Abstract

We analyze the formation of two-dimensional biexcitons and the role of exciton dark states decoupled from the cavity mode in semiconductor microcavities containing a few resonating quantum wells. Although optically inactive, the dark levels are important because they contribute states available to the excitons. A general formalism is presented for the treatment of excitons, photon modes, and biexcitons in resonating microcavities. Scattering by disorder and phonons is also considered. Results for the biexciton binding energy, radius, and damping are discussed in the physically relevant cases. The cavity biexciton photoluminescence spectra are also investigated; they are found to be qualitatively different depending on the relative magnitudes of the exciton-cavity detuning, the biexciton binding energy, the exciton–photon coupling, and the damping.

© 1998 Optical Society of America

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  1. E. Burstein and C. Weisbuch, eds., Confined Electrons and Photons: New Physics and Applications (Plenum, New York, 1995); H. Yokoyama and K. Ujihara, eds., Spontaneous Emission and Laser Oscillations in Microcavities (CRC, Boca Raton, 1995); and references therein.
  2. V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
    [CrossRef]
  3. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
    [CrossRef] [PubMed]
  4. H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
    [CrossRef]
  5. T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
    [CrossRef] [PubMed]
  6. T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
    [CrossRef] [PubMed]
  7. A. L. Ivanov and H. Haug, Phys. Rev. Lett. 74, 438 (1995);A. L. Ivanov and H. Haug, Nuovo Cimento D 17, 1255 (1995).
    [CrossRef] [PubMed]
  8. F. Tassone, F. Bassani, and L. C. Andreani, Nuovo Cimento D 12, 1673 (1990);L. C. Andreani, Phys. Lett. A 192, 99 (1994);D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
    [CrossRef]
  9. For polarization along the growth direction, the fundamental mode of the cavity has the same dispersion as a free photon, and a situation similar to that of Ref. 7 would result.
  10. If the distance of the wells from the cavity center is comparable to the wavelength, appropriate phase factors should be included in all following expressions (for instance, in the definition of the exciton state coupled to light, b1k). For the sake of simplicity we have avoided their introduction, which does not alter any of the physically significant effects.
  11. D. A. Kleinman, Phys. Rev. B 28, 871 (1983).
    [CrossRef]
  12. R. M. Hochstrasser and J. D. Whiteman, J. Chem. Phys. 56, 5945 (1972).
    [CrossRef]
  13. V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
    [CrossRef]
  14. D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
    [CrossRef]
  15. This may lead to an additional luminescence band between the Raby split lines [see also the discussion in R. Houdre, R. P. Stanley, and M. Ilegems, Phys. Rev. A 53, 2711 (1996)]. A dark state partially activated by mixing with an optically active one may also be responsible for the so called weak-coupling component observed in resonant Raman scattering [ A. Fainstein, B. Jusserand, and V. Thierry-Mieg, Phys. Rev. Lett. 78, 1576 (1997)].
    [CrossRef]
  16. Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
    [CrossRef]
  17. F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
    [CrossRef]
  18. Short-wavelength phonons as well as interface and confined-phonon modes associated with the multiple-quantum-well structure may lead to a partial mixing of the b states because they are coupled to excitons in different wells.
  19. V. M. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun. 102, 631 (1997).
    [CrossRef]
  20. A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
    [CrossRef] [PubMed]
  21. It would be interesting to calculate the biexciton properties in the presence of the cavity along the lines followed in Ref. 7 for a free quantum well.
  22. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory (Pergamon, London, 1958), Sect. 45, pp. 153–156; B. Simon, Ann. Phys. (N.Y.) 97, 279 (1976).
    [CrossRef]
  23. R. Cingolani and K. Ploog, Adv. Phys. 40, 535 (1991);J. C. Kim, D. R. Wake, and J. P. Wolfe, Phys. Rev. B 50, 15099 (1994).
    [CrossRef]
  24. V. M. Agranovich and S. Mukamel, Phys. Lett. A 147, 155 (1990).
    [CrossRef]

1997 (1)

V. M. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun. 102, 631 (1997).
[CrossRef]

1996 (5)

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

This may lead to an additional luminescence band between the Raby split lines [see also the discussion in R. Houdre, R. P. Stanley, and M. Ilegems, Phys. Rev. A 53, 2711 (1996)]. A dark state partially activated by mixing with an optically active one may also be responsible for the so called weak-coupling component observed in resonant Raman scattering [ A. Fainstein, B. Jusserand, and V. Thierry-Mieg, Phys. Rev. Lett. 78, 1576 (1997)].
[CrossRef]

Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
[CrossRef]

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

1995 (3)

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
[CrossRef]

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

A. L. Ivanov and H. Haug, Phys. Rev. Lett. 74, 438 (1995);A. L. Ivanov and H. Haug, Nuovo Cimento D 17, 1255 (1995).
[CrossRef] [PubMed]

1994 (1)

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

1993 (1)

D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
[CrossRef]

1992 (1)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
[CrossRef] [PubMed]

1991 (1)

R. Cingolani and K. Ploog, Adv. Phys. 40, 535 (1991);J. C. Kim, D. R. Wake, and J. P. Wolfe, Phys. Rev. B 50, 15099 (1994).
[CrossRef]

1990 (3)

V. M. Agranovich and S. Mukamel, Phys. Lett. A 147, 155 (1990).
[CrossRef]

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

F. Tassone, F. Bassani, and L. C. Andreani, Nuovo Cimento D 12, 1673 (1990);L. C. Andreani, Phys. Lett. A 192, 99 (1994);D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

1983 (1)

D. A. Kleinman, Phys. Rev. B 28, 871 (1983).
[CrossRef]

1972 (1)

R. M. Hochstrasser and J. D. Whiteman, J. Chem. Phys. 56, 5945 (1972).
[CrossRef]

Afshar, A. M.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Agranovich, V. M.

