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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 23153–23159
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Three-color Sagnac source of polarization-entangled photon pairs

Michael Hentschel, Hannes Hübel, Andreas Poppe, and Anton Zeilinger  »View Author Affiliations


Optics Express, Vol. 17, Issue 25, pp. 23153-23159 (2009)
http://dx.doi.org/10.1364/OE.17.023153


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Abstract

We demonstrate a compact and stable source of polarization-entangled pairs of photons, one at 810 nm wavelength for high detection efficiency and the other at 1550 nm for long-distance fiber communication networks. Due to a novel Sagnac-based design of the interferometer no active stabilization is needed. Using only one 30 mm ppKTP bulk crystal the source produces photons with a spectral brightness of 1.13 × 106 pairs/s/mW/THz with an entanglement fidelity of 98.2%. Both photons are single-mode fiber coupled and ready to be used in quantum key distribution (QKD) or transmission of photonic quantum states over large distances.

© 2009 OSA

1. Introduction

Our choice of asymmetric SPDC with the signal wavelength close to the visible and the idler in the telecom region comes from the particular demands of real-world applications. In the case of QKD, the system should operate with optical fibers and also deliver a high key rate. Clearly, designs with both photons below 1μm, like standard BBO sources, are not compatible with the telecom infrastructure, and sources where both signal and idler photons are at telecom wavelengths will not achieve high rates. The latter comes from the low detection efficiencies (~15%) and high noise figures of InGaAs-avalanche photo diodes (APDs) employed in the infrared. Single photons around 800 nm however can be detected with efficiencies of up to 50% with far lower background noise using Si-APDs. Hence asymmetric SPDC sources, first demonstrated in 2000 [5

5. G. Ribordy, J. Brendel, J. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63(1), 012309 ( 2000). [CrossRef]

], combine the high detection efficiency in one arm (locally) with the low loss transmission in optical fibers for the other arm. As long as the detection problem in the infrared is not solved, asymmetric setups will be needed for applications requiring high coincidence rates and telecom compatibility.

A recent QKD experiment [6

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

], based on a polarization-entangled asymmetric SPDC source, showed that such systems suffer from chromatic dispersion in the optical fiber. Since in that experiment the idler bandwidth was filtered to only around 3.6 nm, chromatic dispersion broadened the coincidence peak after 25 km of standard fiber to ~1.6 ns, which is comparable to the typical gate width of an InGaAs-APD. For longer fiber distances either counts will be lost or a larger gate width will lead to higher errors. Asymmetric SPDC source have therefore to be designed to yield a narrow bandwidth minimizing dispersion effects.

2. Design considerations

The photon flux and bandwidth generated and collected by the optical fibers inherently depend on design parameters such as crystal length, geometry of pump focusing, and fiber coupling arrangement. For collinear down conversion the photon emission occurs in a manifold of concentric cones, fulfilling momentum and energy conservation by wavelength pairs. Ultimately, for one set of wavelengths on-axis emission is observed exhibiting a strong overlap with the fundamental Gaussian mode, which can be efficiently coupled into single-mode optical fibers. Hence, proper design of the crystal length and coupling geometry is equivalent to frequency filtering [7

7. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72(6), 062301 ( 2005). [CrossRef]

] and may obviate the customary use of lossy band-pass filters. As derived in [7

7. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72(6), 062301 ( 2005). [CrossRef]

] the intrinsic bandwidth for a certain emission angle (spatially filtered solely by single-mode fiber coupling) scales as Δλ~1/L. Furthermore, the authors of [7

7. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72(6), 062301 ( 2005). [CrossRef]

] conclude that, given optimal focusing conditions, the pair production rate also benefits from the crystal length and scales as R~L. Hence, the spectral brightness B, a commonly used benchmark parameter for entangled photon sources, defined as photon pair number per unit of time [s], pump power [mW] and bandwidth [THz] relates to the crystal length as B~LL.

The Sagnac-type design (Fig. 1
Fig. 1 Principle of the Sagnac interferometer. Depending on the polarization of the entering pump photon (green) the loop is passed in either clockwise (a) or counterclockwise (b) direction. The pump photons are transformed into signal (red) and idler (purple) by SPDC. The pump or the signal and idler photons are polarization flipped in cases a and b, respectively.
) has proved to be very successful in incorporating long crystals in SPDC sources producing entanglement. So far those sources were however limited to generation of (near) degenerate pairs of photons [9

9. 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]

]. The reason stems from the difficulty to design a Sagnac loop capable of accepting a broad range of wavelengths as it is necessary for asymmetric SPDC. In particular the polarizing beamsplitter and the polarization flip in one arm have to work for all wavelengths present in the loop. In near degenerate setups only two wavelengths have to be matched, namely the pump wavelength and the signal/idler wavelength. It is therefore possible to use special dual beamsplitters and dual half-waveplates which are readily available from stock. Contrarily, in a three color Sagnac loop, needed for asymmetric SPDC, the choice of suitable broadband elements is limited and very costly.

