Abstract

While the most direct method to increase the brightness of a type-I entanglement source is to increase the collected solid angle of the down-conversion, this leads to effective decoherence caused by an angle-dependent phase shift. Using specially designed compensation crystals, we have reversed this effect and created the brightest source of entangled photons to date, over two million measured pairs per second, recorded while measuring the largest reported violation of Bell’s inequality (1239 σ).

© 2005 Optical Society of America

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Corrections

G. M. Akselrod, J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, "Phase-compensated ultra-bright source of entangled photons: erratum," Opt. Express 15, 5260-5261 (2007)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-15-8-5260

References

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
  2. R. Raussendorf and H. J. Briegel, �??A One-Way Quantum Computer,�?? Phys. Rev. Lett. 86, 5188�??5191 (2001).
    [CrossRef] [PubMed]
  3. C. H. Bennett, G. Brassard, C. Crépeaux, R. Jozsa, A. Peres, and W. K. Wooters, �??Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,�?? Phys. Rev. Lett. 70, 1895�??1899 (1993).
    [CrossRef] [PubMed]
  4. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, �??Experimental quantum teleportation,�?? Nature 390, 575�??579 (1997).
    [CrossRef]
  5. D. Boschi, S. Branca, F. de Martini, L. Hardy, and S. Popescu, �??Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,�?? Phys. Rev. Lett. 80, 1121�??1125 (1998).
    [CrossRef]
  6. J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, �??Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation,�?? Phys. Rev. Lett. 86, 4435�??4438 (2001).
    [CrossRef] [PubMed]
  7. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, �??New high-intensity source of polarization-entangled photon pairs,�?? Phys. Rev. Lett. 75, 4337�??4341 (1995).
    [CrossRef] [PubMed]
  8. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, �??Ultrabright source of polarization-entangled photons,�?? Phys. Rev. A 60, R773�??R776 (1999).
    [CrossRef]
  9. C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, �??High-efficiency entangled photon pair collection in type-II parametric fluorescence,�?? Phys. Rev. A 64(023802) (2001).
    [CrossRef]
  10. Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, and Y. Shih, �??Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,�?? Phys. Rev. A 63(062301) (2001).
    [CrossRef]
  11. Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, �??Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses,�?? Phys. Rev. A 66(033816) (2002).
    [CrossRef]
  12. G. Bitton,W. P. Grice, J. Moreau, and L. Zhang, �??Cascaded ultrabright source of polarization-entangled photons,�?? Phys. Rev. A 65(063805) (2002).
    [CrossRef]
  13. M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, �??Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,�?? Phys. Rev. A 69(041801) (2003).
  14. B.-S. Shi and A. Tomita, �??Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,�?? Phys. Rev. A 69(013803) (2004).
    [CrossRef]
  15. M. Fiorentino, C. E. Kuklewicz, and F. N. C. Wong, �??Source of polarization entanglement in a single periodically poled KTiOPO4,�?? Opt. Express 13, 127 (2005). URL <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-127.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-127</a>
    [CrossRef] [PubMed]
  16. P. G. Kwiat, P. H. Eberhard, A. M. Steinberg, and R. Y. Chiao, �??Proposal for a loophole-free Bell inequality experiment,�?? Phys. Rev. A 49, 3209�??3220 (1994).
    [CrossRef] [PubMed]
  17. F. N. C. Wong, private communication (2005).
  18. A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, �??Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,�?? Phys. Rev. A 53, 4360�??4371 (1996).
    [CrossRef] [PubMed]
  19. N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, �??Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,�?? Opt. Eng. 39, 1016�??1024 (2000).
    [CrossRef]
  20. S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, �??On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,�?? New Journal of Physics 6, 87 (2004).
    [CrossRef]
  21. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, Berlin, 1999).
  22. A. Migdall, �??Polarization directions of noncollinear phase-matched optical parametric downconversion output,�?? J. Opt. Soc. Am. B 14, 1093�??1098 (1997).
    [CrossRef]
  23. We have not studied the effects of phase compensation in conjunction with single-mode collection optics. However, it is the untested conjecture of the authors that rather than causing decoherence, angle-dependent phases may cause the coupling efficiency of the |HH> and |VV> terms to vary independently. The compensators presented here would cause them to vary jointly, with specially designed compensators allowing optimal and balanced coupling.
  24. A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, �??Nonmaximally Entangled States: Production, Characterization, and Utilization,�?? Phys. Rev. Lett. 83, 3103 (1999).
    [CrossRef]
  25. J. B. Altepeter, D. F. V. James, and P. G. Kwiat, Quantum State Estimation, vol. 649 of Lecture Notes in Physics (Springer, Berlin, 2004).
  26. This technique, proposed and first implemented by A. G. White (Univ. of Queensland, Australia), attempts to eliminate some of the loss due to high reflectivity (40%) spectral filters. By placing a QWP between the measurement PBS and the filter-detector assemblies, any reflected light will travel through the quarter waveplate, be reflected at the PBS, be retroreflected by a mirror, and travel back through the PBS toward the filter-detector assembly for a second chance at detection. The effective transmission of the filter is thus increased from 0.6 to ~ (0.6+0.4�?0.6) = 0.84
  27. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, �??Proposed Experiment to Test Local Hidden-Variable Theories,�?? Phys. Rev. Lett. 23, 880 (1969).
    [CrossRef]

