical crystal waveguide and theoretically study the line widths of signal and idler photons from the SPDC process. From our theoretical calculation, the approach is promising to generate very narrow line width (~GHz to sub-GHz) signal and idler photons via the spontaneous parametric downconversion, an entangled photon source very useful for quantum information and communication applications.

References and links

1.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

2.

D. Bouwmeester, J. W. Pan, K. Mattele, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997). [CrossRef]

3.

O. Landry, J. A. W. van Houwelingen, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation over the Swisscom telecommunication network,” J. Opt. Soc. Am. B 24(2), 398 (2007). [CrossRef]

4.

J. Yang, X. Bao, H. Zhang, S. Chen, C. Peng, Z. Chen, and J. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80(4), 042321 (2009). [CrossRef]

5.

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental nonlocality proof of quantum teleportation and entanglement swapping,” Phys. Rev. Lett. 88, 017903 (1998).

6.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007). [CrossRef]

7.

R. Kaltenbaek, R. Prevedel, M. Aspelmeyer, and A. Zeilinger, “High-fidelity entanglement swapping with fully independent sources,” Phys. Rev. A 79, 040302(R) (2009). [CrossRef]

8.

H. Takesue and B. Miquel, “Entanglement swapping using telecom-band photons generated in fibers,” Opt. Express 17(13), 10748–10756 (2009). [CrossRef] [PubMed]

9.

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “ High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801(R) (2010). [CrossRef]

10.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef] [PubMed]

11.

G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15(20), 12769–12776 (2007). [CrossRef] [PubMed]

12.

A. Martin, V. Cristofori, P. Aboussouan, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Integrated optical source of polarization entangled photons at 1310 nm,” Opt. Express 17(2), 1033–1041 (2009). [CrossRef] [PubMed]

13.

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide,” Opt. Express 17(14), 12019–12030 (2009). [CrossRef] [PubMed]

14.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008). [CrossRef] [PubMed]

15.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, I. A. Walmsley, and P. Road, “Towards high-speed optical quantum memories,” arXiv:0912.2970v1, 15 Dec (2009).

16.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995). [CrossRef] [PubMed]

17.

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15(23), 15377–15386 (2007). [CrossRef] [PubMed]

18.

O. Kuzucu and F. N. C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77(3), 032314 (2008). [CrossRef]

19.

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999). [CrossRef]

20.

Y. J. Lu, R. L. Campbell, and Z. Y. Ou, “Mode-locked two-photon states,” Phys. Rev. Lett. 91(16), 163602 (2003). [CrossRef] [PubMed]

21.

H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70(4), 043804 (2004). [CrossRef]

22.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006). [CrossRef] [PubMed]

23.

J. S. Neergaard-Nielsen, B. M. Nielsen, H. Takahashi, A. I. Vistnes, and E. S. Polzik, “High purity bright single photon source,” Opt. Express 15(13), 7940–7949 (2007). [CrossRef] [PubMed]

24.

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, “Narrow-band single photons from a single-resonant optical parametric oscillator far below threshold,” Appl. Phys. Lett. 91(19), 191104 (2007). [CrossRef]

25.

F. Wolfgramm, X. Xing, A. Cerè, A. Predojević, A. M. Steinberg, and M. W. Mitchell, “Bright filter-free source of indistinguishable photon pairs,” Opt. Express 16(22), 18145–18151 (2008). [CrossRef] [PubMed]

26.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023825 (2005). [CrossRef]

27.

K. Thyagarajan, R. Das, O. Alibart, M. d. Micheli, D. B. Ostrowsky, and S. Tanzilli, “Increased pump acceptance bandwidth in spontaneous parametric downconversion process using Bragg reflection waveguides,” Opt. Express 16(6), 3577–3582 (2008). [CrossRef] [PubMed]

28.

A. C. Chiang, Y. Y. Lin, T. D. Wang, Y. C. Huang, and J. T. Shy, “Distributed-feedback optical parametric oscillation by use of a photorefractive grating in periodically poled lithium niobate,” Opt. Lett. 27(20), 1815–1817 (2002). [CrossRef]

29.

L. Ma, O. Slattery, T. Chang, and X. Tang, “Non-degenerated sequential time-bin entanglement generation using periodically poled KTP waveguide,” Opt. Express 17(18), 15799–15807 (2009). [CrossRef] [PubMed]

30.

Y.-C. Huang and Y.-Y. Lin, “Coupled-wave theory for distributed-feedback optical parametric amplifiers and oscillators,” J. Opt. Soc. Am. B 21(4), 777–790 (2004). [CrossRef]

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(270.5565) Quantum optics : Quantum communications

ToC Category:
Quantum Optics

History
Original Manuscript: December 22, 2009
Revised Manuscript: February 3, 2010
Manuscript Accepted: March 3, 2010
Published: March 10, 2010

Citation
Li Yan, Lijun Ma, and Xiao Tang, "Bragg-grating-enhanced narrowband spontaneous parametric downconversion," Opt. Express 18, 5957-5963 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5957


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References

  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  2. D. Bouwmeester, J. W. Pan, K. Mattele, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997). [CrossRef]
  3. O. Landry, J. A. W. van Houwelingen, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation over the Swisscom telecommunication network,” J. Opt. Soc. Am. B 24(2), 398 (2007). [CrossRef]
  4. J. Yang, X. Bao, H. Zhang, S. Chen, C. Peng, Z. Chen, and J. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80(4), 042321 (2009). [CrossRef]
  5. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental nonlocality proof of quantum teleportation and entanglement swapping,” Phys. Rev. Lett. 88, 017903 (1998).
  6. M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007). [CrossRef]
  7. R. Kaltenbaek, R. Prevedel, M. Aspelmeyer, and A. Zeilinger, “High-fidelity entanglement swapping with fully independent sources,” Phys. Rev. A 79, 040302(R) (2009). [CrossRef]
  8. H. Takesue and B. Miquel, “Entanglement swapping using telecom-band photons generated in fibers,” Opt. Express 17(13), 10748–10756 (2009). [CrossRef] [PubMed]
  9. P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “ High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801(R) (2010). [CrossRef]
  10. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef] [PubMed]
  11. G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15(20), 12769–12776 (2007). [CrossRef] [PubMed]
  12. A. Martin, V. Cristofori, P. Aboussouan, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Integrated optical source of polarization entangled photons at 1310 nm,” Opt. Express 17(2), 1033–1041 (2009). [CrossRef] [PubMed]
  13. T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide,” Opt. Express 17(14), 12019–12030 (2009). [CrossRef] [PubMed]
  14. H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008). [CrossRef] [PubMed]
  15. K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, I. A. Walmsley, and P. Road, “Towards high-speed optical quantum memories,” arXiv:0912.2970v1, 15 Dec (2009).
  16. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995). [CrossRef] [PubMed]
  17. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15(23), 15377–15386 (2007). [CrossRef] [PubMed]
  18. O. Kuzucu and F. N. C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77(3), 032314 (2008). [CrossRef]
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