Abstract

In this paper, we reveal that some kinds of optical nonlinearities are further enhanced when incoherent light, instead of a laser, is used as a pump light. This idea was confirmed both theoretically and experimentally in the case of sum-frequency generation (SFG) using the optical second nonlinearity. The conversion efficiency of the SFG with incoherent light pumping increased as the bandwidth of the incoherent pump light decreased, finally reaching twice the conversion efficiency of conventional second harmonic generation (SHG) by laser pumping. This method dramatically relaxes the severe requirements of phase matching in the nonlinear optical process. The conversion efficiency became less sensitive to misalignment of the wavelength of pump light and also of device operation temperature when the bandwidth of the incoherent pump light was sufficiently broad, although the improvement of the conversion efficiency had an inverse relationship with the insensitivity to the phase-matching condition. The temperature tuning range was enhanced by more than two orders of magnitude in comparison with the conventional SHG method. As an example of a promising application of this new idea, we performed the generation of quantum entangled photon-pairs using cascaded optical nonlinearities (SFG and the subsequent spontaneous parametric down conversion) in a single periodically poled LiNbO3 waveguide device, in which the incoherent light was used as the pump source for both the parametric processes. We have achieved high fidelity exceeding 99% in quantum-state tomography experiments.

© 2014 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [CrossRef]
  2. M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
    [CrossRef]
  3. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
    [CrossRef]
  4. C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995).
    [CrossRef]
  5. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
    [CrossRef]
  6. A. W. Smith, N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. 6(3), 361–362 (1962).
    [CrossRef]
  7. P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987).
    [CrossRef]
  8. J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24(2), 276–288 (1988).
    [CrossRef]
  9. D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002).
    [CrossRef]
  10. J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012).
    [CrossRef]
  11. T. Kishimoto, K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO3 wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. 23(3), 161–163 (2011).
    [CrossRef]
  12. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ(2) processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011).
    [CrossRef] [PubMed]
  13. M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO3 waveguide,” Opt. Lett. 35(8), 1239–1241 (2010).
    [CrossRef] [PubMed]
  14. S. Arahira, H. Murai, “Nearly degenerate wavelength-multiplexed polarization entanglement by cascaded optical nonlinearities in a PPLN ridge waveguide device,” Opt. Express 21(6), 7841–7850 (2013).
    [CrossRef] [PubMed]
  15. H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express 16(8), 5721–5727 (2008).
    [CrossRef] [PubMed]
  16. H. C. Lim, A. Yoshizawa, H. Tsuchida, K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express 16(17), 12460–12468 (2008).
    [CrossRef] [PubMed]
  17. D. F. V. James, P. G. Kwiat, W. J. Munro, A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
    [CrossRef]
  18. K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46(11), 7175–7187 (2007).
    [CrossRef]
  19. S. Arahira, T. Kishimoto, H. Murai, “1.5-μm band polarization entangled photon-pair source with variable Bell states,” Opt. Express 20(9), 9862–9875 (2012).
    [CrossRef] [PubMed]

2013 (1)

2012 (2)

J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012).
[CrossRef]

S. Arahira, T. Kishimoto, H. Murai, “1.5-μm band polarization entangled photon-pair source with variable Bell states,” Opt. Express 20(9), 9862–9875 (2012).
[CrossRef] [PubMed]

2011 (2)

T. Kishimoto, K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO3 wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. 23(3), 161–163 (2011).
[CrossRef]

S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ(2) processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011).
[CrossRef] [PubMed]

2010 (1)

2008 (2)

2007 (1)

K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46(11), 7175–7187 (2007).
[CrossRef]

2002 (1)

D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002).
[CrossRef]

2001 (1)

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

1999 (1)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

1996 (1)

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

1995 (1)

C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

1988 (1)

J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24(2), 276–288 (1988).
[CrossRef]

1987 (1)

P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987).
[CrossRef]

1962 (2)

A. W. Smith, N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. 6(3), 361–362 (1962).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Arahira, S.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Asobe, M.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Braslau, N.

A. W. Smith, N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. 6(3), 361–362 (1962).
[CrossRef]

Brener, I.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Chaban, E. E.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

Chmela, P.

P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987).
[CrossRef]

Chou, M. H.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

Christman, S. B.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

Dam, J. S.

J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Edamatsu, K.

K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46(11), 7175–7187 (2007).
[CrossRef]

Fejer, M. M.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Ficek, Z.

P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987).
[CrossRef]

Fukuda, H.

Hoffmann, D. M.

D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002).
[CrossRef]

Hunault, M.

Inoue, S.

Itabashi, S.

James, D. F. V.

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

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Kawahara, M.

C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995).
[CrossRef]

Kern, K.

D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002).
[CrossRef]

Kielich, S.

P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987).
[CrossRef]

Kikuchi, K.

Kishimoto, T.

Kuhnke, K.

