Abstract

Generation of time-bin entangled photon pairs requires the use of the Franson interferometer which consists of two spatially separated unbalanced Mach-Zehnder interferometers through which the signal and idler photons from spontaneous parametric down-conversion (SPDC) are made to transmit individually. There have been two SPDC pumping regimes where the scheme works: the narrowband regime and the double-pulse regime. In the narrowband regime, the SPDC process is pumped by a narrowband cw laser with the coherence length much longer than the path length difference of the Franson interferometer. In the double-pulse regime, the longitudinal separation between the pulse pair is made equal to the path length difference of the Franson interferometer. In this paper, we propose another regime by which the generation of time-bin entanglement is possible and demonstrate the scheme experimentally. In our scheme, differently from the previous approaches, the SPDC process is pumped by a cw multi-mode (i.e., short coherence length) laser and makes use of the coherence revival property of such a laser. The high-visibility two-photon Franson interference demonstrates clearly that high-quality time-bin entanglement source can be developed using inexpensive cw multi-mode diode lasers for various quantum communication applications.

© 2013 OSA

1. Introduction

Entanglement is one of the most fascinating non-classical properties [1]. It is also a very important resource for many quantum information applications such as quantum computation [2], quantum cryptography [3], quantum teleportation [46], and quantum metrology [79]. For photons, polarization-entanglement [1012] is widely utilized in quantum information research [13, 14], but it is not ideal for fiber-based quantum communication applications due to the polarization mode dispersion. Time-bin entanglement is often the best choice for such applications as it is robust against various decoherence effects resulting from long-distance fiber transmission [15, 16].

The generation scheme for time-bin entanglement is based on the Franson interferometer (FI) [17], which consists of two spatially separated unbalanced Mach-Zehnder interferometers through which the signal and idler photons from spontaneous parametric down-conversion (SPDC) are made to transmit individually, see Fig. 1. In quantum interference experiments, it is essential to ensure that the relevant quantum probability amplitudes are made indistinguishable and in the experiments involving the FI, this is achieved by choosing proper pumping schemes. There have been two SPDC pumping regimes where the scheme works: the narrowband regime and the double-pulse regime. In the narrowband regime [1823], the SPDC process is pumped by a narrowband cw laser with the coherence length much longer than the path length difference of the FI. In the double-pulse regime [2427], the longitudinal separation between the pulse pair is made equal to the path length difference of the FI.

 

Fig. 1 The schematic of Franson interferometer. Post-selecting the central peak in the TC-SPC histogram allows one to prepare/detect the time-bin entanglement. For this to happen, the pump laser for the SPDC process must meet certain conditions. See text for details.

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In this paper, we propose another regime by which the generation of time-bin entanglement is possible and demonstrate the scheme experimentally. In our scheme, differently from the previous approaches, the SPDC process is pumped by a cw multi-mode (i.e., short coherence length) laser. By making use of the coherence revival property of a cw multi-mode laser, observed for the first-order coherence in [28, 29] and for the second-order coherence in [30], we demonstrate high-visibility quantum interference due to two-photon energy-time entanglement. Our results clearly show that high-quality time-bin entanglement source can be developed using inexpensive cw multi-mode diode lasers, as opposed to using expensive narrowband lasers or pulsed lasers, for various quantum communication applications.

2. Theory

We begin by briefly introducing the Franson interferometer shown in Fig. 1 [17]. A pair of photons, typically called the signal and the idler photons, are generated from the SPDC process in a nonlinear crystal. Each photon is directed to an unbalanced Mach-Zehnder interferometer (MZI) and the photon may take the long path (L1 and L2) or the short path (S1 and S2) of the MZI. To ensure that there is no first-order interference at the output of the MZI, the path length difference between the long path and the short path is made much larger than the coherence length of the input (signal and idler) photon. The photons are then detected at the single-photon detectors (D1 and D2) located at the output ports of the MZI and the difference of photons’ time of arrival τ = t1t2 is recorded by using Time-Correlated Single-Photon Counting (TCSPC) electronics.

