Abstract

We theoretically investigate the sequential two-step up-conversion of correlated photon pairs with positive and negative energy correlations, in terms of how the up-conversion efficiency depends on the incident pulse delay. A three-level atomic system having a metastable state is used to evaluate the up-conversion efficiency. It is shown that a photon pair with a positive energy correlation can drastically enhance the up-conversion efficiency compared with uncorrelated photons and correlated photons with a negative energy correlation.

© 2010 Optical Society of America

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  1. R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
    [CrossRef]
  2. F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
    [CrossRef]
  3. A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
    [CrossRef]
  4. C. V. Bennett, and B. H. Kolner, "Upconversion time microscope demonstrating 103 × magnification of femtosecond waveforms," Opt. Lett. 24, 783-785 (1999).
    [CrossRef]
  5. K. A. O’Donnell and A. B. U’Ren, "Time-resolved up-conversion of entangled photon pairs," Phys. Rev. Lett. 103, 123602 (2009).
    [CrossRef]
  6. J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
    [CrossRef] [PubMed]
  7. J. Javanainen, and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
    [CrossRef] [PubMed]
  8. N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
    [CrossRef] [PubMed]
  9. V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).
  10. J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
    [CrossRef] [PubMed]
  11. M. Hendrych, M. Micuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339-2341 (2007).
    [CrossRef] [PubMed]
  12. R. Shimizu, and K. Edamatsu, "High-flux and broadband biphoton sources with controlled frequency entanglement," Opt. Express 17, 16385-16393 (2009).
    [CrossRef] [PubMed]
  13. H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
    [CrossRef]
  14. M. Bixon, and J. Jortner, "Long radiative lifetimes of small molecules," J. Chem. Phys. 50, 3284-3290 (1969).
    [CrossRef]
  15. C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).
  16. See, for example,D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach Science, New York, 1988).
  17. C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
    [CrossRef] [PubMed]
  18. We adopt the energies of an Er atom, 4I15/2, 4I11/2, 4I9/2, and 4F7/2 for |g〉, |mB〉, |mA〉, and |e〉, respectively. Further, we ignore influences of other energy levels for simplicity.
  19. H. Oka, "Efficient selective two-photon excitation by tailored quantum-correlated photons," Phys. Rev. A 81, 063819 (2010).
    [CrossRef]
  20. H. Oka, "Real-time analysis of two-photon excitation by correlated photons: Pulse-width dependence of excitation efficiency," Phys. Rev. A 81, 053837 (2010).
    [CrossRef]
  21. See, for example,D. A. Kalashnikov, K. G. Katamadze, and S. P. Kulik, "Controlling the spectrum of a two photon field: Inhomogeneous broadening due to a temperature gradient," JETP Lett. 89, 224-228 (2009).
    [CrossRef]

2010 (2)

H. Oka, "Efficient selective two-photon excitation by tailored quantum-correlated photons," Phys. Rev. A 81, 063819 (2010).
[CrossRef]

H. Oka, "Real-time analysis of two-photon excitation by correlated photons: Pulse-width dependence of excitation efficiency," Phys. Rev. A 81, 053837 (2010).
[CrossRef]

2009 (3)

See, for example,D. A. Kalashnikov, K. G. Katamadze, and S. P. Kulik, "Controlling the spectrum of a two photon field: Inhomogeneous broadening due to a temperature gradient," JETP Lett. 89, 224-228 (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]

K. A. O’Donnell and A. B. U’Ren, "Time-resolved up-conversion of entangled photon pairs," Phys. Rev. Lett. 103, 123602 (2009).
[CrossRef]

2007 (1)

M. Hendrych, M. Micuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339-2341 (2007).
[CrossRef] [PubMed]

2005 (2)

J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
[CrossRef] [PubMed]

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

2003 (1)

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
[CrossRef]

2002 (2)

V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

2000 (1)

R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
[CrossRef]

1999 (1)

C. V. Bennett, and B. H. Kolner, "Upconversion time microscope demonstrating 103 × magnification of femtosecond waveforms," Opt. Lett. 24, 783-785 (1999).
[CrossRef]

1995 (1)

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

1990 (1)

J. Javanainen, and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

1989 (1)

J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
[CrossRef] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

1969 (1)

M. Bixon, and J. Jortner, "Long radiative lifetimes of small molecules," J. Chem. Phys. 50, 3284-3290 (1969).
[CrossRef]

Bennett, C. V.

