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Entangled photon generation in two-period quasi-phase-matched parametric down-conversion

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Abstract

We proposed and demonstrated a simple but deterministic scheme for generating polarization-entangled photon pairs at telecommunication wavelengths with type-II quasi-phase-matched spontaneous parametric down-conversion (QPM-SPDC) having two poling periods. We fabricated a LiNbO3 crystal having two poling periods so as to generate entangled photons at two wavelengths, i.e., 1506 nm and 1594 nm. We characterized the two-photon polarization state with state tomography and confirmed that the state was highly entangled.

© 2012 Optical Society of America

1. Introduction

Entanglement is a key resource for quantum information technology, including quantum communication and quantum computation. Photons are often used to conduct proof-of-principle experiments on quantum information such as Bell’s inequality violation [1], quantum telepor-tation [2], and linear optics quantum gate [3], by virtue of their robustness against decoherence. Especially, polarized photons are used as qubits because photon polarization provides an ideal two-level quantum system that is easy to deal with in practical experiments. Therefore, it is desirable to establish efficient methods for the generation and detection of polarization-entangled photon pairs for practical applications in quantum information processing. Spontaneous parametric down-conversion (SPDC) is the main method so far used to generate entangled photon pairs [4]. Quasi-phase matching (QPM) is a fascinating method that can generate entangled photon pairs with high efficiency [5]. To date, a number of methods to generate polarization-entangled photon pairs with type-II QPM have been reported [68]. However, some of them are not deterministic, while others require complex optical systems. In this paper, we report a simple but deterministic scheme for generating polarization-entangled photon pairs with type-II quasi-phase-matched SPDC (QPM-SPDC) having two poling periods.

2. Methods

In the SPDC process, when pump photons of frequency ωp illuminate a nonlinear optical crystal, these photons are converted into twin (signal and idler) photons of frequency ωs and ωi according to the conservation of photon energy ωp = ωs + ωi. The conversion efficiency is highest when their momenta are also conserved, i.e., under the phase-matching condition

Δkkp(ωp)ks(ωs)ki(ωi)=0
is satisfied, where kp, ks, and ki are the wave vectors of the pump, signal, and idler photons, respectively. QPM is a technique that compensates for a phase mismatch with the help of periodic modulation of nonlinear susceptibility χ(2). In ferroelectric crystals such as LiNbO3, χ(2) can be modulated by periodic domain inversion, i.e., periodic poling. The QPM condition involves an additional term that depends on the poling period Λ to the phase mismatch Δk;
ΔkQPMkp(ωp)ks(ωs)ki(ωi)2πΛ=0.

Periodically poled LiNbO3 (PPLN) is the most major device used for QPM. Figure 1 shows the calculated tuning curves, i.e., signal and idler wavelengths where the phase-matching condition (2) is satisfied, for type-II collinear QPM-SPDC in PPLN (pump wavelength λp=775 nm, temperature T=166°C) as a function of the poling period Λ. The refractive indices of LiNbO3 were calculated using the Sellmeier equations [9, 10]. As the figure shows, when Λ = Λa = 9.25 μm, the ordinary ray (o-ray) at λ1 = 2πc/ω1 = 1590 nm and the extraordinary ray (e-ray) at λ2 = 2πc/ω2 = 1510 nm are emitted. On the other hand, when Λ = Λb = 9.50 μm, the e-ray at ω1 and the o-ray at ω2 are emitted. We designed a PPLN crystal consisting of two adjacent areas (a and b) having two different poling periods (Λa and Λb), as shown in Fig. 2. These two areas have almost the same lengths: LaLb, so that both equally contribute to the down-conversion. In the following, we consider a crystal orientation in which the o-ray and e-ray have horizontal and vertical polarizations, respectively. The state of the superposed emission from the PPLN crystal can be written as

