Abstract

The dependence of the excitonic two-photon absorption on the quantum correlations (entanglement) of exciting biphotons by a semiconductor quantum well is studied. We show that entangled photon absorption can display very unusual features depending on space-time-polarization biphoton parameters and absorber density of states for both bound exciton states as well as for unbound electron-hole pairs. We report on the connection between biphoton entanglement, as quantified by the Schmidt number, and absorption by a semiconductor quantum well. Comparison between frequency-anti-correlated, unentangled and frequency-correlated biphoton absorption is addressed. We found that exciton oscillator strengths are highly increased when photons arrive almost simultaneously in an entangled state. Two-photon-absorption becomes a highly sensitive probe of photon quantum correlations when narrow semiconductor quantum wells are used as two-photon absorbers.

© 2012 Optical Society of America

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
  2. Y. Shih, “Entangled biphoton source - property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
    [CrossRef]
  3. For a recent review see K. Edamatsu, “Entangled photons: Generation, observation, and characterization,” Jap. J. Appl. Phys. 46, 7175–7187 (2007).
    [CrossRef]
  4. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
    [CrossRef]
  5. A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
    [CrossRef]
  6. L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
    [CrossRef] [PubMed]
  7. M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
    [CrossRef]
  8. B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175(5), 1555–1563 (1968).
    [CrossRef]
  9. G. S. Agarwal, “Field-correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
    [CrossRef]
  10. A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
    [CrossRef]
  11. S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
    [CrossRef]
  12. A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
    [CrossRef]
  13. J. Kojima and Q. -V. Nguyen, “Entangled biphoton virtual-state spectroscopy of the A2Σ2 – X2Π system of OH,” Chem. Phys. Lett. 396(4–6), 323–328 (2004).
    [CrossRef]
  14. D. -I. Lee and T. Goodson, “Entangled photon absorption in an organic Porphyrin Dendrimer,” J. Phys. Chem. B 110(51), 25582–25585 (2006).
    [CrossRef] [PubMed]
  15. M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
    [CrossRef] [PubMed]
  16. A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
    [CrossRef] [PubMed]
  17. F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
    [CrossRef]
  18. H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett. 93(9), 093002 (2004).
    [CrossRef] [PubMed]
  22. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
    [CrossRef]
  23. F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
    [CrossRef]
  24. A. Hayat, P. Ginzburg, and M. Orenstein, “High-rate entanglement source via two-photon emission from semiconductor quantum wells,” Phys. Rev. B 76(3), 035339 (2007).
    [CrossRef]
  25. R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
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    [CrossRef]
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    [CrossRef]
  28. M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, “Gaussian modelling and Schmidt modes of SPDC biphoton states,” J. Phys. B: At. Mol. Opt. Phys. 42(17), 175503 (2009).
    [CrossRef]
  29. T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
    [CrossRef]
  30. H. N. Spector, “Two-photon absorption in semiconducting quantum-well structures,” Phys. Rev. B 35(11), 5876–5879 (1987).
    [CrossRef]
  31. A. Pasquarello and A. Quattropani, “Gauge-invariant two-photon transitions in quantum wells,” Phys. Rev. B 38(9), 6206–6210 (1988).
    [CrossRef]
  32. A. Pasquarello and A. Quattropani, “Two-photon transitions to excitons in quantum wells,” Phys. Rev. B 42(14), 9073–9079 (1990).
    [CrossRef]
  33. G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
    [CrossRef]
  34. S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
    [CrossRef]
  35. A. Shimizu, “Two-photon absorption in quantum-well structures near half the direct band gap,” Phys. Rev. B 40(2), 1403–1406 (1989).
    [CrossRef]
  36. P. Harrison, Quantum Wells, Wires and Dots, 3rd edition (John Wiley and Sons Ltd., Chichester, 2009).
  37. H. Oka, “Efficient selective two-photon excitation by tailored quantum-correlated photons,” Phys. Rev. A 81(6), 063819 (2010); , “Efficient two-step up-conversion by quantum-correlated photon pairs,” Opt. Express 18(25), 25839–25846 (2010).
    [CrossRef]

2011 (3)