A Sagnac-type source for entanglement at asymmetric wavelengths was recently reported [10

10. S. Sauge, M. Swillo, M. Tengner, and A. Karlsson, “A single-crystal source of path-polarization entangled photons at non-degenerate wavelengths,” Opt. Express 16(13), 9701–9707 ( 2008). [CrossRef] [PubMed]

], which worked around this problem by unfolding the Sagnac loop into two parts. Pump light (532 nm) and idler (1550 nm) traveled in the first loop, whereas the signal (810 nm) traveled in the second loop. This design loosened the constrictions on triple-wavelength components but lead to the loss of the inherent phase stability of the Sagnac interferometer. Since the two loops were spatially separated their relative phase was no longer constant and an active phase stabilization with nano-positioning devices had to be introduced.

3. Source of polarization-entangled photons

To generate pairs of polarization-entangled photons by means of SPDC a Sagnac-type interferometer has been built. In this concept the two interfering modes occupy physically the same optical paths, but are passed in opposite directions. Therefore, in case of operation at a single wavelength only, exact phase compensation results. This is also valid for the free-space parts in our multi-wavelength scenario, due to the absence of material dispersion (neglecting the dispersion of air). However, inside optical elements mechanical drifts as well as temperature changes are self-compensated to first order approximation only, which shall be derived in the following:

The entangled two-photon state can be written as
|φ=12(|H|H+ei(Φ0+ΔΦ)|V|V),
(1)
where Φ0 is the global phase (e.g. zero for a |ϕ +〉 state) and ΔΦ accounts for a (temperature induced) phase drift consisting of contributions of the three light fields involved:

ΔΦ=Δϕs+ΔϕiΔϕp.
(2)

The negative sign arises from the counter-propagating direction of the pump component with respect to signal and idler and is the manifestation of the self-compensating effect. Each term in Eq. (2) can be written as
Δϕx=2πLλx(dnxdT+nxα)ΔT,
(3)
where x denotes signal, idler and pump, respectively, λ is the wavelength, n and L are the refractive index and the length of the material, α is the thermal expansion coefficient, and ΔT is the temperature change. The material parameters shown in Table 1

Table 1. Refractive index, its temperature dependence and thermal expansion coefficient of BK7-glass.

table-icon
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are obtained from the temperature dependent Sellmeier equations [11

11. Schott optical glass catalogue.

]. Considering for instance the warming of a single optical element within the loop (e.g. 8 mm of BK7-glass) by ΔT = 1 K we end up with a total phase shift of only ΔΦ = 0.019 π. Hence, sufficient phase stability is ensured, even in our highly non-degenerate case. In comparison, a Mach-Zehnder-type interferometer providing no compensation would introduce a phase shift (given by Eq. (3) alone) of ΔΦ = Δφ ≈0.36 π for the same conditions, and hence rendering the quantum state unusable for long term applications.

In our setup several optimizations concerning three-color operation, stability and space requirements have been put in place. All the optics are designed for broadband operation by means of total internal reflection (or grazing incidence in case of one silver mirror), thus the interferometer is potentially suitable for all wavelengths in the range of 400 nm - 2 μm. All optical elements are free from angular dispersion ensuring ease of alignment for both signal and idler beams. The two round-trip paths are balanced in terms of group delay for each of the three wavelengths, providing robust entanglement even for pulsed or low-coherence pump lasers. The polarization and wavelength dependent phase shift induced by the totally reflecting elements is static and can be included in the global phase (Φ0 in Eq. (1)). The complete interferometer base has been milled from a solid block of aluminum ensuring mechanical stability and having a footprint of 5 × 5 cm only. Stable operation (in terms of count rates as well as phase) has been observed over several hours and on a day-to-day basis.

The source is pumped by a 532 nm single frequency DPSS-laser (Laser Quantum, Torus). Special care has been taken to remove spurious wavelength components around 808 nm and 1064 nm by means of multiple reflections off dichroic mirrors.

