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Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones

Marco Fiorentino, Christopher E. Kuklewicz, and Franco N. C. Wong

Open Access Open Access

Abstract

We present a simple polarization entanglemenet source based on type-II phase-matched parametric down-conversion in periodically poled KTiOPO4. By use of noncritical phase matching in a noncollinear geometry the single-crystal source emits a cone of polarization-entangled photons. Two beams on opposite sides of the cone are selected for measurements to yield an observed flux of 820 pairs/s per mW of pump power with a two-photon fringe visibility of 96%. With this source we measure a violation of Bell’s inequality of 140 standard deviations in 160 s.

©2005 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Definition of angles δ and ϕ to denote the direction of wave vectors. The axes of reference coincide with the crystal’s principal axes, z is the direction along which the ferroelectric domains are oriented. The pump propagates along x and is polarized along y. For collinear down-conversion signal and idler are polarized along y and z, respectively.

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Fig. 2.
Fig. 2. Plot of phase-matched wavelengths versus external propagation angle δ for signal (solid blue) and idler (dashed red), calculated for ϕ=0. Operating condition: collinear frequency-degenerate signal and idler at δ=0. Green line represents the degenerate wavelength equal to 2λp =797.2 nm.

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Fig. 3.
Fig. 3. Plot of phase-matched wavelengths versus external propagation angle δ for signal (solid blue) and idler (dashed red), calculated for ϕ=0. Operating condition: noncollinear frequency-degenerate signal and idler in two overlapping cones. Green line represents the degenerate wavelength equal to 2λp =797.2 nm.

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Fig. 4.
Fig. 4. External propagation angles for degenerate down-converted signal (λs =2λp =797.2 nm). Operating conditions: (a) collinear output T=35.65°C, (b) noncollinear output cone with ~14 mrad full divergence T=34.7°C, and (c) noncollinear output cone with ~24 mrad full divergence T=32.8°C. Propagation cones are slightly flattened on the sides due to crystal birefringence.

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Fig. 5.
Fig. 5. Snapshots (in false colors) of (a) signal and (b) idler down-converted photons taken with a CCD camera. Images were taken with a 10-mm-long PPKTP crystal (9 µm poling period) kept at a temperature of 22°C and pumped with a 398.54-nm continuous-wave pump. Images were taken with a 0.11-nm interference filter centered around the degenerate wavelength of 797.08 nm; exposure time: 20 s. Ring diameters are ~3.6 mm corresponding to a full angle aperture of ~24 mrad.

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Fig. 6.
Fig. 6. Schematic of experimental setup used to verify polarization entanglement. CC, compensating crystal; PA, polarization analyzer composed of a half-wave plate and a polarizer; IF, 1-nm interference filter centered at 797 nm.

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Fig. 7.
Fig. 7. Coincidence counts for the polarization-entangled triplet state versus analyzer angle θ A in arm A for analyzer angle θ B in arm B set to 0° (solid triangles), 45° (open diamonds), 90° (open circles) and -45° (solid squares). Each data point is the result of an average over 10 s and the curves are best fits to the data. Pump power, 5 mW; iris diameter, 1 mm; 1-nm interference filter centered at 797 nm.

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Fig. 8.
Fig. 8. Plot of visibility V +(θ B =+45°) versus iris diameter for output triplet state. Inset: coincidence counts/s per mW of pump power versus iris diameter. A 1-nm interference filter centered at 797 nm was used.

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Equations (7)

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ω p = ω s + ω i ,
k p = k s + k i ,
∣ k j ∣ = 2 π n j ( T , λ j , δ j , ϕ j ) λ j
k p = k s + k i + 2 π Λ x .
∂ n p ∂ T ∣ T = 20 ° C = 28 × 10 − 6 ⁄ ° C .
C ( θ A ) = A 1 sin 2 ( θ A − θ B ) + A 2 ,
∣ ψ 〉 = ( ∣ H A V B 〉 + ∣ V A H B 〉 ) 2 ,
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