C. V. Bennett, and B. H. Kolner, "Upconversion time microscope demonstrating 103 × magnification of femtosecond waveforms," Opt. Lett. 24, 783-785 (1999).
[CrossRef]

Bettinelli, M.

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

Biswas, A.

R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
[CrossRef]

Bixon, M.

M. Bixon, and J. Jortner, "Long radiative lifetimes of small molecules," J. Chem. Phys. 50, 3284-3290 (1969).
[CrossRef]

Boyer, J.

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

Capobianco, J. A.

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

Carrasco, S.

J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
[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]

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Friend, C. S.

R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
[CrossRef]

Gea-Banacloche, J.

J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
[CrossRef] [PubMed]

Georgiades, N. P.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Giovannetti, V.

V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).

Gould, P. L.

J. Javanainen, and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

Güdel, H. U.

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

Hendrych, M.

M. Hendrych, M. Micuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339-2341 (2007).
[CrossRef] [PubMed]

Hofmann, H. F.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Javanainen, J.

J. Javanainen, and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

Jortner, J.

M. Bixon, and J. Jortner, "Long radiative lifetimes of small molecules," J. Chem. Phys. 50, 3284-3290 (1969).
[CrossRef]

Kalashnikov, D. A.

See, for example,D. A. Kalashnikov, K. G. Katamadze, and S. P. Kulik, "Controlling the spectrum of a two photon field: Inhomogeneous broadening due to a temperature gradient," JETP Lett. 89, 224-228 (2009).
[CrossRef]

Kapoor, R.

R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
[CrossRef]

Katamadze, K. G.

See, for example,D. A. Kalashnikov, K. G. Katamadze, and S. P. Kulik, "Controlling the spectrum of a two photon field: Inhomogeneous broadening due to a temperature gradient," JETP Lett. 89, 224-228 (2009).
[CrossRef]

Kimble, H. J.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Kojima, K.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
[CrossRef]

Kolner, B. H.

C. V. Bennett, and B. H. Kolner, "Upconversion time microscope demonstrating 103 × magnification of femtosecond waveforms," Opt. Lett. 24, 783-785 (1999).
[CrossRef]

Kulik, S. P.

See, for example,D. A. Kalashnikov, K. G. Katamadze, and S. P. Kulik, "Controlling the spectrum of a two photon field: Inhomogeneous broadening due to a temperature gradient," JETP Lett. 89, 224-228 (2009).
[CrossRef]

Maccone, L.

V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).

Macià, F.

J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
[CrossRef] [PubMed]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Micuda, M.

M. Hendrych, M. Micuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339-2341 (2007).
[CrossRef] [PubMed]

O’Donnell, K. A.

K. A. O’Donnell and A. B. U’Ren, "Time-resolved up-conversion of entangled photon pairs," Phys. Rev. Lett. 103, 123602 (2009).
[CrossRef]

Oka, H.

H. Oka, "Efficient selective two-photon excitation by tailored quantum-correlated photons," Phys. Rev. A 81, 063819 (2010).
[CrossRef]

H. Oka, "Real-time analysis of two-photon excitation by correlated photons: Pulse-width dependence of excitation efficiency," Phys. Rev. A 81, 053837 (2010).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Parkins, A. S.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Polzik, E. S.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Prasad, P. N.

R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
[CrossRef]

Richards, B. S.

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

Sasaki, K.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
[CrossRef]

Shalav, A.

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

Shapiro, J. H.

V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).

Shimizu, R.

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

Speghini, A.

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

Takeuchi, S.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
[CrossRef]

Torner, L.

J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
[CrossRef] [PubMed]

Torres, J. P.

M. Hendrych, M. Micuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339-2341 (2007).
[CrossRef] [PubMed]

J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
[CrossRef] [PubMed]

Trupke, T.

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

U’Ren, A. B.

K. A. O’Donnell and A. B. U’Ren, "Time-resolved up-conversion of entangled photon pairs," Phys. Rev. Lett. 103, 123602 (2009).
[CrossRef]

Vetrone, F.

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

Wong, F. N. C.

V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).

Würfel, P.

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

F. Vetrone, J. Boyer, J. A. Capobianco, A. Speghini, and M. Bettinelli, "980 nm excited upconversion in an Er-doped ZnO-TeO2 glass," Appl. Phys. Lett. 80, 1752-1754 (2002).
[CrossRef]

A. Shalav, B. S. Richards, T. Trupke, P. Würfel, and H. U. Güdel, "Application of NaYF4:Er3+ up-converting phosphors for enhanced near-infrared silicon solar cell response," Appl. Phys. Lett. 86, 013505 (2005).
[CrossRef]

J. Chem. Phys. (1)

M. Bixon, and J. Jortner, "Long radiative lifetimes of small molecules," J. Chem. Phys. 50, 3284-3290 (1969).
[CrossRef]

JETP Lett. (1)

See, for example,D. A. Kalashnikov, K. G. Katamadze, and S. P. Kulik, "Controlling the spectrum of a two photon field: Inhomogeneous broadening due to a temperature gradient," JETP Lett. 89, 224-228 (2009).
[CrossRef]

Opt. Express (1)

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

Opt. Lett. (4)

C. V. Bennett, and B. H. Kolner, "Upconversion time microscope demonstrating 103 × magnification of femtosecond waveforms," Opt. Lett. 24, 783-785 (1999).
[CrossRef]

J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314-316 (2005).
[CrossRef] [PubMed]

M. Hendrych, M. Micuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339-2341 (2007).
[CrossRef] [PubMed]

R. Kapoor, C. S. Friend, A. Biswas, and P. N. Prasad, "Highly efficient infrared-to-visible energy upconversion in Er3+:Y2O3," Opt. Lett. 25, 338-340 (2000).
[CrossRef]

Phys. Rev. A (4)

J. Javanainen, and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom," Phys. Rev. A 68, 043813 (2003).
[CrossRef]

H. Oka, "Efficient selective two-photon excitation by tailored quantum-correlated photons," Phys. Rev. A 81, 063819 (2010).
[CrossRef]

H. Oka, "Real-time analysis of two-photon excitation by correlated photons: Pulse-width dependence of excitation efficiency," Phys. Rev. A 81, 053837 (2010).
[CrossRef]

Phys. Rev. Lett. (5)

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

N. P. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, and A. S. Parkins, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).

K. A. O’Donnell and A. B. U’Ren, "Time-resolved up-conversion of entangled photon pairs," Phys. Rev. Lett. 103, 123602 (2009).
[CrossRef]

J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
[CrossRef] [PubMed]

Other (3)

We adopt the energies of an Er atom, 4I15/2, 4I11/2, 4I9/2, and 4F7/2 for |g〉, |mB〉, |mA〉, and |e〉, respectively. Further, we ignore influences of other energy levels for simplicity.

C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).

See, for example,D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach Science, New York, 1988).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the sequential two-step up-conversion geometry. (b) One-dimensional atom model.

Fig. 2
Fig. 2

|ψ2p|2 for (a) uncorrelated photons, (b) TB photons, and (c) DB photons. (d) Spectra corresponding to (a), (b), and (c). Δ = 0 and σ ≈ 30λ, where λ = 2π/k0.

Fig. 3
Fig. 3

mA〉 and 〈e〉 as a function of r/σ for (a) uncorrelated photons, (b) TB photons, and (c) DB photons.

Fig. 4
Fig. 4

(a) ξ as a function of Δ/σ. (b) ξ as a function of σ/λ for Δ/σ = 0 and 10.

Equations (9)

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H ^ = d k k a ^ k a ^ k + ω e | e e | + = A , B ω m | m m | + d k Γ mg π ( | m A g | a ^ k + H . c . ) + d k Γ em π ( | e m B | a ^ k + H . c . ) + d k Γ eg π ( | e g | a ^ k + H . c . ) + H ^ relax .
H ^ relax = dq q p ^ q p ^ q + dq γ π ( | m A m B | p ^ q + H . c . ) ,
| Ψ ( t ) = exp ( i H ^ t ) | Ψ ( 0 ) ,
| Ψ ( 0 ) = 1 2 dk d k ψ 2 p ( k , k ) a ^ k a ^ k | 0 | g ,
ψ 2 p ( k , k ) = ψ ( k ) ψ ( k ) e ik r 0 e i k r 0 ,
ψ 2 p ( k , k ) = ψ ( k ) δ ( k + k 2 k 0 ) e i k r 0 e i k r 0 ,
ψ 2 p ( k , k ) = ψ ( k ) δ ( k k ) e ik r 0 e i k r 0 ,
ψ ( k ) e ik r 0 = 1 2 π d r ψ ( r ) exp ( ikr )
ψ ( r ) exp [ ( r r 0 ) 2 / σ 2 + i k 0 ( r r 0 ) ] ,

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