|Ψ=12(|H,ω1|V,ω2|ϕa+eiφ|V,ω1|H,ω2|ϕb),
where |H(V), ω1(ω2)〉 indicates the single-photon state having horizontal (vertical) polarization and frequency ω1 (ω2). The twin photons emitted from the poled areas a and b are associated by the two-photon wave packets |ϕa〉 and |ϕb〉, respectively. The difference between |ϕa〉 and |ϕb〉 arises from the longitudinal walk-off, i.e., the temporal separation between orthogonally polarized photon wave packets, and produces distinguishability between the photons emitted from the two areas [11, 12]. When the twin photons emerge from the crystal, the relative phase φ in (3) is given by
φ=φ0=2π(1Λa1Λb)Lb.
From the state (3), we can split the photon pair deterministically in terms of their frequencies [13] to paths 1 and 2, so that
|Ψ=12(|HV|ϕa+eiφ|VH|ϕb),
where |HV〉 (|VH〉) corresponds to the state where one photon, in horizontal (vertical) polarization, is in path 1 and the other, in vertical (horizontal) polarization, is in path 2. The density matrix ρ(p) of the polarization state is obtained by taking a partial trace of the state (5) with respect to |ϕa〉 and |ϕb〉 as
ρ(p)=Tr(ϕ)|ΨΨ|=12(|HVHV|+v|VHHV|+v*|HVVH|+|VHVH|),
where
v=eiφϕa|ϕb.
Note that the state (6) becomes the maximally entangled Bell state when |ν| = 1, i.e., |ϕa〉 = |ϕb〉. Therefore a pure polarization-entangled state requires indistinguishability between the two-photon wave packets. In other words, partial distinguishability between |ϕa〉 and |ϕb〉 degrades the purity and entanglement in the state (6). In our case, as we will discuss later, we expect |v| ≤ 0.954.

 figure: Fig. 1

Fig. 1 Calculated tuning curves of the type-II collinear QPM-SPDC in PPLN pumped at λp=775 nm and T =166°C. Solid and dashed curves correspond to the ordinary and extraordinary rays having horizontal (H) and vertical (V) polarizations, respectively.

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 figure: Fig. 2

Fig. 2 Two-period quasi-phase-matched device. The crystallographic axes of the lithium niobate crystal are referred to as x, y, and z. The pump (o-ray), signal (o-ray), and idler (e-ray) beams propagate collinearly along the x axis, having linear polarizations along y, y, and z, respectively.

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The experimental setup is shown in Fig. 3. A PPLN crystal (0.5 mm thick, LaLb ≃ 20 mm), having the two poling periods Λa = 9.25 μm and Λb = 9.50 μm, was fabricated from a congruent z-cut LiNbO3 crystal by the full-cover electrode method [1416]. To produce SPDC, the crystal was illuminated by the pump pulses at 775 nm, which is the second harmonics of an amplified external cavity laser diode. The pulse width, repetition rate, and average power of the pump were 2.5 ns, 4 MHz, and 9 mW, respectively. The crystal temperature was controlled by an oven with the stability of ± 0.01°C. In order to observe the parametric emission spectra, we used a grating spectrometer followed by an InGaAs linear photodiode array (not shown in the figure). A polarization-division Michelson interferometer was used in order to compensate for the group velocity difference between the photons having orthogonal polarizations and thus to maximize the visibility |ν| in Eq. (7). The relative phase φ was also adjusted by the interferometer;

φ=φ0+ω1ω2cΔl,
where Δl = lVlH is the pass-length difference of the interferometer having arm lengths of lH and lV for the horizontal and vertical polarizations, respectively. Then, a dichroic mirror split the photon pair in a deterministic way in terms of their frequencies to paths 1 and 2. Then each photon passed through a polarization analyzer (PA), which consisted of a half-wave plate and a polarizing beam splitter, and was detected by a single photon detector (id Quantique, id201). The coincidence signal between the two detectors was collected by a time-interval analyzer (EG&G, 9308).

 figure: Fig. 3

Fig. 3 Schematic of the experimental setup for polarization correlation measurement. SHG, second harmonics generator; PBS, polarizing beam splitter; QWP, quarter-wave plate; PA, polarization analyzer; D, detector