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

J. Svozilk, M. Hendrych, A. S. Helmy, and J. P. Torres, “Generation of paired photons in a quantum separable state in Bragg reflection waveguides,” Opt. Express 19(4), 3115–3123 (2011).
[CrossRef]

2010 (2)

H. Oka, “Efficient selective two-photon excitation by tailored quantum-correlated photons,” Phys. Rev. A 81(6), 063819 (2010); , “Efficient two-step up-conversion by quantum-correlated photon pairs,” Opt. Express 18(25), 25839–25846 (2010).
[CrossRef]

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

2009 (5)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
[CrossRef]

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, “Gaussian modelling and Schmidt modes of SPDC biphoton states,” J. Phys. B: At. Mol. Opt. Phys. 42(17), 175503 (2009).
[CrossRef]

T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
[CrossRef]

2008 (1)

Y. M. Mikhailova, P. A. Volkov, and M. V. Fedorov, “Biphoton wave packets in parametric down-conversion: Spectral and temporal structure and degree of entanglement,” Phys. Rev. A 78(6), 062327 (2008).
[CrossRef]

2007 (3)

A. Hayat, P. Ginzburg, and M. Orenstein, “High-rate entanglement source via two-photon emission from semiconductor quantum wells,” Phys. Rev. B 76(3), 035339 (2007).
[CrossRef]

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

For a recent review see K. Edamatsu, “Entangled photons: Generation, observation, and characterization,” Jap. J. Appl. Phys. 46, 7175–7187 (2007).
[CrossRef]

2006 (2)

S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
[CrossRef]

D. -I. Lee and T. Goodson, “Entangled photon absorption in an organic Porphyrin Dendrimer,” J. Phys. Chem. B 110(51), 25582–25585 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
[CrossRef]

2004 (4)

L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
[CrossRef] [PubMed]

J. Kojima and Q. -V. Nguyen, “Entangled biphoton virtual-state spectroscopy of the A2Σ2 – X2Π system of OH,” Chem. Phys. Lett. 396(4–6), 323–328 (2004).
[CrossRef]

F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
[CrossRef]

A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett. 93(9), 093002 (2004).
[CrossRef] [PubMed]

2003 (1)

Y. Shih, “Entangled biphoton source - property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
[CrossRef]

1999 (2)

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

1998 (2)

B. E. A. Saleh, B. M. Jost, H.- Bing Fei, and M. C. Teich, “Entangled-photon virtual-state spectroscopy,” Phys. Rev. Lett. 80(16), 3483–3486 (1998).
[CrossRef]

J. Peřina, B. E. A. Saleh, and M. C. Teich, “Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state,” Phys. Rev. A 57(5), 3972–3986 (1998).
[CrossRef]

1997 (1)

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

1991 (1)

S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
[CrossRef]

1990 (1)

A. Pasquarello and A. Quattropani, “Two-photon transitions to excitons in quantum wells,” Phys. Rev. B 42(14), 9073–9079 (1990).
[CrossRef]

1989 (1)

A. Shimizu, “Two-photon absorption in quantum-well structures near half the direct band gap,” Phys. Rev. B 40(2), 1403–1406 (1989).
[CrossRef]

1988 (1)

A. Pasquarello and A. Quattropani, “Gauge-invariant two-photon transitions in quantum wells,” Phys. Rev. B 38(9), 6206–6210 (1988).
[CrossRef]

1987 (1)

H. N. Spector, “Two-photon absorption in semiconducting quantum-well structures,” Phys. Rev. B 35(11), 5876–5879 (1987).
[CrossRef]

1982 (1)

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
[CrossRef]

1970 (1)

G. S. Agarwal, “Field-correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
[CrossRef]

1968 (1)

B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175(5), 1555–1563 (1968).
[CrossRef]

Agarwal, G. S.

A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett. 93(9), 093002 (2004).
[CrossRef] [PubMed]

G. S. Agarwal, “Field-correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
[CrossRef]

Bastard, G.

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
[CrossRef]

Bauerle, P.

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

Bing Fei, H.-

B. E. A. Saleh, B. M. Jost, H.- Bing Fei, and M. C. Teich, “Entangled-photon virtual-state spectroscopy,” Phys. Rev. Lett. 80(16), 3483–3486 (1998).
[CrossRef]

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

Blatt, R.