J. Opt. Soc. Am. B (1)

Lecture Notes in Physics (1)

J. B. Altepeter, D. F. V. James, and P. G. Kwiat, Quantum State Estimation, vol. 649 of Lecture Notes in Physics (Springer, Berlin, 2004).

Nature (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, �??Experimental quantum teleportation,�?? Nature 390, 575�??579 (1997).
[CrossRef]

New Journal of Physics 6 (1)

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, �??On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,�?? New Journal of Physics 6, 87 (2004).
[CrossRef]

Opt. Eng. (1)

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, �??Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,�?? Opt. Eng. 39, 1016�??1024 (2000).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (9)

P. G. Kwiat, P. H. Eberhard, A. M. Steinberg, and R. Y. Chiao, �??Proposal for a loophole-free Bell inequality experiment,�?? Phys. Rev. A 49, 3209�??3220 (1994).
[CrossRef] [PubMed]

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, �??Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,�?? Phys. Rev. A 53, 4360�??4371 (1996).
[CrossRef] [PubMed]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, �??Ultrabright source of polarization-entangled photons,�?? Phys. Rev. A 60, R773�??R776 (1999).
[CrossRef]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, �??High-efficiency entangled photon pair collection in type-II parametric fluorescence,�?? Phys. Rev. A 64(023802) (2001).
[CrossRef]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, and Y. Shih, �??Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion,�?? Phys. Rev. A 63(062301) (2001).
[CrossRef]

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, �??Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses,�?? Phys. Rev. A 66(033816) (2002).
[CrossRef]

G. Bitton,W. P. Grice, J. Moreau, and L. Zhang, �??Cascaded ultrabright source of polarization-entangled photons,�?? Phys. Rev. A 65(063805) (2002).
[CrossRef]

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, �??Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,�?? Phys. Rev. A 69(041801) (2003).

B.-S. Shi and A. Tomita, �??Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,�?? Phys. Rev. A 69(013803) (2004).
[CrossRef]

Phys. Rev. Lett. (7)

D. Boschi, S. Branca, F. de Martini, L. Hardy, and S. Popescu, �??Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,�?? Phys. Rev. Lett. 80, 1121�??1125 (1998).
[CrossRef]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, �??Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation,�?? Phys. Rev. Lett. 86, 4435�??4438 (2001).
[CrossRef] [PubMed]

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

R. Raussendorf and H. J. Briegel, �??A One-Way Quantum Computer,�?? Phys. Rev. Lett. 86, 5188�??5191 (2001).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeaux, R. Jozsa, A. Peres, and W. K. Wooters, �??Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,�?? Phys. Rev. Lett. 70, 1895�??1899 (1993).
[CrossRef] [PubMed]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, �??Nonmaximally Entangled States: Production, Characterization, and Utilization,�?? Phys. Rev. Lett. 83, 3103 (1999).
[CrossRef]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, �??Proposed Experiment to Test Local Hidden-Variable Theories,�?? Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

Other (5)

This technique, proposed and first implemented by A. G. White (Univ. of Queensland, Australia), attempts to eliminate some of the loss due to high reflectivity (40%) spectral filters. By placing a QWP between the measurement PBS and the filter-detector assemblies, any reflected light will travel through the quarter waveplate, be reflected at the PBS, be retroreflected by a mirror, and travel back through the PBS toward the filter-detector assembly for a second chance at detection. The effective transmission of the filter is thus increased from 0.6 to ~ (0.6+0.4�?0.6) = 0.84

We have not studied the effects of phase compensation in conjunction with single-mode collection optics. However, it is the untested conjecture of the authors that rather than causing decoherence, angle-dependent phases may cause the coupling efficiency of the |HH> and |VV> terms to vary independently. The compensators presented here would cause them to vary jointly, with specially designed compensators allowing optimal and balanced coupling.