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3. Results

We measured the temperature dependence of the parametric emission spectra generated from the PPLN crystal having two poling periods. Figure 4(a) shows the emission spectra at temperatures from 120°C to 140°C. Note that we have two wavelength regions for the parametric emission: λ1 ∼ 1510 nm and λ2 ∼ 1590 nm. The decreased intensity in the wavelength region longer than 1600 nm was caused by the decreased sensitivity of the detector. Also note that these unpolarized spectra contain both o-ray and e-ray emissions. Two spectral peaks, one corresponding to the o-ray and the other to the e-ray, were observed for each spectral region at temperatures other than 120°C. The two peaks merged into a single peak at 120°C, having center wavelengths at 1506 nm and 1594 nm and a full width at half maximum of 1.4 nm. Figure 4(b) presents the temperature dependence of the peak positions shown in Fig. 4(a). The solid and dashed curves are the calculated values for the ordinary and extraordinary rays, respectively. As observed, the spectral peak positions for the o-ray and e-ray become identical at 120°C. Note that this spectral identity was expected at 166°C, as shown in Fig. 1. In the calculation for Fig. 4(b), the temperature was shifted so that the calculated curves fit the experimental values. The disagreement would originate from a slight difference between the actual refractive indices of our congruent LiNbO3 crystal and those calculated from the Sellmeier equations [9, 10]. Slight changes in the actual polling periods from the designed values are also possible reasons. It is noteworthy that, despite these possible deviations from the designed values, one can achieve the spectral identity at a certain temperature, even if the temperature and wavelengths differ somewhat from the original design.

 figure: Fig. 4

Fig. 4 (a) Parametric emission spectra around 1510 nm and 1590 nm at various temperatures. (b) Temperature dependence of the peak positions in the parametric emission spectra.

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In order to characterize the polarization state of the photon pair, we examined their polarization correlation. In the experiment, the crystal was kept at 120.0°C where the o-ray and e-ray have identical emission spectra, and the coincidence signals from the two detectors were collected as a function of θ1 and θ2, which represent the directions of linear polarizations transmitted by the polarization analyzers (PA) shown in Fig. 3. We adjusted the path-length difference Δl in Eq. (8) so as to obtain φ = 0 and the maximum fringe visibility of the polarization correlation. Figures 5(a) and (b) present the observed polarization correlation as a function of θ2, while θ1 was fixed either at 0°, 90°, 45°, or −45°. Assuming that the polarization state is in the state (6), the probability p(θ12) to find the photons in the linear polarizations of θ1 and θ2 is given by

p(θ1,θ2)=14(1cos2θ1cos2θ2+Re(v)sin2θ1sin2θ2).
For θ1=0° or 90°, we obtain
p(θ2)=14(1cos2θ2).
For θ1=45° or −45°,
p(θ2)=14(1±Re(v)sin2θ2).
The curves in Figs. 5(a) and (b) were calculated from Eqs. (10) and (11), respectively. In the case of θ1=0° or 90°, we observed the fringe visibility (V) of almost unity, as expected from the theory. In the case of θ1=45° or −45°, however, it is expected from Eq. (11) that V = Re(ν). In practice, we obtained a degraded visibility V = 0.90 from Fig. 5(b).

 figure: Fig. 5

Fig. 5 Results of the polarization correlation measurement. Circles are the measured coincidence counts as a function of θ2 while θ1 was fixed at 0° or 90° in (a), ±45° in (b). The curves are calculated by Eqs. (10) and (11).

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To obtain the density matrix of the two-photon polarization state, we carried out the correlation measurements of 16 polarization combinations including not only linear but also circular polarizations. Then we reconstructed the density matrix applying the maximum-likelihood estimation [17] to the measured data. Figure 6 shows the density matrix of the two-photon polarization state thus obtained. The fidelity F of the reconstructed density matrix ρ to the ideal Bell state

|ψ+=12(|HV+|VH)
was obtained as
F=Ψ+|ρ|Ψ+=0.94.
This value is much higher than the classical limit of 0.5, indicating that the obtained state is close to the ideal state. The concurrence (C) [18, 19] and the entanglement of formation (EF) [19,20] obtained from ρ were 0.93 and 0.90, respectively, demonstrating that the obtained state had a high degree of entanglement with slight degradation. Thus, our source demonstrated the generation of a highly entangled polarization state of the photon pairs.

 figure: Fig. 6

Fig. 6 Real (left) and imaginary (right) parts of the reconstructed density matrices of the two-photon polarization state.