It is well-known that the TCSPC histogram exhibits three distinctive peaks as shown in Fig. 1 and they come from the four probability amplitudes for joint detection of the photon pair: |S1|S2, |L1|L2, |S1|L2, and |L1|S2. The left (right) peak is due to |S1|L2 (|L1|S2) and the central peak is due to both |S1|S2 and |L1|L2 which is why the central peak is twice as tall as the side peaks. Note that the separation between peaks is determined by the optical path length difference of the MZI ΔL1,2 = L1,2S1,2 and the width of the peak (typically around 1 ∼ 2 ns) is mostly determined by the resolution of the electronics. Since Lc ≪ ΔL1,2, where Lc is the coherence length of the single-photons (signal and idler photons), there is no first-order interference observed at either detectors D1 and D2. We then further impose the condition ΔL1,2Lp, where Lp is the coherence length of the SPDC pump laser, and post-select only the central peak of the TCSPC histogram by using a narrow coincidence window. We have thus obtained a time-bin entangled state

|ψ=12(|S1|S2+eiϕ|L1|L2),
where ϕ is the phase difference between two probability amplitudes, which can be controlled by scanning ΔL1,2 of the MZI. The visibility drops if the side peaks are not completely excluded.

The description so far is the narrowband regime as the pump bandwidth should be sufficiently narrow to satisfy ΔL1,2Lp, which is essential for providing quantum coherence between |S1|S2 and |L1|L2 [1823]. Another way to ensure quantum coherence between the two amplitudes |S1|S2 and |L1|L2 is to pump the SPDC process with a pair of coherent pulses, the double-pulse regime, whose longitudinal separation is identical to ΔL1,2 [2427]. Unlike these schemes, our new scheme for generating time-bin entanglement does not use the narrowband pumping nor coherent pulses. In fact, the pump laser in our scheme has a coherence length much smaller than the path length difference of the MZI, Lp ≪ ΔL1,2. Instead, our scheme is based on the coherence revival property of multi-mode emission from a cavity [2830].

Let us begin by describing the SPDC process pumped by a multi-mode laser. The two-photon state from multi-mode pumped SPDC can be written as a mixed state [8, 30]

ρ=dωp𝒮(ωp)|ψψ|.
Here, 𝒮 (ωp) is the spectral power density of the pump laser given as the sum of multiple incoherent longitudinal modes,
𝒮(ωp)=n=NN𝒮0(ωp)δ(ωpωp0nΔωp)n=NN𝒮0(ωp0+nΔωp),
where ωp0, Δωp, and n are the central frequency of the pump, the mode spacing, and the mode number and we have assumed that the spectral power density has a Gaussian spectral profile with the bandwidth θ, 𝒮0(ωp)~exp[(ωpωp0)22θ2]. The two-photon quantum state of SPDC |ψ〉, pumped by a single-mode laser with frequency ωp is given as
|ψ=dωsdωiδ(Δω)sinc(Δkl/2)eiΔkl/2|ωs,ωi,
where Δωωpωsωi, Δkkpkski, and l is the thickness of the SPDC crystal. The subscripts p, s, and i refer the pump, signal, and idler photons, respectively. Note that |ωs,ωi=as(ωs)ai(ωi)|0 where as(ωs) ( ai(ωi)) represents the creation operator for the signal (idler) photon of frequency ωs (ωi) and |0〉 is the vacuum.

Let us now suppose that the signal (idler) photon is sent to D1 (D2) through the unbalanced MZIs in Fig. 1. We also assume that interference filters are placed in front of the detectors and they have the Gaussian transmission function ϕ(ω)=1θfπexp[(ωω0)22θf2], where ω0 and θf are the central frequency and bandwidth of the filter, respectively, and ∫ |ϕ (ω)|2 = 1. Consequently, the positive frequency component of the electric field operator for a single-photon detector Dj∈{1,2} at time t is expressed as EDj(+)(t)=dωϕ(ω)eiωtaDj(ω), where aDj (ω) is the annihilation operator for a photon of frequency ω at the detector Dj.