D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002).
[CrossRef]

Kwiat, P. G.

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

Lim, H. C.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Munro, W. J.

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

Murai, H.

Nakamura, K.

T. Kishimoto, K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO3 wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. 23(3), 161–163 (2011).
[CrossRef]

Namekata, N.

Nishida, Y.

Okayama, H.

C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995).
[CrossRef]

Pedersen, C.

J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Shah, J.

J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24(2), 276–288 (1988).
[CrossRef]

Smith, A. W.

A. W. Smith, N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. 6(3), 361–362 (1962).
[CrossRef]

Tadanaga, O.

Takesue, H.

Tidemand-Lichtenberg, P.

J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012).
[CrossRef]

Tokura, Y.

Tsuchida, H.

Tsuchizawa, T.

Watanabe, T.

White, A. G.

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

Xu, C. Q.

C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995).
[CrossRef]

Yaegashi, H.

Yamada, K.

Yoo, S. J. B.

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

Yoshizawa, A.

IBM J. Res. Develop. (1)

A. W. Smith, N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. 6(3), 361–362 (1962).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24(2), 276–288 (1988).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999).
[CrossRef]

T. Kishimoto, K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO3 wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. 23(3), 161–163 (2011).
[CrossRef]

J. Lightwave Technol. (1)

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46(11), 7175–7187 (2007).
[CrossRef]

Nat. Photonics (1)

J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012).
[CrossRef]

Opt. Commun. (1)

P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Phys. Rev. A (1)

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

Rev. Sci. Instrum. (1)

D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002).
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Sum-frequency generation (SFG) of incoherent light in an optical second nonlinear (χ(2)) device.

Fig. 2
Fig. 2

Electric fields of input incoherent light under study.

Fig. 3
Fig. 3

Calculated results of (a) SFG power (PSFG) and (b) SFG bandwidth (ΔfSFG) as a function of bandwidth of input incoherent light (Δfpump). Solid, dashed, and dotted curves correspond to the cases when the spectrum of input incoherent light is Gaussian, rectangular, and Lorentzian, respectively. Vertical scales are normalized to the SHG power (PSHG) and the SHG bandwidth (ΔfSHG) in the case of conventional SHG with laser pumping. The horizontal scales are also normalized to ΔfSHG.

Fig. 4
Fig. 4

Different pumping methods of SFG with incoherent light pumping. (a) pump with optical amplifier (Amp.) and optical bandpass filter (OBF). (b), (c) pump with LED array.

Fig. 5
Fig. 5

Experimental setup. EDFA: Erbium-doped fiber amplifier. OBF: optical bandpass filter. Pol.: fiber polarizer.

Fig. 6
Fig. 6

(a) Dependence of SFG power on pump power as a function of Δfpump for the 6-cm-long PPLN device. Dashed line in Fig. (a) is the result of the SHG with conventional laser pumping. (b) Relationship between the peak SFG intensity and the ( I p u m p ) 2 Δ f p u m p as a function of Δfpump. The resolution of the optical spectrum analyzer was 0.02 nm.

Fig. 7
Fig. 7

Comparison between the SFG spectrum (black solid curve) with incoherent light pumping and the SHG curve (red open circles) with conventional CW laser pumping. The averaged pump powers for the SFG and SHG were + 10 dBm and + 6 dBm, respectively. The resolution of the optical spectrum analyzer was 0.02 nm.

Fig. 8
Fig. 8

Dependence of (a) SFG power and (b) SFG bandwidth on the bandwidth of input incoherent light. The averaged pump powers remained at 0 dBm. Black closed circles: results for the 6-cm-long device. Red closed triangles: results for the 2-cm-long device. Solid curves are calculated curves assuming Gaussian spectral shapes. The SFG powers are normalized to the SHG power with conventional laser pumping at the same pump power (0 dBm).

Fig. 9
Fig. 9

Temperature dependence of SFG powers as a function of the bandwidth of the input incoherent light. The pump powers remained at the same (0 dBm). Dashed curve is reference of the SHG by the conventional laser pumping.

Fig. 10
Fig. 10

Dependence of tunable temperature range (δT) on the bandwidth of input incoherent light. Red closed circles: experimental results. Dashed curve: calculated results.

Fig. 11
Fig. 11

Temperature tuning characteristics of the SHG power when a multi-longitudinal-mode Fabry-Perot laser was used for the pump light.

Fig. 12
Fig. 12

Experimental setup for correlated photon-pair generation by cascaded SFG/SPDC with incoherent light source. EDFA: Erbium-doped fiber amplifier. OBF: optical bandpass filter. Pol.: fiber polarizer. LPF: optical low pass filter. HPF: optical high pass filter. D1, D2: single photon detector.

Fig. 13
Fig. 13

Dependence of coincidence counts (Rm-Rum) on (a) averaged pump power and (b) SFG power as a function of the bandwidth of input incoherent pump light. Dashed lines are the results of cascaded SHG/SPDC with conventional laser pumping.