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4. Discussion

Although we have obtained highly entangled photons as described above, it is valuable to discuss the theoretical degree of entanglement expected from our scheme. As given in Eqs. (6) and (7), the polarization state we generated would be the maximally entangled state only if |ϕa〉 = |ϕb〉. However, the longitudinal walk-off, i.e., the temporal separation between orthogonally polarized photon wave packets, is inherent to all SPDC schemes using Type-II phase matching. Since the amount of walk-off is proportional to the photons’ travel length in the crystal, it labels the position where the twin photons are created. This effect produces the change in |ϕa〉 and |ϕb〉, and thus establishes distinguishability between the photons created in the poling areas a and b in our crystal. Compensation for this effect is essential for good entanglement. Thus far, two methods have been used to compensate for the longitudinal walk-off effect. One is to use a polarization-division Michelson interferometer [21], as in the present experiment. The other is to use a crystal compensator, which has half the length and a 90° rotation of the crystal orientation with respect to those of the SPDC crystal [4, 6].

We first examine the interferometer method by evaluating v in Eq. (7). The phase φ is given in Eq. (8) and 〈ϕa|ϕb〉 can be calculated as follows [11, 12]. In our calculation, we assumed a continuous pump because the pump pulse width we used was sufficiently longer than the photons’ traveling time across the crystal. In this assumption, 〈ϕa|ϕb〉 is given by

ϕa|ϕb=dtϕa*(t)ϕb(t),
where t = t1t2, and t1 (t2) is the arrival time of the photon at detector D1 (D2). The wave packet functions ϕa(t) and ϕb(t) are given by
ϕa(t)={(DaLa)1DaLbttDa(La+Lb)t0otherwise
and
ϕb(t)={(DbLb)1DbLb+ttt0otherwise,
where t′ = Δl/c. The parameters Da and Db are defined as
Da1uo(ω1)1ue(ω2)
and
Db1uo(ω2)1ue(ω1),
where uo(ω) and ue(ω) are the group velocities of the o-ray and e-ray having frequency ω, respectively. In our case, both Da and Db have positive values and 0 < Da < Db. Figure 7 is the plot of 〈ϕa|ϕb〉 as a function of t′ when La = Lb = L. We see that 〈ϕa|ϕb〉 exhibits the highest value
ϕa|ϕbmax=DaDb,
within the range 2DaL ≤ 2t′ ≤ (Da + Db)L. We can adjust Δl of the interferometer in order to achieve this condition. Note that 〈ϕa|ϕbmax = 1 when ω1 = ω2. In our case, since ω1ω2, we obtain 〈ϕa|ϕbmax = 0.954. This is the expected upper limit of the visibility of our scheme. From this value, we expect the fidelity of our state to be F = 0.977. The observed fringe visibility (V = 0.90) and fidelity (F = 0.94) were slightly lower than the expected values. This degradation might originate from a slight misalignment of the interferometer and from a slight deviation of the phase φ from 0.

 figure: Fig. 7

Fig. 7 Plot of 〈ϕa|ϕb〉 as a function of t′.

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A crystal compensator is another powerful and commonly used device for obtaining desirable entanglement when signal and idler photons are degenerate in frequency [4, 6]. When the photons are non-degenerate, as in our case, the compensator crystal adds a phase change between the two terms in the state (3) as

φ=φ0+{kH(ω1)kV(ω2)+kV(ω1)+kH(ω2)}Lc.
The additional phase is dependent on the length (Lc) of the compensator crystal. However, unlike the case of the interferometer we used, it is difficult to adjust the phase by using the crystal compensator alone. The wave-packet functions ϕa(t) and ϕb(t) are given by
φa(t)={(DaLa)1DaLbDbLctDa(La+Lb)DbLc0otherwise
and
ϕb(t)={(DbLb)1DbLb+DaLctDaLc0otherwise.
When La = Lb = L, we again obtain Eq. (19) for the range 2DaL ≤ (Da + Db)Lc ≤ (Da + Db)L. Thus, when Lc = L, we can achieve the same degrees of visibility and fidelity as in the case of the interferometer we used. In applications where the phase-control ability is not important, the use of a crystal compensator would be a good option.