The joint detection rate between the two detectors D1 and D2 is then proportional to

RΔτΔτdτtr[ρED1()(t)ED2()(t+τ)ED2(+)(t+τ)ED1(+)(t)],
where EDj{1,2}(+)(t)=12[ESj(+)(t)+ELj(+)(tξj)], ξj = ΔLj/c with c being the speed of light in vacuum, and τ = t1t2. In evaluating the integral in Eq. (5), we set the value of Δτ such that only the central peak in the TCSPC histogram (see Fig. 1) is selected (i.e., two side peaks are thrown out). Thus, the field operator ED2(+)(t+τ)ED1(+)(t) becomes 12[ES2(+)(t+τ)ES1(+)(t)+EL2(+)(t+τξ2)EL1(+)(tξ1)] without containing the terms representing the side peaks ES2(+)EL1(+) and EL2(+)ES1(+). Therefore, Eq. (5) becomes
Rdτtr[ρ(ES2()(t+τ)ES1()(t)+EL2()(t+τξ2)EL1()(tξ1))×(ES2(+)(t+τ)ES1(+)(t)+EL2(+)(t+τξ2)EL1(+)(tξ1))].
Considering the fact that the signal (idler) photon propagates toward D1 (D2) and given that the field operators for the signal and the idler photons are given as Ej(+)(t)=dωϕ(ω)eiωtaj(ω) with j ∈ {s, i}, we can write ES1(+)(t)=12Es(+)(t), ES2(+)(t)=12Ei(+)(t), and similarly for EL1(+)(t) and EL2(+)(t). After substituting Eq. (2) for ρ in Eq. (6), we finally obtain the joint detection rate
R=12+Γ2n=NN𝒮eff(ωp0+nΔωp)cos((ωp0+nΔωp)(ξ1+ξ2))n=NN𝒮eff(ωp0+nΔωp),
where Γ=exp[θf2(ξ1ξ2)2/8] and 𝒮eff (ωp) identical to 𝒮0 (ωp) except that the bandwidth θ is replaced with the effective bandwidth θeff (calculated from 1/θeff2=1/θ2+1/θf2). We have assumed that the filter bandwidth θf is sufficiently narrower than the natural bandwidth of SPDC (calculated from sinc(Δkl/2)) so that the SPDC spectral amplitude is equal to the filter transmission function ϕ(ω).

Figure 2 shows the theoretical results of Eq. (7). Here we have assumed that the multi-mode pump laser is centered at λp0 = 405 nm with the bandwidth of σ = 0.28 nm and the mode spacing is Δλp = 0.0289 nm. The SPDC photons are assumed to be generated at a type-I BBO crystal of thickness l = 6 mm and centered at λ0 = 810 nm. The bandwidth of the filter transmission function is assumed to be σf = 17 nm. These parameters are converted to frequencies by using the following relations ω0 = 2πc/λ0, θ=2πcσ/λ02, and Δωp=2πcΔλp/λp02. Note that, at these conditions, the multi-mode pump laser exhibits the coherence revival at the period of Lr=λp02/Δλp=5.668 mm [29, 30].

 

Fig. 2 Theoretical plot of Eq. (7) as a function of ΔL1 for different ΔL2. (a) ΔL2 = 5.668 mm and (b) ΔL2 = 11.336 mm. (c) The joint count rate when ΔL1 and ΔL2 are simultaneously scanned exhibits the coherence revival property [29, 30].

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We first consider the cases where one of the MZIs is unbalanced at integer multiples of Lr. Figures 2(a) and 2(b) show the coincidence rates as a function of ΔL1, while ΔL2 is fixed at Lr and 2Lr, respectively. As demonstrated in the theoretical plots, two-photon time-bin interference fringes are expected whenever the scanning ΔL1 becomes identical to ΔL2 within the single-photon coherence length. It is important to point out that, since the individual MZI is unbalanced, there is no first-order interference. Note also that, in this case, the interference fringes exhibit modulation at the wavelength of SPDC photons λ0 = 810 nm. Consider now that both ΔL1 and ΔL2 are scanned simultaneously shown in Fig. 2(c). In this case, two-photon interference is expected at the modulation period equal to the pump wavelength λp0 = 405 nm. Furthermore, coherence revival of the two-photon time-bin interference fringes is expected at the period of Lr=λp02/Δλp=5.668 mm [29, 30] which is due to the fact that Γ=exp[θf2(ξ1ξ2)2/8] in Eq. (7) is not degraded as long as ΔL1L2. However, if ΔL1 differs significantly from ΔL2, Γ degrades quickly so the revival of two-photon interference does not occur as shown in Figs. 2(a) and 2(b).