Figure 2
Fig. 2 Schematic of the source: half-wave plate (HWP), quartz wedges (QW), quartz block (QB), focusing lens (L), trichroic mirror (TM), calcite block (CB), Glan-Thompson polarizer (GT), parallel-faced periscope (P1), cross-faced periscope (P2), periodically poled Potassium Titanium Oxide Phosphate crystal (ppKTP), dichroic mirror (DM), fiber couplers (FC1 & FC2). Insert left: principle of operation of the two periscopes. Insert right: 3-dimensional view of the implemented interferometer.
shows the schematic of the optical setup. A half-wave plate is used to adjust the ratio of pump power in the horizontal (H) and vertical (V) polarization direction. The relative phase between the H and V component is controlled with two birefringent quartz wedges, the longitudinal walk-off (group delay between coherent wave packets) of which is undone by an orthogonally oriented block of the same material and approximately the same length. A singlet lens (f = 166 mm) produces a beam waist of ~80 μm 1/e2-diameter precisely at the center of the ppKTP crystal. The two polarization modes are separated with a high extinction ratio (1:105) by a customized Glan-Thompson polarizer avoiding angular dispersion. Again its temporal walk-off is compensated for with a piece of calcite of equal length. The polarization of the vertically polarized beam is flipped by a cross-faced periscope (instead of a half-wave plate usually used), while the horizontally polarized beam is accordingly displaced in height by a parallel-faced periscope (insert in Fig. 1). Hence, the ppKTP crystal, lying on a lower level than the Glan-Thompson polarizer, is pumped from both sides with horizontally polarized light. The crystal is heated to 65°C in order to fulfill type-I phase matching conditions for 532 nm → 810 nm + 1550 nm. Since we work at highly non-degenerate wavelengths the signal and idler modes can be separated by means of their color. Hence, there is no need for two distinctive output modes directly from the source (as in a type-II down conversion scheme [1

1. 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]

,9

9. 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]

]) and the superior type-I nonlinear susceptibility of KTP can be utilized. The generated photon pairs continue their way through the Sagnac loop, one of them being polarization flipped in the cross-faced periscope. Subsequently they are recombined into one beam at the polarizer and reflected off the trichroic mirror. Finally the photons at the two wavelengths are separated by a dichroic mirror and launched into single-mode fibers with appropriate couplers. It should be stressed that both periscopes work purely on a geometrical effect and the polarizer is based on total internal reflection allowing those components to perform over a large spectral range. This fact allows for the Sagnac loop to be operated between 532 and 1550 nm.

4. Performance

The created photon pairs were characterized in detail (Fig. 3
Fig. 3 Setup for efficiency measurement and quantum state tomography. The signal photon at 810 nm is detected by a Si-APD detector. A trigger signal is sent to an InGaAs-APD detector where the appropriately delayed 1550 nm idler photon can be detected. Quarter-wave plates and polarizers in both arms are used for the characterization of the polarization state.
). The signal photons (810 nm) were detected using a free running home-built single-photon counting module incorporating a Si-APD with a quantum efficiency of ~30%. At an average pump power of P = 1 mW in each polarization (H and V) single-count rates of Rs = 600000 s−1 per mode have been measured with a dark count background of Rd = 1000 s−1. The idler photons (1550 nm) were detected with a commercial InGaAs based photon counting module (id Quantique, id201) set to a quantum efficiency of 15%. This detector was gated with a coincidence window of τ = 2.5 ns and triggered from the output of the Si-APD. Coincidence rates of Rc = 9300 s−1 were obtained for each of the two polarizations, giving a coincidence-to-singles ratio of 1.55%. The accidental coincidences were determined to be Ra = 400 s−1 by shifting the trigger off the coincidence peak.

In order to quantify the entanglement of the two-photon state a tomography measurement was carried out. Coincidences at 16 independent settings of polarization for the signal and idler, respectively were measured [12

12. D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 ( 2001). [CrossRef]

]. Thus, the density matrix of the quantum state was reconstructed (Fig. 4
Fig. 4 Real and imaginary part of the reconstructed density matrix of the measured state. Accidental coincidences and dark counts have been subtracted.
) and compared to the theoretical matrix of a |ϕ +〉 state. The analysis yields a fidelity F = 97.5 ± 0.15% (the overlap with the maximally entangled state). The error bar of this result was estimated by performing a 1000 run Monte Carlo simulation of the whole state tomography analysis, with Poissonian noise added to the count statistics in each run. When the background of accidental coincidences was subtracted the fidelity increased to F = 98.2%.