5. Conclusion

We proposed a simple but deterministic scheme for generating polarization-entangled photons using type-II two-period QPM-SPDC that produces non-degenerate, entangled photon pairs at a telecommunication wavelength. Using a PPLN crystal having two poling periods, we demonstrate a scheme in which highly entangled photon pairs are generated. We showed that the generated state had high visibility in the polarization correlation measurement and high fidelity to the ideally entangled state, although they were perfect in neither theory nor practice. We note that our two-period device is fabricated on a single crystal chip. Thus the scheme we proposed is readily applicable to waveguide devices, from which we expect to obtain the much higher generation rates required for practical applications.

Acknowledgments

This work was supported by a Grant-in-Aid for Creative Scientific Research (17GS1204) from the Japan Society for the Promotion of Science.

References and links

1. A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bellfs inequalities using time- varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982). [CrossRef]  

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

3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001). [CrossRef]   [PubMed]  

4. 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, 4337–4341 (1995). [CrossRef]   [PubMed]  

5. S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002). [CrossRef]  

6. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004). [CrossRef]  

7. T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006). [CrossRef]  

8. Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011). [CrossRef]  

9. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997). [CrossRef]  

10. M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22, 243–244 (1966). [CrossRef]  

11. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994). [CrossRef]   [PubMed]  

12. Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002). [CrossRef]  

13. Y.-H. Kim, S. P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A , 63, 060301(R) (2001). [CrossRef]  

14. S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003). [CrossRef]  

15. S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007). [CrossRef]  

16. S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009). [CrossRef]  

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

18. S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997). [CrossRef]  

19. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998). [CrossRef]  

20. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A , 54, 3824–3851 (1996). [CrossRef]   [PubMed]  

21. R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17, 16385–16393 (2009). [CrossRef]   [PubMed]  

References

  • View by:

  1. A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bellfs inequalities using time- varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
    [Crossref]
  2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [Crossref] [PubMed]
  3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [Crossref] [PubMed]
  4. 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, 4337–4341 (1995).
    [Crossref] [PubMed]
  5. S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
    [Crossref]
  6. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
    [Crossref]
  7. T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
    [Crossref]
  8. Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
    [Crossref]
  9. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [Crossref]
  10. M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22, 243–244 (1966).
    [Crossref]
  11. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994).
    [Crossref] [PubMed]
  12. Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
    [Crossref]
  13. Y.-H. Kim, S. P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A,  63, 060301(R) (2001).
    [Crossref]
  14. S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
    [Crossref]
  15. S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
    [Crossref]
  16. S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
    [Crossref]
  17. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [Crossref]
  18. S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
    [Crossref]
  19. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [Crossref]
  20. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A,  54, 3824–3851 (1996).
    [Crossref] [PubMed]
  21. R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17, 16385–16393 (2009).
    [Crossref] [PubMed]

2011 (1)

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

2009 (2)

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17, 16385–16393 (2009).
[Crossref] [PubMed]

2007 (1)

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

2006 (1)

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

2004 (1)

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[Crossref]

2003 (1)

S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
[Crossref]

2002 (2)

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

2001 (3)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A,  63, 060301(R) (2001).
[Crossref]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

1998 (1)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

1997 (2)

1996 (1)

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A,  54, 3824–3851 (1996).
[Crossref] [PubMed]

1995 (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, 4337–4341 (1995).
[Crossref] [PubMed]

1994 (1)

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994).
[Crossref] [PubMed]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

1982 (1)

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bellfs inequalities using time- varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[Crossref]

1966 (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22, 243–244 (1966).
[Crossref]

Aspect, A.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bellfs inequalities using time- varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[Crossref]

Baldi, P.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A,  54, 3824–3851 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Dalibard, J.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bellfs inequalities using time- varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[Crossref]

DiVincenzo, D. P.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A,  54, 3824–3851 (1996).
[Crossref] [PubMed]

Edamatsu, K.