3. Experiment

To demonstrate high-visibility two-photon quantum interference due to time-bin entanglement using the multi-mode pump laser, it is essential that the path length differences of the MZIs are set integer multiples of Lr and the side peaks due to |S1|L2 and |S2|L1 are sufficiently far away from the main peak. Considering the detector jitter and TCSPC electronics resolution, about 3 ns separation is desired and this translates to ΔL1,2 = 900 mm. To avoid practical problems involving MZIs with such a large path length difference while still demonstrating the essential features of time-bin entanglement using multi-mode pumped SPDC, we employ the postselection-free energy-time entanglement scheme in [22]. In this scheme, beam splitters in the MZIs are replaced with polarization beam splitters and the input state is given in the form of a polarization entangled state. As a result, the |S1|L2 and |S2|L1 amplitudes which generate the side peaks do not occur naturally and therefore no postselection is necessary. Note however that, since the photonic path (long and short) is correlated to the polarization (vertical and horizontal), it is necessary to erase the polarization information by projecting it onto the 45° oriented polarizers [22].

The experimental setup is shown in Fig. 3. Type-I SPDC photon pairs generated in a 6-mm-thick β-BaB2O4 crystal pumped by a 405 nm multi-mode diode laser are used for the experiment. For the 405 nm pump laser, the coherence length and the first-order coherence revival period are measured as Lp = 216 μm and Lr = 5.668 mm, respectively. From these results, we can find that the mode spacing of the pump laser is Δωp = 3.33 × 1011 Hz as simulated in the previous section. The degenerate phase matching condition was applied for the SPDC so the wavelengths of both signal and idler SPDC photons are centered at 810 nm.

 

Fig. 3 Experimental setup. PBS: polarization beam splitter, QWP: quarter wave plate, D1 and D2: single photon detectors.

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First, the polarization entangled state of the form |Φ+=12(|H1|H2+|V1|V2), where |H〉 and |V〉 are horizontal and vertical polarization, is prepared by interfering the two photons at a beam splitter [10, 11]. Second, each photon of the polarization entangled state is sent to a unbalanced Michelson interferometer which consists of a polarizing beam splitter (PBS) and two quarter wave plates (QWP). This scheme ensures that the |H〉 photon at the input of the PBS takes the long path (|L1 or |L2) of the interferometer and exits the PBS as the |V〉 photon. Similarly, |V〉 photon at the input of the PBS takes the short path (|S1 or |S2) of the interferometer and exits the PBS as the |H〉 photon. Finally, 45° oriented polarizers are used to erase the polarization information. As a result, the polarization-entangled state has been converted to the time-bin entangled state of the form in Eq. (1) with no need for TCSPC postselection. Note that the relative phase ϕ can be adjusted by scanning either ΔL1 or ΔL2.

The experimental data are shown in Fig. 4. Figures 4(a) and 4(b) show the coincidence count rate as a function of ΔL1 while ΔL2 is fixed at 5.668 mm and 11.336 mm, respectively. As expected in Eq. (7) and in Figs. 2(a) and 2(b), two-photon quantum interference due to time-bin entanglement occurs only when the condition ΔL1 = ΔL2 is satisfied. Figure 4(c) shows the coincidence count rate when both ΔL1 and ΔL2 are simultaneously scanned. In this case, as expected in Fig. 2(c), recurrence or revival of two-photon interference is observed with the period of 5.668 mm. The observed quantum interference visibilities are 95% for Fig. 4(a) and 4(b) and 93% for Fig. 4(c). Since the visibility threshold for the two-photon quantum interference for the Bell’s inequality violation is 70.7% [31], the experimental data in Fig. 4 show that the photon pair is time-bin entangled, hence suitable for a variety of quantum communications applications.