L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
[CrossRef] [PubMed]

Boitier, F.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
[CrossRef]

Carrasco, S.

S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
[CrossRef]

Ceré, A.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

Chang, L. L.

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
[CrossRef]

Chemla, D. S.

S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
[CrossRef]

Chuang, I. L.

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

Chuang, S.-L.

S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
[CrossRef]

Cundiff, S. T.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Dayan, B.

A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
[CrossRef]

Delaye, P.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

Dubreuil, N.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

Edamatsu, K.

For a recent review see K. Edamatsu, “Entangled photons: Generation, observation, and characterization,” Jap. J. Appl. Phys. 46, 7175–7187 (2007).
[CrossRef]

Esaki, L.

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
[CrossRef]

Fabre, C.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
[CrossRef]

Fedorov, M. V.

M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, “Gaussian modelling and Schmidt modes of SPDC biphoton states,” J. Phys. B: At. Mol. Opt. Phys. 42(17), 175503 (2009).
[CrossRef]

Y. M. Mikhailova, P. A. Volkov, and M. V. Fedorov, “Biphoton wave packets in parametric down-conversion: Spectral and temporal structure and degree of entanglement,” Phys. Rev. A 78(6), 062327 (2008).
[CrossRef]

Friesem, A. A.

A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
[CrossRef]

Ginzburg, P.

A. Hayat, P. Ginzburg, and M. Orenstein, “High-rate entanglement source via two-photon emission from semiconductor quantum wells,” Phys. Rev. B 76(3), 035339 (2007).
[CrossRef]

Godard, A.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
[CrossRef]

Goodson, T.

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

D. -I. Lee and T. Goodson, “Entangled photon absorption in an organic Porphyrin Dendrimer,” J. Phys. Chem. B 110(51), 25582–25585 (2006).
[CrossRef] [PubMed]

Guzman, A. R.

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

Haley, M. M.

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

Harpham, M. R.

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

Harrison, P.

P. Harrison, Quantum Wells, Wires and Dots, 3rd edition (John Wiley and Sons Ltd., Chichester, 2009).

Hayat, A.

A. Hayat, P. Ginzburg, and M. Orenstein, “High-rate entanglement source via two-photon emission from semiconductor quantum wells,” Phys. Rev. B 76(3), 035339 (2007).
[CrossRef]

Helmy, A. S.

Hendrych, M.

Hudson, A. J.

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

Hunter, A. E.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Jost, B. M.

B. E. A. Saleh, B. M. Jost, H.- Bing Fei, and M. C. Teich, “Entangled-photon virtual-state spectroscopy,” Phys. Rev. Lett. 80(16), 3483–3486 (1998).
[CrossRef]

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

Kira, M.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Kitano, M.

T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
[CrossRef]

Kobayashi, H.

T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
[CrossRef]

Koch, S. W.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Kojima, J.

J. Kojima and Q. -V. Nguyen, “Entangled biphoton virtual-state spectroscopy of the A2Σ2 – X2Π system of OH,” Chem. Phys. Lett. 396(4–6), 323–328 (2004).
[CrossRef]

Lee, D. -I.

D. -I. Lee and T. Goodson, “Entangled photon absorption in an organic Porphyrin Dendrimer,” J. Phys. Chem. B 110(51), 25582–25585 (2006).
[CrossRef] [PubMed]

Lissandrin, F.

F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
[CrossRef]

Ma, C. Q.

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

Mendez, E. E.

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
[CrossRef]

Mikhailova, Y. M.

M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, “Gaussian modelling and Schmidt modes of SPDC biphoton states,” J. Phys. B: At. Mol. Opt. Phys. 42(17), 175503 (2009).
[CrossRef]

Y. M. Mikhailova, P. A. Volkov, and M. V. Fedorov, “Biphoton wave packets in parametric down-conversion: Spectral and temporal structure and degree of entanglement,” Phys. Rev. A 78(6), 062327 (2008).
[CrossRef]

Miller, D. A. B.

S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
[CrossRef]

Molina-Terriza, G.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

Mollow, B. R.

B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175(5), 1555–1563 (1968).
[CrossRef]

Muthukrishnan, A.

A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett. 93(9), 093002 (2004).
[CrossRef] [PubMed]

Nakanishi, T.