R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17, 16385–16393 (2009).
[Crossref] [PubMed]

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

Fiorentino, M.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[Crossref]

Gisin, N.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Gong, Y.-X.

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

Grice, W. P.

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

Hill, S.

S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
[Crossref]

Hobden, M. V.

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22, 243–244 (1966).
[Crossref]

Ito, H.

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

James, D. F. V.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Jundt, D. H.

Kim, T.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

Kim, Y.-H.

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A,  63, 060301(R) (2001).
[Crossref]

Klyshko, D. N.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994).
[Crossref] [PubMed]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Konishi, M.

S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
[Crossref]

Kuklewicz, C. E.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[Crossref]

Kulik, S. P.

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A,  63, 060301(R) (2001).
[Crossref]

Kwiat, P. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

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, 4337–4341 (1995).
[Crossref] [PubMed]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Mattle, K.

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, 4337–4341 (1995).
[Crossref] [PubMed]

Messin, G.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[Crossref]

Micheli, M. D.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Minakata, M.

S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
[Crossref]

Munro, W. J.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Nagano, S.

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
[Crossref]

Ostrowsky, D. B.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Riedmatten, H. D.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Roger, G.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bellfs inequalities using time- varying analyzers,” Phys. Rev. Lett. 49, 1804–1807 (1982).
[Crossref]

Rubin, M. H.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994).
[Crossref] [PubMed]

Sergienko, A. V.

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, 4337–4341 (1995).
[Crossref] [PubMed]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994).
[Crossref] [PubMed]

Shapiro, J. H.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[Crossref]

Shih, Y.

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A,  63, 060301(R) (2001).
[Crossref]

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, 4337–4341 (1995).
[Crossref] [PubMed]

Shih, Y. H.

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in Type-II optical parametric down-conversion,” Phys. Rev.A 50, 5122–5133 (1994).
[Crossref] [PubMed]

Shimizu, R.

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17, 16385–16393 (2009).
[Crossref] [PubMed]

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

Shiomi, T.

S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
[Crossref]

Smolin, J. A.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A,  54, 3824–3851 (1996).
[Crossref] [PubMed]

Sugiura, Y.

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

Suizu, K.

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

Syouji, A.

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

Tanzilli, S.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Tittel, W.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Warner, J.

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22, 243–244 (1966).
[Crossref]

Weinfurter, H.

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, 4337–4341 (1995).
[Crossref] [PubMed]

White, A. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Wong, F. N. C.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73, 012316 (2006).
[Crossref]

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “Highflux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69, 013807 (2004).
[Crossref]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
[Crossref]

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A,  54, 3824–3851 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Xie, Z.-D.

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

Xu, P.

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

Xue, P.

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

Yu, X.-Q.

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

Zbinden, H.

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

Zeilinger, A.

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, 4337–4341 (1995).
[Crossref] [PubMed]

Zhu, S.-N.

Y.-X. Gong, Z.-D. Xie, P. Xu, X.-Q. Yu, P. Xue, and S.-N. Zhu, “Compact sources of narrow-band counter-propagation polarization-entangled photon pairs using a single dual-periodically-poled crystal,” Phys. Rev. A 84, 053825 (2011).
[Crossref]

Eur. Phys. J. D (1)

S. Tanzilli, W. Tittel, H. D. Riedmatten, H. Zbinden, P. Baldi, M. D. Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160 (2002).
[Crossref]

J. Mod. Opt. (1)

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[Crossref]

Jpn. J. Appl. Phys. (3)

S. Nagano, M. Konishi, T. Shiomi, and M. Minakata, “Study on formation of small polarization domain inversion for high-efficiency quasi-phase-matched second-harmonic generation device,” Jpn. J. Appl. Phys. 42, 4334–4339 (2003).
[Crossref]

S. Nagano, R. Shimizu, Y. Sugiura, K. Suizu, K. Edamatsu, and H. Ito, “800-nm band cross-polarized photon pair source using type-II parametric down-conversion in periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46, L1064–L1067 (2007).
[Crossref]