4. Conclusion

We have demonstrated a polarization-entangled photon source at highly non-degenerate wavelengths using a modified Sagnac-type interferometer. To our knowledge this is the first time that such a design was employed for the production of polarization-entanglement at asymmetric wavelengths. Due to the Sagnac-type architecture, a passive self-compensation of phase is achieved. Our setup can make use of a single 30 mm long crystal, thereby reducing the bandwidth of the produced photons to 180 GHz. A tomographic measurement of the entangled state showed a fidelity of F = 97.5% at a detected coincidence rate of 9300 c/s per polarization mode. The source is very compact (5 × 5 cm) and robust making it a promising candidate for fiber based quantum information applications like quantum key distribution.

Acknowledgments

We would like to thank Sven Ramelow for discussions on the components of the polarization flip and Robert Prevedel for supplying invaluable support for the state tomography measurement. This work was supported by the Austrian Science Foundation FWF (TRP-L135 and SFB-1520).

References and links

1.

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]

2.

E. J. Mason, M. A. Albota, F. König, and F. N. Wong, “Efficient generation of tunable photon pairs at 0.8 and 1.6 microm,” Opt. Lett. 27(23), 2115–2117 ( 2002). [CrossRef] [PubMed]

3.

S. M. Spillane, M. Fiorentino, and R. G. Beausoleil, “Spontaneous parametric down conversion in a nanophotonic waveguide,” Opt. Express 15(14), 8770–8780 ( 2007). [CrossRef] [PubMed]

4.

S. Zhang, J. Yao, W. Liu, Z. Huang, J. Wang, Y. Li, C. Tu, and F. Lu, “Second harmonic generation of periodically poled potassium titanyl phosphate waveguide using femtosecond laser pulses,” Opt. Express 16(18), 14180–14185 ( 2008). [CrossRef] [PubMed]

5.

G. Ribordy, J. Brendel, J. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63(1), 012309 ( 2000). [CrossRef]

6.

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

7.

D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72(6), 062301 ( 2005). [CrossRef]

8.

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]

9.

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]

10.

S. Sauge, M. Swillo, M. Tengner, and A. Karlsson, “A single-crystal source of path-polarization entangled photons at non-degenerate wavelengths,” Opt. Express 16(13), 9701–9707 ( 2008). [CrossRef] [PubMed]

11.

Schott optical glass catalogue.

12.

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 ( 2001). [CrossRef]

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5565) Quantum optics : Quantum communications
(270.5568) Quantum optics : Quantum cryptography

ToC Category:
Quantum Optics

History
Original Manuscript: October 30, 2009
Revised Manuscript: November 25, 2009
Manuscript Accepted: November 27, 2009
Published: December 2, 2009

Citation
Michael Hentschel, Hannes Hübel, Andreas Poppe, and Anton Zeilinger, "Three-color Sagnac source of polarization-entangled photon pairs," Opt. Express 17, 23153-23159 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23153


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References

  1. 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]
  2. E. J. Mason, M. A. Albota, F. König, and F. N. Wong, “Efficient generation of tunable photon pairs at 0.8 and 1.6 microm,” Opt. Lett. 27(23), 2115–2117 (2002). [CrossRef] [PubMed]
  3. S. M. Spillane, M. Fiorentino, and R. G. Beausoleil, “Spontaneous parametric down conversion in a nanophotonic waveguide,” Opt. Express 15(14), 8770–8780 (2007). [CrossRef] [PubMed]
  4. S. Zhang, J. Yao, W. Liu, Z. Huang, J. Wang, Y. Li, C. Tu, and F. Lu, “Second harmonic generation of periodically poled potassium titanyl phosphate waveguide using femtosecond laser pulses,” Opt. Express 16(18), 14180–14185 (2008). [CrossRef] [PubMed]
  5. G. Ribordy, J. Brendel, J. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63(1), 012309 (2000). [CrossRef]
  6. A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Lorünser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “Fully automated entanglement-based quantum cryptography system for telecom fiber networks,” N. J. Phys. 11(4), 045013 (2009). [CrossRef]
  7. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72(6), 062301 (2005). [CrossRef]
  8. 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]
  9. 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]
  10. S. Sauge, M. Swillo, M. Tengner, and A. Karlsson, “A single-crystal source of path-polarization entangled photons at non-degenerate wavelengths,” Opt. Express 16(13), 9701–9707 (2008). [CrossRef] [PubMed]
  11. Schott optical glass catalogue.
  12. D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001). [CrossRef]

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