F. N. C. Wong, private communication (2005).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, Berlin, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

Entangled photon source. (a) A 45°-polarized 351-nm pump beam down-converts in two adjacent nonlinear crystals (BBO) into the two-photon state ψ ( ϕ ) = 1 2 ( HH + e i ϕ VV ) . The phase factor ϕ depends on the angle of the down-conversion photons within the crystals, such that the states corresponding to paths 1’ and 2’ are |ψ(1’)〉 and |ψ(2’)〉, respectively. The addition of these states results in effective decoherence. The use of larger collection apertures increases the effect. (b) By placing additional specially designed birefringent crystals into the down-conversion path, this phase variation can be compensated for, largely eliminating the decohering effect of large collection apertures. The quarter waveplate (QWP), half waveplate (HWP), polarizing beam splitter (PBS) combinations in each arm allow projection into any separable polarization basis. A sequence of these projections allows complete tomographic reconstruction of any two-qubit density matrix. Quoted high count rates were collected using 9-mm irises (120 cm from the source) and 25-nm (FWHM) frequency filters.

Fig. 2.
Fig. 2.

Diagram illustrating all relevant vectors, angles, and variables used for calculating angle-dependent phase differences due to birefringent crystals. Arbitrarily polarized light is incident from the left onto a negative uniaxial crystal (e.g., BBO) with its optic axis (Ô) in the plane of the page.

Fig. 3.
Fig. 3.

Theoretical (a-b) and experimental (d-e) plots of the phase difference ϕ as a function of signal direction k̂ α , combined with the predicted (c) and measured (f) density matrices. To match experimentally collected data, the direction k̂ α is represented as a transverse position in space ~ 120 cm from the down-conversion crystals. Here, x = 0,y = 0 corresponds to the central 702-nm down-conversion directions, ~ 3° (6.35 cm) from the pump axis. (a) The phasemap due solely to the down-conversion crystals (each 600-μm thick, 33.9° optic axis, BBO), superimposed with the phasemap due to two BBO compensation crystals, one in each arm, each 245 μm thick and cut with a 33.9° optic axis. The slope of each phasemap is approximately ±14° per mm. (b) The sum of both phasemaps from (a). The flat character indicates that approximately the same entangled state will be present at each position on this plot, corresponding to a high-fidelity state measured using large irises. (c) The theoretically predicted density matrix that would result from a measurement over this flat phase surface, using 1-cm diameter irises. (d) Experimentally measured phase for the uncompensated configuration. Each black dot represents an experimental measurement of this phase, extracted from the result of a full state tomography. The mesh graphically represents these points by linearly connecting nearest neighbors. The phase difference is nearly linear, approximately 17° per millimeter, and varying in the radial direction out from the pump beam axis. (e) The compensated configuration. The surface is very flat, with a maximum slope of less than 3°/mm, and a total phase variation of approximately 25° over a centimeter, a seven-fold improvement over the uncompensated case. (f) The experimentally recorded density matrix (absolute value shown here) describing the ultra-bright entangled state: 1.02 × 106 measured pairs per second, 97.7% fidelity with a maximally entangled state.

Fig. 4.
Fig. 4.

The effects of iris size on the fidelity and rate of measured entangled states. Note that for this measurement, the diameters of both irises are adjusted, with each positioned in the plane normal to the pump direction and 120 cm from the down-conversion crystals. Shown here are both the standard (uncompensated) and compensated configurations. The y-axis on the right describes the detected source intensity (for a 280-mW pump and 25-nm filters), quadratically increasing as a function of iris size.

Equations (14)

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ψ o asin ( sin ( α ) n o ) ,
ψ e asin ( sin ( α ) n e ( θ ) ) ,
n e ( θ ) = n o 1 + tan 2 θ 1 + ( n o n e tan θ ) 2 .
ρ = ( θ atan [ n o 2 n e 2 tan θ ] ) sgn ( n o n e ) .
Φ o = d cos ( ψ o ) n o ( S ̂ o · κ ̂ o ) 2 π λ = d cos ( ψ o ) n o 2 π λ ,
Φ e = d cos ( β ) n e ( θ ) ( S ̂ e · κ ̂ e ) 2 π λ ,
Φ Δ = 2 π λ Δ = 2 π λ ( d cos ( ψ o ) S ̂ o · k ̂ α · d cos ( β ) S ̂ e · k ̂ α ) .
ϕ dc ( k ̂ α ) = 2 ( Φ dc , e + Φ dc , Δ ) ,
ψ k ̂ α = 1 2 ( HH + e i 2 ( Φ dc , e + Φ dc , Δ ) VV ) .
ψ Iris = Iris ψ k ̂ α k ̂ α d k ̂ α .
ρ = Iris ψ k ̂ α ψ k ̂ α d k ̂ α .
ϕ c ( k ̂ α ) = 2 ( Φ c , o Φ c , e Φ c , Δ ) ,
ψ comp , k ̂ α = 1 2 ( HH + e i ( ϕ dc , + ϕ c ) VV ) .
F ( ψ , ρ ) ψ ρ ψ ,

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