T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
[CrossRef]

Nguyen, Q. -V.

J. Kojima and Q. -V. Nguyen, “Entangled biphoton virtual-state spectroscopy of the A2Σ2 – X2Π system of OH,” Chem. Phys. Lett. 396(4–6), 323–328 (2004).
[CrossRef]

Nicoll, C. A.

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

Nielsen, M. A.

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

Oka, H.

H. Oka, “Efficient selective two-photon excitation by tailored quantum-correlated photons,” Phys. Rev. A 81(6), 063819 (2010); , “Efficient two-step up-conversion by quantum-correlated photon pairs,” Opt. Express 18(25), 25839–25846 (2010).
[CrossRef]

Orenstein, M.

A. Hayat, P. Ginzburg, and M. Orenstein, “High-rate entanglement source via two-photon emission from semiconductor quantum wells,” Phys. Rev. B 76(3), 035339 (2007).
[CrossRef]

Pasquarello, A.

A. Pasquarello and A. Quattropani, “Two-photon transitions to excitons in quantum wells,” Phys. Rev. B 42(14), 9073–9079 (1990).
[CrossRef]

A. Pasquarello and A. Quattropani, “Gauge-invariant two-photon transitions in quantum wells,” Phys. Rev. B 38(9), 6206–6210 (1988).
[CrossRef]

Pe’er, A.

A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
[CrossRef]

Perina, J.

J. Peřina, B. E. A. Saleh, and M. C. Teich, “Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state,” Phys. Rev. A 57(5), 3972–3986 (1998).
[CrossRef]

Popescu, S.

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

Quattropani, A.

A. Pasquarello and A. Quattropani, “Two-photon transitions to excitons in quantum wells,” Phys. Rev. B 42(14), 9073–9079 (1990).
[CrossRef]

A. Pasquarello and A. Quattropani, “Gauge-invariant two-photon transitions in quantum wells,” Phys. Rev. B 38(9), 6206–6210 (1988).
[CrossRef]

Rabl, P.

L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
[CrossRef] [PubMed]

Ritchie, D. A.

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

Rosencher, E.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
[CrossRef]

Saleh, B. E. A.

S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
[CrossRef]

F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
[CrossRef]

B. E. A. Saleh, B. M. Jost, H.- Bing Fei, and M. C. Teich, “Entangled-photon virtual-state spectroscopy,” Phys. Rev. Lett. 80(16), 3483–3486 (1998).
[CrossRef]

J. Peřina, B. E. A. Saleh, and M. C. Teich, “Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state,” Phys. Rev. A 57(5), 3972–3986 (1998).
[CrossRef]

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

Schmitt-Rink, S.

S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
[CrossRef]

Scully, M. O.

A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett. 93(9), 093002 (2004).
[CrossRef] [PubMed]

Sergienko, A. V.

S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
[CrossRef]

F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
[CrossRef]

Shi, X.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

Shields, A. J.

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

Shih, Y.

Y. Shih, “Entangled biphoton source - property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
[CrossRef]

Shimizu, A.

A. Shimizu, “Two-photon absorption in quantum-well structures near half the direct band gap,” Phys. Rev. B 40(2), 1403–1406 (1989).
[CrossRef]

Silberberg, Y.

A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
[CrossRef]

Smith, R. P.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Spector, H. N.

H. N. Spector, “Two-photon absorption in semiconducting quantum-well structures,” Phys. Rev. B 35(11), 5876–5879 (1987).
[CrossRef]

Stevenson, R. M.

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

Sugiyama, K.

T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
[CrossRef]

Süzer, Ö.

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

Svozilk, J.

Teich, M. C.

S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
[CrossRef]

F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
[CrossRef]

B. E. A. Saleh, B. M. Jost, H.- Bing Fei, and M. C. Teich, “Entangled-photon virtual-state spectroscopy,” Phys. Rev. Lett. 80(16), 3483–3486 (1998).
[CrossRef]

J. Peřina, B. E. A. Saleh, and M. C. Teich, “Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state,” Phys. Rev. A 57(5), 3972–3986 (1998).
[CrossRef]

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

Tian, L.

L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
[CrossRef] [PubMed]

Torres, J. P.