V. M. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun. 102, 631 (1997).
[CrossRef]

V. M. Agranovich and S. Mukamel, Phys. Lett. A 147, 155 (1990).
[CrossRef]

Anan, T.

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

Andreani, L. C.

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
[CrossRef]

F. Tassone, F. Bassani, and L. C. Andreani, Nuovo Cimento D 12, 1673 (1990);L. C. Andreani, Phys. Lett. A 192, 99 (1994);D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

Arakawa, Y.

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
[CrossRef] [PubMed]

Armitage, A.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Bassani, F.

F. Tassone, F. Bassani, and L. C. Andreani, Nuovo Cimento D 12, 1673 (1990);L. C. Andreani, Phys. Lett. A 192, 99 (1994);D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

Benisty, H.

V. M. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun. 102, 631 (1997).
[CrossRef]

Bjork, G.

Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
[CrossRef]

Brorson, S. D.

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

Cao, H.

Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
[CrossRef]

Cingolani, R.

R. Cingolani and K. Ploog, Adv. Phys. 40, 535 (1991);J. C. Kim, D. R. Wake, and J. P. Wolfe, Phys. Rev. B 50, 15099 (1994).
[CrossRef]

Citrin, D. S.

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
[CrossRef]

Fisher, T. A.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Haug, H.

A. L. Ivanov and H. Haug, Phys. Rev. Lett. 74, 438 (1995);A. L. Ivanov and H. Haug, Nuovo Cimento D 17, 1255 (1995).
[CrossRef] [PubMed]

Hochstrasser, R. M.

R. M. Hochstrasser and J. D. Whiteman, J. Chem. Phys. 56, 5945 (1972).
[CrossRef]

Houdre, R.

This may lead to an additional luminescence band between the Raby split lines [see also the discussion in R. Houdre, R. P. Stanley, and M. Ilegems, Phys. Rev. A 53, 2711 (1996)]. A dark state partially activated by mixing with an optically active one may also be responsible for the so called weak-coupling component observed in resonant Raman scattering [ A. Fainstein, B. Jusserand, and V. Thierry-Mieg, Phys. Rev. Lett. 78, 1576 (1997)].
[CrossRef]

Ilegems, M.

This may lead to an additional luminescence band between the Raby split lines [see also the discussion in R. Houdre, R. P. Stanley, and M. Ilegems, Phys. Rev. A 53, 2711 (1996)]. A dark state partially activated by mixing with an optically active one may also be responsible for the so called weak-coupling component observed in resonant Raman scattering [ A. Fainstein, B. Jusserand, and V. Thierry-Mieg, Phys. Rev. Lett. 78, 1576 (1997)].
[CrossRef]

Ippen, E. P.

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

Ishikawa, A.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
[CrossRef] [PubMed]

Ivanov, A. L.

A. L. Ivanov and H. Haug, Phys. Rev. Lett. 74, 438 (1995);A. L. Ivanov and H. Haug, Nuovo Cimento D 17, 1255 (1995).
[CrossRef] [PubMed]

Kinsler, P.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Kleinman, D. A.

D. A. Kleinman, Phys. Rev. B 28, 871 (1983).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory (Pergamon, London, 1958), Sect. 45, pp. 153–156; B. Simon, Ann. Phys. (N.Y.) 97, 279 (1976).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory (Pergamon, London, 1958), Sect. 45, pp. 153–156; B. Simon, Ann. Phys. (N.Y.) 97, 279 (1976).
[CrossRef]

Mukamel, S.

V. M. Agranovich and S. Mukamel, Phys. Lett. A 147, 155 (1990).
[CrossRef]

Nishi, K.

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

Nishioka, M.

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
[CrossRef] [PubMed]

Norris, T. B.

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

Pau, S.

Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
[CrossRef]

Piermarocchi, C.

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

Ploog, K.

R. Cingolani and K. Ploog, Adv. Phys. 40, 535 (1991);J. C. Kim, D. R. Wake, and J. P. Wolfe, Phys. Rev. B 50, 15099 (1994).
[CrossRef]

Quattropani, A.

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
[CrossRef]

Rhee, J.-K.

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

Roberts, J. S.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Savona, V.

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
[CrossRef]

Schwendimann, P.

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
[CrossRef]

Skolnick, M. S.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Stanley, R. P.

This may lead to an additional luminescence band between the Raby split lines [see also the discussion in R. Houdre, R. P. Stanley, and M. Ilegems, Phys. Rev. A 53, 2711 (1996)]. A dark state partially activated by mixing with an optically active one may also be responsible for the so called weak-coupling component observed in resonant Raman scattering [ A. Fainstein, B. Jusserand, and V. Thierry-Mieg, Phys. Rev. Lett. 78, 1576 (1997)].
[CrossRef]

Sturge, M. D.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Sung, C.-Y.

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

Tassone, F.

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

F. Tassone, F. Bassani, and L. C. Andreani, Nuovo Cimento D 12, 1673 (1990);L. C. Andreani, Phys. Lett. A 192, 99 (1994);D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

Weisbuch, C.

V. M. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun. 102, 631 (1997).
[CrossRef]

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
[CrossRef] [PubMed]

Whiteman, J. D.

R. M. Hochstrasser and J. D. Whiteman, J. Chem. Phys. 56, 5945 (1972).
[CrossRef]

Whittaker, D. M.

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Yamada, H.

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

Yamamoto, Y.

Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
[CrossRef]

Yokoyama, H.

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

Adv. Phys. (1)

R. Cingolani and K. Ploog, Adv. Phys. 40, 535 (1991);J. C. Kim, D. R. Wake, and J. P. Wolfe, Phys. