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]
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]
K. A. O’Donnell and A. B. U’Ren, “Time-resolved up-conversion of entangled photon pairs,” Phys. Rev. Lett. 103, 123602 (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]
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]
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. 68043813 (2003).
[Crossref]
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]
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]
J. Javanainen and P. L. Gould, “Linear intensity dependence of a two-photon transition rate,” Phys. Rev. A. 41, 5088–5091 (1990).
[Crossref]
[PubMed]
J. Gea-Banacloche, “Two-photon absorption of nonclassical light,” Phys. Rev. Lett. 62, 1603–1606 (1989).
[Crossref]
[PubMed]
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 592044–2046 (1987).
[Crossref]
[PubMed]
M. Bixon and J. Jortner, “Long radiative lifetimes of small molecules,” J. Chem. Phys. 50, 3284–3290 (1969).
[Crossref]
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]
M. Bixon and J. Jortner, “Long radiative lifetimes of small molecules,” J. Chem. Phys. 50, 3284–3290 (1969).
[Crossref]
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]
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]
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]
C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).
J. Gea-Banacloche, “Two-photon absorption of nonclassical light,” Phys. Rev. Lett. 62, 1603–1606 (1989).
[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).
J. Javanainen and P. L. Gould, “Linear intensity dependence of a two-photon transition rate,” Phys. Rev. A. 41, 5088–5091 (1990).
[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]
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. 68043813 (2003).
[Crossref]
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 592044–2046 (1987).
[Crossref]
[PubMed]
J. Javanainen and P. L. Gould, “Linear intensity dependence of a two-photon transition rate,” Phys. Rev. A. 41, 5088–5091 (1990).
[Crossref]
[PubMed]
M. Bixon and J. Jortner, “Long radiative lifetimes of small molecules,” J. Chem. Phys. 50, 3284–3290 (1969).
[Crossref]
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]
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]
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]
See, for example, D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach Science, New York, 1988).
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. 68043813 (2003).
[Crossref]
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]
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).
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 592044–2046 (1987).
[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]
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]
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 592044–2046 (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]
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]
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]
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. 68043813 (2003).
[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]
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]
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. 68043813 (2003).
[Crossref]
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]
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]
K. A. O’Donnell and A. B. U’Ren, “Time-resolved up-conversion of entangled photon pairs,” Phys. Rev. Lett. 103, 123602 (2009).
[Crossref]
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]
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).
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]
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]
M. Bixon and J. Jortner, “Long radiative lifetimes of small molecules,” J. Chem. Phys. 50, 3284–3290 (1969).
[Crossref]
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. 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]
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]
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]
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. 68043813 (2003).
[Crossref]
J. Javanainen and P. L. Gould, “Linear intensity dependence of a two-photon transition rate,” Phys. Rev. A. 41, 5088–5091 (1990).
[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]
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 592044–2046 (1987).
[Crossref]
[PubMed]
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).