J. Svozilk, M. Hendrych, A. S. Helmy, and J. P. Torres, “Generation of paired photons in a quantum separable state in Bragg reflection waveguides,” Opt. Express 19(4), 3115–3123 (2011).
[CrossRef]

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

Valencia, A.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

Volkov, P. A.

M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, “Gaussian modelling and Schmidt modes of SPDC biphoton states,” J. Phys. B: At. Mol. Opt. Phys. 42(17), 175503 (2009).
[CrossRef]

Y. M. Mikhailova, P. A. Volkov, and M. V. Fedorov, “Biphoton wave packets in parametric down-conversion: Spectral and temporal structure and degree of entanglement,” Phys. Rev. A 78(6), 062327 (2008).
[CrossRef]

Young, R. J.

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

Zeilinger, A.

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

Zoller, P.

L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

J. Kojima and Q. -V. Nguyen, “Entangled biphoton virtual-state spectroscopy of the A2Σ2 – X2Π system of OH,” Chem. Phys. Lett. 396(4–6), 323–328 (2004).
[CrossRef]

J. Am. Chem. Soc. (2)

M. R. Harpham, Ö. Süzer, C. Q. Ma, P. Bauerle, and T. Goodson, “Thiophene Dendrimers as entangled photon sensor materials,” J. Am. Chem. Soc. 131(3), 973–979 (2009).
[CrossRef] [PubMed]

A. R. Guzman, M. R. Harpham, Ö. Süzer, M. M. Haley, and T. Goodson, “Spatial control of entangled two-photon absorption with organic chromophores,” J. Am. Chem. Soc. 132(23), 7840–7841 (2010).
[CrossRef] [PubMed]

J. Phys. B: At. Mol. Opt. Phys. (1)

M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, “Gaussian modelling and Schmidt modes of SPDC biphoton states,” J. Phys. B: At. Mol. Opt. Phys. 42(17), 175503 (2009).
[CrossRef]

J. Phys. Chem. B (1)

D. -I. Lee and T. Goodson, “Entangled photon absorption in an organic Porphyrin Dendrimer,” J. Phys. Chem. B 110(51), 25582–25585 (2006).
[CrossRef] [PubMed]

J. Phys. Soc. Japan (1)

T. Nakanishi, H. Kobayashi, K. Sugiyama, and M. Kitano, “Full quantum analysis of two-photon absorption using two-photon wave function: Comparison of two-photon absorption with one-photon absorption,” J. Phys. Soc. Japan 78(10), 104401 (2009); quant-ph/0906.0213.
[CrossRef]

Jap. J. Appl. Phys. (1)

For a recent review see K. Edamatsu, “Entangled photons: Generation, observation, and characterization,” Jap. J. Appl. Phys. 46, 7175–7187 (2007).
[CrossRef]

Nature Commun. (1)

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nature Commun. 2, 425 (2011).
[CrossRef]

Nature Phys. (2)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nature Phys. 5(4), 267–270 (2009).
[CrossRef]

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Opt. Express (1)

Phys. Rev. (1)

B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175(5), 1555–1563 (1968).
[CrossRef]

Phys. Rev. A (5)

G. S. Agarwal, “Field-correlation effects in multiphoton absorption processes,” Phys. Rev. A 1(5), 1445–1459 (1970).
[CrossRef]

S. Carrasco, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spectral engineering of entangled two-photon states,” Phys. Rev. A 73(6), 063802 (2006).
[CrossRef]

J. Peřina, B. E. A. Saleh, and M. C. Teich, “Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state,” Phys. Rev. A 57(5), 3972–3986 (1998).
[CrossRef]

Y. M. Mikhailova, P. A. Volkov, and M. V. Fedorov, “Biphoton wave packets in parametric down-conversion: Spectral and temporal structure and degree of entanglement,” Phys. Rev. A 78(6), 062327 (2008).
[CrossRef]

H. Oka, “Efficient selective two-photon excitation by tailored quantum-correlated photons,” Phys. Rev. A 81(6), 063819 (2010); , “Efficient two-step up-conversion by quantum-correlated photon pairs,” Opt. Express 18(25), 25839–25846 (2010).
[CrossRef]

Phys. Rev. B (8)