 

Fig. 4 Experimental data. The coincidence count rate as a function of ΔL1 for different ΔL2 values. (a) ΔL2 = 5.668 mm and (b) ΔL2 = 11.336 mm. The two-photon interference visibility is measure to be 95% for both cases. (c) ΔL1 and ΔL2 are scanned simultaneously. The two-photon interference visibility is measured to be 93%. The experimental data agree well with the theoretical results shown in Fig. 2.

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4. Conclusion

We have shown in theory and in experiment that time-bin entangled photon pairs can be generated with the SPDC process pumped with a cw multi-mode laser. Unlike previous schemes where the pump laser must have coherence length longer than the path length difference of the ranson interferometer [1823] or the SPDC process must be pumped with a pair of coherent laser pulses whose spatial separation is equal to the path length difference of the Franson interferometer [2427], our scheme makes use of a unique coherence revival property of the cw multi-mode laser for generating a time-bin entangled photon pair [2830]. Clearly, the main difference between the multi-mode cw laser and the mode-locked pulsed laser is the lack of or presence of coherence among the spectral modes. This point is clearly described in Eq. (3) in which the spectral power density of the cw multi-mode laser is given as the incoherent sum of multiple equally-spaced longitudinal modes. We have shown that it is nevertheless possible to use such a laser in the Franson interferometer to prepare time-bin entangled photon pairs. Note that the coherence revival feature of the pump laser, which we make use of for generating the two-photon time-bin entanglement, comes from the fact that the spectral modes are equally-spaced albeit with no phase coherence. Thus, our scheme is not applicable to SPDC pumped with a chaotic light source, e.g, a blue light emitting diode [32].

As multi-mode diode lasers suitable for SPDC pumping are widely available at a low cost, we believe our results offer a wide variety of applications in preparing time-bin entangled photon pairs inexpensively and reliably for various quantum information tasks, such as quantum cryptography, quantum communication, and quantum computation.

Acknowledgments

This work was supported in part by the National Research Foundation of Korea (Grants No. 2013R1A2A1A01006029 and No. 2011-0021452). OK and YSK acknowledge support from the KIST Institutional Program (Project No. 2E24013). KKP acknowledges support from Global Ph.D. Fellowship by National Research Foundation of Korea (Grant No. 2011-0030856).

References and links

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

6. Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001). [CrossRef]   [PubMed]  

7. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011). [CrossRef]  

8. O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A 81, 063801 (2010). [CrossRef]  

9. Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun. 4, 2451 (2013). [CrossRef]  

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13. H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011). [CrossRef]   [PubMed]  

14. Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012). [CrossRef]  

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References

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  1. J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum revolution,” Phil. Trans. R. Soc. Lond. A361, 1655–1674 (2003).
    [CrossRef]
  2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
  3. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
    [CrossRef] [PubMed]
  4. 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]
  5. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
    [CrossRef]
  6. Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett.86, 1370–1373 (2001).
    [CrossRef] [PubMed]
  7. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics5, 222–229 (2011).
    [CrossRef]
  8. O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A81, 063801 (2010).
    [CrossRef]
  9. Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
    [CrossRef]
  10. Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
    [CrossRef] [PubMed]
  11. Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett.61, 50–53 (1988).
    [CrossRef] [PubMed]
  12. 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]
  13. H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
    [CrossRef] [PubMed]
  14. Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
    [CrossRef]
  15. R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
    [CrossRef]
  16. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express17, 11440–11449 (2009).
    [CrossRef] [PubMed]
  17. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989).
    [CrossRef] [PubMed]
  18. J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett.66, 1142–1145 (1991).
    [CrossRef] [PubMed]
  19. J. G. Rarity and P. R. Tapster, “Fourth-order interference effects at large distances,” Phys. Rev. A45, 2052–2056 (1992).
    [CrossRef] [PubMed]
  20. Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment,” Phys. Rev. A47, 1288–1293 (1993).
    [CrossRef] [PubMed]
  21. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A47, R2472–R2475 (1993).
    [CrossRef] [PubMed]
  22. D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (1996).
    [CrossRef] [PubMed]
  23. T. Honjo, H. Takesue, and K. Inoue, “Generation of energy-time entangled photon pairs in 1.5-μ m band with periodically poled lithium niobate waveguide,” Opt. Express15, 1679–1683 (2007).
    [CrossRef] [PubMed]
  24. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
    [CrossRef]
  25. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
    [CrossRef] [PubMed]
  26. I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
    [CrossRef]
  27. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett.81, 3563–3566 (1998).
    [CrossRef]
  28. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A63, 053801 (2001).
    [CrossRef]
  29. S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode lase using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys.46, 7720–7723 (2007).
    [CrossRef]
  30. O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express17, 13059–13069 (2009).
    [CrossRef] [PubMed]
  31. J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D10, 526–535 (1974).
    [CrossRef]
  32. J. Galinis, M. Karpiński, G. Tamošauskas, K. Dobek, and A. Piskarskas, “Photon coincidences in spontaneous parametric down-converted radiation excited by a blue LED in bulk LiIO3 crystal,” Opt. Express19, 10351–10358 (2011).
    [CrossRef] [PubMed]