Fig. 14
Fig. 14

Experimental setup for generation of polarization-entangled photon pairs. PBSC: polarization beam splitter/combiner. BSC: Babinet-Soreil compensator. HWP: half-wave plate. QWP: quarter-wave plate.

Fig. 15
Fig. 15

Reconstructed density matrices at different pump powers. (a) pump power = + 3.2 dBm/facet. (b) pump power = + 12.9 dBm. The mean number of photon-pairs per gate was estimated to be (a) 0.0055 and (b) 0.367, respectively.

Fig. 16
Fig. 16

Summary of quantum-state tomography experiments. Black circles: purity (P). Red triangles: fidelity (F). Blue squares: fidelity of the Werner state.

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

p ( f o ) Δf=2d l=1 N ( e l Δf )( e l Δf ) e j( k l + k l )zj( ϕ l + ϕ l )
d e f 0 dz Δf=j2dA l=1 N ( e l Δf )( e l Δf ) e jΔ k l zj( ϕ l + ϕ l )
Δ k l k f 0 k l k l K
e f 0 =j2dAL l=1 N e l e l Δf e j( ϕ l + ϕ l )
i SFG ( f 0 )Δf=B | e f 0 | 2 =4 d 2 A 2 B L 2 ( Δf ) 2 ( l=1 N e l e l e j( ϕ l + ϕ l ) )( m=1 N e m e m e +j( ϕ m + ϕ m ) )
i SFG ( f 0 )=4 d 2 A 2 B L 2 ( Δf ) l=1 N | e l | 2 | e l | 2
i SFG ( f 0 )=4 d 2 C( Δf ) l=1 N i l i l
S in ( f )= I pump e 4ln( 2 ) (f f 0 /2) 2 / ( Δ f pump ) 2
( Δf ) l=1 N i l i l f 0 /2 + { S in ( f ) } 2 df= ( I pump ) 2 2 π 8ln( 2 ) ( Δ f pump )
P pump = S in ( f ) df= I pump π 4ln( 2 ) ( Δ f pump )
i SFG ( f 0 )=2 d 2 C 2ln( 2 ) π ( P pump ) 2 ( Δ f pump )
P SFG 1.129 i SFG ( f 0 )Δ f SHG
P SFG =1.129×2 d 2 C 2ln( 2 ) π ( P pump ) 2 ( Δ f pump ) ( Δ f SHG )1.5 d 2 C ( P pump ) 2 ( Δ f SHG ) ( Δ f pump ) .
P SHG = d 2 C ( P pump ) 2
i SFG ( f )=4 d 2 C 0 + sin 2 ( ΔL ) ( ΔL ) 2 S in ( f/2 +x ) S in ( f/2 x ) dx
Δ k f k f/2 +x k f/2 x K
P SFG = i SFG ( f ) df
Δ k f k f/2 +x k f/2 x K= 2π n f λ f 2πa λ f 4πbK
Δ 2π n f λ f 2πa λ f 4πbK= 2π n f λ f 4πa λ f/2 4πbK= k f 2 k f/2 K
i SFG ( f )=4 d 2 C sin 2 ( ΔL ) ( ΔL ) 2 0 + S in ( f/2 +x ) S in ( f/2 x ) dx
sin 2 { 0.8859π( f f 0 ) / Δ f SHG } / { 0.8859π( f f 0 ) / Δ f SHG } 2
i SFG ( f )=2 d 2 C 2ln( 2 ) π ( P pump ) 2 ( Δ f pump ) sin 2 { 0.8859π( f f 0 ) / Δ f SHG } { 0.8859π( f f 0 ) / Δ f SHG } 2 e 2ln( 2 ) ( f f 0 +2 δ p ) 2 / ( Δ f pump ) 2
P SHG = d 2 C ( P pump ) 2 sin 2 ( 2 δ p Δ f SHG ×0.8859π ) ( 2 δ p Δ f SHG ×0.8859π ) 2
i SFG ( f )2 d 2 C 2ln( 2 ) π ( P pump ) 2 ( Δ f pump ) e 2ln( 2 ) ( f f 0 ) 2 / ( Δ f pump ) 2
P SFG =2 d 2 C ( P pump ) 2
δ p,max Δ f pump / 2
δ p,max Δ f SHG /2
i SFG ( f 0 )=2 d 2 C π 8ln( 2 ) ( I pump ) 2 Δ f pump
Δ f SHG 2 <Δ f pump <1.2Δ f SHG
ρ W =( 1a )| Φ ( + ) Φ ( + ) |+ 1 4 aI= 1 2 ( 1a/2 0 0 1a 0 a/2 0 0 0 0 a/2 0 1a 0 0 1a/2 )
F= 1+3V 4
P= 1+3 V 2 4

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