A. Hayat, P. Ginzburg, and M. Orenstein, “High-rate entanglement source via two-photon emission from semiconductor quantum wells,” Phys. Rev. B 76(3), 035339 (2007).
[CrossRef]

H. N. Spector, “Two-photon absorption in semiconducting quantum-well structures,” Phys. Rev. B 35(11), 5876–5879 (1987).
[CrossRef]

A. Pasquarello and A. Quattropani, “Gauge-invariant two-photon transitions in quantum wells,” Phys. Rev. B 38(9), 6206–6210 (1988).
[CrossRef]

A. Pasquarello and A. Quattropani, “Two-photon transitions to excitons in quantum wells,” Phys. Rev. B 42(14), 9073–9079 (1990).
[CrossRef]

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Exciton binding energy in quantum wells,” Phys. Rev. B 26(4), 1974–1979 (1982).
[CrossRef]

S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Exciton Greens-function approach to optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 43(2), 1500–1509 (1991).
[CrossRef]

A. Shimizu, “Two-photon absorption in quantum-well structures near half the direct band gap,” Phys. Rev. B 40(2), 1403–1406 (1989).
[CrossRef]

F. Lissandrin, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum theory of entangled-photon photoemission,” Phys. Rev. B 69(16), 165317 (2004).
[CrossRef]

Phys. Rev. Lett. (7)

H.- Bing Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78(9), 1679–1682 (1997).
[CrossRef]

B. E. A. Saleh, B. M. Jost, H.- Bing Fei, and M. C. Teich, “Entangled-photon virtual-state spectroscopy,” Phys. Rev. Lett. 80(16), 3483–3486 (1998).
[CrossRef]

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99(24), 243601 (2007).
[CrossRef]

A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, “Temporal shaping of entangled photons,” Phys. Rev. Lett. 94(7), 073601 (2005).
[CrossRef]

R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-Inequality violation with a triggered photon-pair source,” Phys. Rev. Lett.,  102(3), 030406 (2009).
[CrossRef] [PubMed]

A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett. 93(9), 093002 (2004).
[CrossRef] [PubMed]

L. Tian, P. Rabl, R. Blatt, and P. Zoller, “Interfacing quantum-optical and solid-state qubits,” Phys. Rev. Lett. 92(24), 247902 (2004).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

Y. Shih, “Entangled biphoton source - property and preparation,” Rep. Prog. Phys. 66, 1009–1044 (2003).
[CrossRef]

Rev. Mod. Phys. (2)

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[CrossRef]

Other (2)

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

P. Harrison, Quantum Wells, Wires and Dots, 3rd edition (John Wiley and Sons Ltd., Chichester, 2009).

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Figures (7)

Fig. 1
Fig. 1

SPDC-II produced biphotons shining a semiconductor QW. Orthogonal signal/idler polarizations are shown. T denotes the laser pump duration whereas τ is associated with the entanglement-time of the signal/idler pair as generated by the SPDC nonlinear crystal.

Fig. 2
Fig. 2

(a) Biphoton entanglement measure, Schmidt K number, as a function of τ T . (b), (c) and (d): Joint spectral intensity from Eq. (3). The Schmidt number for graphs (b) and (d) is the same, K = 3. In (b) τ T < 1 corresponding to a a FAC biphoton while in (d) τ T > 1 related to a FC biphoton. For graph (c) the Schmidt number is K = 1 corresponding to an unentangled biphoton state. Axes display the signal and idler frequencies in units of ω p ( 0 ) with ω p ( 0 ) τ = 500 .

Fig. 3
Fig. 3

Schematic diagram of energy levels for a semiconductor quantum well. Two photon transitions involving electron-hole states (brown arrows) and exciton states (green arrows) are depicted. Ci is the ith conduction sub-band, HHi is the ith heavy hole valence sub-band and Xi denote discrete exciton states.

Fig. 4
Fig. 4

ETPA, as a function of ω/ωg, by a L = aB/2 QW when excitonic effects are not included. Main graph corresponds to highly quantum correlated biphotons with ωgτ = 50. Blue curve describes frequency-anti-correlated biphotons with K = 1.3. Black curve denotes unentangled biphotons, K = 1. Red curve corresponds to frequency-correlated bipho-tons with K = 1.3. Upper inset: ETPA from weakly quantum correlated biphotons with ωgτ = 500. Bottom inset: Differential ETPA for K = 1.3 biphotons: FAC, blue curve; FC, red curve.