2013 (1)

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

2012 (1)

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
[CrossRef]

2011 (3)

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics5, 222–229 (2011).
[CrossRef]

J. Galinis, M. Karpiński, G. Tamošauskas, K. Dobek, and A. Piskarskas, “Photon coincidences in spontaneous parametric down-converted radiation excited by a blue LED in bulk LiIO3 crystal,” Opt. Express19, 10351–10358 (2011).
[CrossRef] [PubMed]

2010 (1)

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A81, 063801 (2010).
[CrossRef]

2009 (2)

2007 (2)

T. Honjo, H. Takesue, and K. Inoue, “Generation of energy-time entangled photon pairs in 1.5-μ m band with periodically poled lithium niobate waveguide,” Opt. Express15, 1679–1683 (2007).
[CrossRef] [PubMed]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode lase using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys.46, 7720–7723 (2007).
[CrossRef]

2003 (1)

J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum revolution,” Phil. Trans. R. Soc. Lond. A361, 1655–1674 (2003).
[CrossRef]

2002 (2)

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

2001 (2)

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A63, 053801 (2001).
[CrossRef]

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett.86, 1370–1373 (2001).
[CrossRef] [PubMed]

2000 (1)

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
[CrossRef]

1998 (1)

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett.81, 3563–3566 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[CrossRef]

1996 (1)

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (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]

1993 (3)

Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment,” Phys. Rev. A47, 1288–1293 (1993).
[CrossRef] [PubMed]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A47, R2472–R2475 (1993).
[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]

1992 (1)

J. G. Rarity and P. R. Tapster, “Fourth-order interference effects at large distances,” Phys. Rev. A45, 2052–2056 (1992).
[CrossRef] [PubMed]

1991 (2)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett.66, 1142–1145 (1991).
[CrossRef] [PubMed]

1989 (1)

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989).
[CrossRef] [PubMed]

1988 (2)

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett.61, 50–53 (1988).
[CrossRef] [PubMed]

1974 (1)

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D10, 526–535 (1974).
[CrossRef]

Alley, C. O.

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

Asobe, M.

Bae, J.

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

Baek, S.-Y.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode lase using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys.46, 7720–7723 (2007).
[CrossRef]

Bennett, C. H.

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]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[CrossRef]

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]

Brendel, J.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
[CrossRef] [PubMed]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett.81, 3563–3566 (1998).
[CrossRef]

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett.66, 1142–1145 (1991).
[CrossRef] [PubMed]

Buchleitner, A.

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

Burlakov, A. V.

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A63, 053801 (2001).
[CrossRef]

Chekhova, M. V.

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A63, 053801 (2001).
[CrossRef]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A47, R2472–R2475 (1993).
[CrossRef] [PubMed]

Chuang, I. L.

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

Clauser, J. F.

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D10, 526–535 (1974).
[CrossRef]

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]

de Riedmatten, H.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

Dobek, K.

Dowling, J. P.

J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum revolution,” Phil. Trans. R. Soc. Lond. A361, 1655–1674 (2003).
[CrossRef]

Dynes, J. F.