S. Nagano, A. Syouji, R. Shimizu, K. Suizu, H. Ito, and K. Edamatsu, “Generation of cross-polarized photon pairs via type-II third-order quasi-phase matched parametric down-conversion,” Jpn. J. Appl. Phys. 48, 050205 (2009).
[Crossref]

Nature (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22, 243–244 (1966).
[Crossref]

Phys. Rev. A (6)

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Figures (7)

Fig. 1
Fig. 1 Calculated tuning curves of the type-II collinear QPM-SPDC in PPLN pumped at λp=775 nm and T =166°C. Solid and dashed curves correspond to the ordinary and extraordinary rays having horizontal (H) and vertical (V) polarizations, respectively.
Fig. 2
Fig. 2 Two-period quasi-phase-matched device. The crystallographic axes of the lithium niobate crystal are referred to as x, y, and z. The pump (o-ray), signal (o-ray), and idler (e-ray) beams propagate collinearly along the x axis, having linear polarizations along y, y, and z, respectively.
Fig. 3
Fig. 3 Schematic of the experimental setup for polarization correlation measurement. SHG, second harmonics generator; PBS, polarizing beam splitter; QWP, quarter-wave plate; PA, polarization analyzer; D, detector
Fig. 4
Fig. 4 (a) Parametric emission spectra around 1510 nm and 1590 nm at various temperatures. (b) Temperature dependence of the peak positions in the parametric emission spectra.
Fig. 5
Fig. 5 Results of the polarization correlation measurement. Circles are the measured coincidence counts as a function of θ2 while θ1 was fixed at 0° or 90° in (a), ±45° in (b). The curves are calculated by Eqs. (10) and (11).
Fig. 6
Fig. 6 Real (left) and imaginary (right) parts of the reconstructed density matrices of the two-photon polarization state.
Fig. 7
Fig. 7 Plot of 〈ϕa|ϕb〉 as a function of t′.

Equations (22)

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Δ k k p ( ω p ) k s ( ω s ) k i ( ω i ) = 0
Δ k QPM k p ( ω p ) k s ( ω s ) k i ( ω i ) 2 π Λ = 0 .
| Ψ = 1 2 ( | H , ω 1 | V , ω 2 | ϕ a + e i φ | V , ω 1 | H , ω 2 | ϕ b ) ,
φ = φ 0 = 2 π ( 1 Λ a 1 Λ b ) L b .
| Ψ = 1 2 ( | H V | ϕ a + e i φ | V H | ϕ b ) ,
ρ ( p ) = Tr ( ϕ ) | Ψ Ψ | = 1 2 ( | H V H V | + v | V H H V | + v * | H V V H | + | V H V H | ) ,
v = e i φ ϕ a | ϕ b .
φ = φ 0 + ω 1 ω 2 c Δ l ,
p ( θ 1 , θ 2 ) = 1 4 ( 1 cos 2 θ 1 cos 2 θ 2 + Re ( v ) sin 2 θ 1 sin 2 θ 2 ) .
p ( θ 2 ) = 1 4 ( 1 cos 2 θ 2 ) .
p ( θ 2 ) = 1 4 ( 1 ± Re ( v ) sin 2 θ 2 ) .
| ψ + = 1 2 ( | H V + | V H )
F = Ψ + | ρ | Ψ + = 0.94.
ϕ a | ϕ b = d t ϕ a * ( t ) ϕ b ( t ) ,
ϕ a ( t ) = { ( D a L a ) 1 D a L b t t D a ( L a + L b ) t 0 otherwise
ϕ b ( t ) = { ( D b L b ) 1 D b L b + t t t 0 otherwise ,
D a 1 u o ( ω 1 ) 1 u e ( ω 2 )
D b 1 u o ( ω 2 ) 1 u e ( ω 1 ) ,
ϕ a | ϕ b max = D a D b ,
φ = φ 0 + { k H ( ω 1 ) k V ( ω 2 ) + k V ( ω 1 ) + k H ( ω 2 ) } L c .
φ a ( t ) = { ( D a L a ) 1 D a L b D b L c t D a ( L a + L b ) D b L c 0 otherwise
ϕ b ( t ) = { ( D b L b ) 1 D b L b + D a L c t D a L c 0 otherwise .

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