Fig. 5
Fig. 5

ETPA by a L = aB QW with excitonic effects included, for highly quantum correlated biphotons, ωgτ = 100 and different photon entanglement, K. In each plot, FAC (black curves) and FC (red curves). For K = 1 red and black curves are the same.

Fig. 6
Fig. 6

Excitonic ETPA (left column) and continuous electron-hole ETPA (right column) by QWs of thickness L = aB/2 (first row), L = aB (second row) and L = 2aB (third row). Red curves correspond to highly quantum correlated biphotons, ωgτ = 50 and K = 1.3 while unentangled biphoton results, K = 1, are represented by black curves. Notice the different vertical scales.

Fig. 7
Fig. 7

Excitonic ETPA as a function of the pump laser coherence time, T, for two QW thicknesses and different degrees of signal/idler quantum correlation times. Solid curves, ωgτ = 50. Dashed curves, ωgτ = 100. HH2-C1 exciton in black, HH1-C2 exciton in red (X2 exciton state in Fig. 3) and HH3-C2 exciton in green.

Equations (12)

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

ψ ( t 1 , t 2 ) = 0 | a ^ 2 ( t 2 ) a ^ 1 ( t 1 ) | Ψ 2
Ψ ( ω 1 , ω 2 ) = N ¯ e ( ω 1 + ω 2 ω p ( 0 ) ) 2 T 2 Φ ( ω 1 ω 2 δ ω )
Ψ ( ω 1 , ω 2 ) = N ¯ e ( ω 1 + ω 2 ω p ( 0 ) ) 2 T 2 e ( ω 1 ω 2 δ ω ) 2 τ 2
K = 1 2 ( τ T + T τ )
θ ( t ) = { 1 t 0 0 t < 0
α 2 ( n c , n v , k ) = i 8 π 2 P c v L h ¯ m 0 E g e 2 1 2 n c n v ( n c 2 n v 2 ) 2 d t 2 d t 1 θ ( t 2 t 1 ) e i Ω 2 t 2 e i Ω 1 t 1 ψ ( t 1 , t 2 )
h ¯ Ω 1 = E g + h ¯ 2 π 2 2 μ L 2 n 2 + h ¯ 2 k 2 2 μ , n = min { n c , n v }
h ¯ Ω 2 = h ¯ 2 π 2 2 m c * L 2 ( n c 2 n v 2 ) , n c > n v h ¯ Ω 2 = h ¯ 2 π 2 2 m v * L 2 ( n v 2 n c 2 ) , n v > n c
Ψ ˜ ( ω 1 , ω 2 ) = τ T π e ( ω 1 + ω 2 ω p ( 0 ) ) 2 T 2 F [ ( ω 1 ω 2 δ ω ) τ 2 ]
α 2 ( n c , n v , k ) = i 16 π P c v L h ¯ m 0 E g e 2 1 2 n c n v ( n c 2 n v 2 ) 2 Ψ ˜ ( Ω 1 , Ω 2 )
𝒫 2 ( ω ) = Δ n = 1 n ˜ = 1 , 3 , 5 ν = c , v [ n ( n + n ˜ ) ( n ˜ ( 2 n + n ˜ ) ) 2 ] 2 0 d κ κ | Ψ ˜ ( 1 + α ( n 2 + κ 2 ) , α n ˜ ( 2 n + n ˜ ) μ m ν * ) | 2
𝒫 2 ( ω ) = Δ n = 1 n ˜ = 1 , 3 , 5 ν = c , v [ n ( n + n ˜ ) ( n ˜ ( 2 n + n ˜ ) ) 2 ] 2 [ a B 4 L 2 | Φ 1 S ( r = 0 ) | 2 | Ψ ˜ ( 1 + α n 2 α 1 S , α n ˜ ( 2 n + n ˜ ) μ m ν * ) | 2 + 0 d κ κ | Φ e h ( κ , r = 0 ) | 2 | Ψ ˜ ( 1 + α ( n 2 + κ 2 ) , α n ˜ ( 2 n + n ˜ ) μ m ν * ) | 2 ]

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