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[CrossRef]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

Franson, J. D.

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989).
[CrossRef] [PubMed]

Galinis, J.

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics5, 222–229 (2011).
[CrossRef]

Gisin, N.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
[CrossRef] [PubMed]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett.81, 3563–3566 (1998).
[CrossRef]

Harada, K.

Honjo, T.

Horne, M. A.

J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,” Phys. Rev. D10, 526–535 (1974).
[CrossRef]

Inoue, K.

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]

Kamada, H.

Karabutova, O. A.

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A63, 053801 (2001).
[CrossRef]

Karpinski, M.

Kim, Y.-H.

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
[CrossRef]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A81, 063801 (2010).
[CrossRef]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express17, 13059–13069 (2009).
[CrossRef] [PubMed]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode lase using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys.46, 7720–7723 (2007).
[CrossRef]

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett.86, 1370–1373 (2001).
[CrossRef] [PubMed]

Kim, Y.-S.

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
[CrossRef]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

Kulik, S. P.

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett.86, 1370–1373 (2001).
[CrossRef] [PubMed]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A63, 053801 (2001).
[CrossRef]

Kwiat, P. G.

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (1996).
[CrossRef] [PubMed]

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]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A47, R2472–R2475 (1993).
[CrossRef] [PubMed]

Kwon, O.

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
[CrossRef]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A81, 063801 (2010).
[CrossRef]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express17, 13059–13069 (2009).
[CrossRef] [PubMed]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode lase using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys.46, 7720–7723 (2007).
[CrossRef]

Lee, J.-C.

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
[CrossRef]

Lim, H.-T.

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics5, 222–229 (2011).
[CrossRef]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics5, 222–229 (2011).
[CrossRef]

Mandel, L.

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett.61, 50–53 (1988).
[CrossRef] [PubMed]

Marcikic, I.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

Martienssen, W.

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett.66, 1142–1145 (1991).
[CrossRef] [PubMed]

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[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]

Milburn, G. J.

J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum revolution,” Phil. Trans. R. Soc. Lond. A361, 1655–1674 (2003).
[CrossRef]

Mintert, F.

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

Mohler, E.

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett.66, 1142–1145 (1991).
[CrossRef] [PubMed]

Nielsen, M. A.

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

Nishida, Y.

Ou, Z. Y.

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett.61, 50–53 (1988).
[CrossRef] [PubMed]

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[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]

Piskarskas, A.

Pittman, T. B.

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[CrossRef]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A81, 063801 (2010).
[CrossRef]

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[CrossRef] [PubMed]

Scarani, V.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

Sergienko, A. V.

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (1996).
[CrossRef] [PubMed]

Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment,” Phys. Rev. A47, 1288–1293 (1993).
[CrossRef] [PubMed]

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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]

Sharpe, A. W.

Shields, A. J.

Shih, Y.

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett.86, 1370–1373 (2001).
[CrossRef] [PubMed]

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.

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (1996).
[CrossRef] [PubMed]

Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment,” Phys. Rev. A47, 1288–1293 (1993).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
[CrossRef] [PubMed]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A47, R2472–R2475 (1993).
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D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (1996).
[CrossRef] [PubMed]

Tadanaga, O.

Takesue, H.

Tamošauskas, G.

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J. G. Rarity and P. R. Tapster, “Fourth-order interference effects at large distances,” Phys. Rev. A45, 2052–2056 (1992).
[CrossRef] [PubMed]

Thew, R. T.

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
[CrossRef]

Tichy, M. C.

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
[CrossRef]

Tittel, W.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
[CrossRef] [PubMed]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett.81, 3563–3566 (1998).
[CrossRef]

Weinfurter, H.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[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]

Wootters, W. K.

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]

Yuan, Z. L.

Zbinden, H.

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
[CrossRef] [PubMed]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett.81, 3563–3566 (1998).
[CrossRef]

Zeilinger, A.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[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]

Jpn. J. Appl. Phys. (1)

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode lase using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys.46, 7720–7723 (2007).
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Nature (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature390, 575–579 (1997).
[CrossRef]

Nature Commun. (1)

Y.-S. Ra, M. C. Tichy, H.-T. Lim, O. Kwon, F. Mintert, A. Buchleitner, and Y.-H. Kim, “Observation of detection-dependent multi-photon coherence times,” Nature Commun.4, 2451 (2013).
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Nature Phys. (1)

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys.8, 117–120 (2012).
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Opt. Express (4)

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Phys. Rev. A (8)

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉 + |0, N〉 state,” Phys. Rev. A81, 063801 (2010).
[CrossRef]

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A66, 062304 (2002).
[CrossRef]

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I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002).
[CrossRef]

J. G. Rarity and P. R. Tapster, “Fourth-order interference effects at large distances,” Phys. Rev. A45, 2052–2056 (1992).
[CrossRef] [PubMed]

Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment,” Phys. Rev. A47, 1288–1293 (1993).
[CrossRef] [PubMed]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A47, R2472–R2475 (1993).
[CrossRef] [PubMed]

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time entanglement,” Phys. Rev. A54, R1–R4 (1996).
[CrossRef] [PubMed]

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Phys. Rev. Lett. (12)

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[CrossRef]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett.84, 4737–4740 (2000).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett.107, 160401 (2011).
[CrossRef] [PubMed]

Y.-H. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell state measurement,” Phys. Rev. Lett.86, 1370–1373 (2001).
[CrossRef] [PubMed]

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[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]

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

The schematic of Franson interferometer. Post-selecting the central peak in the TC-SPC histogram allows one to prepare/detect the time-bin entanglement. For this to happen, the pump laser for the SPDC process must meet certain conditions. See text for details.

Fig. 2
Fig. 2

Theoretical plot of Eq. (7) as a function of ΔL1 for different ΔL2. (a) ΔL2 = 5.668 mm and (b) ΔL2 = 11.336 mm. (c) The joint count rate when ΔL1 and ΔL2 are simultaneously scanned exhibits the coherence revival property [29, 30].

Fig. 3
Fig. 3

Experimental setup. PBS: polarization beam splitter, QWP: quarter wave plate, D1 and D2: single photon detectors.

Fig. 4
Fig. 4

Experimental data. The coincidence count rate as a function of ΔL1 for different ΔL2 values. (a) ΔL2 = 5.668 mm and (b) ΔL2 = 11.336 mm. The two-photon interference visibility is measure to be 95% for both cases. (c) ΔL1 and ΔL2 are scanned simultaneously. The two-photon interference visibility is measured to be 93%. The experimental data agree well with the theoretical results shown in Fig. 2.

Equations (7)

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| ψ = 1 2 ( | S 1 | S 2 + e i ϕ | L 1 | L 2 ) ,
ρ = d ω p 𝒮 ( ω p ) | ψ ψ | .
𝒮 ( ω p ) = n = N N 𝒮 0 ( ω p ) δ ( ω p ω p 0 n Δ ω p ) n = N N 𝒮 0 ( ω p 0 + n Δ ω p ) ,
| ψ = d ω s d ω i δ ( Δ ω ) sinc ( Δ k l / 2 ) e i Δ k l / 2 | ω s , ω i ,
R Δ τ Δ τ d τ tr [ ρ E D 1 ( ) ( t ) E D 2 ( ) ( t + τ ) E D 2 ( + ) ( t + τ ) E D 1 ( + ) ( t ) ] ,
R d τ tr [ ρ ( E S 2 ( ) ( t + τ ) E S 1 ( ) ( t ) + E L 2 ( ) ( t + τ ξ 2 ) E L 1 ( ) ( t ξ 1 ) ) × ( E S 2 ( + ) ( t + τ ) E S 1 ( + ) ( t ) + E L 2 ( + ) ( t + τ ξ 2 ) E L 1 ( + ) ( t ξ 1 ) ) ] .
R = 1 2 + Γ 2 n = N N 𝒮 eff ( ω p 0 + n Δ ω p ) cos ( ( ω p 0 + n Δ ω p ) ( ξ 1 + ξ 2 ) ) n = N N 𝒮 eff ( ω p 0 + n Δ ω p ) ,

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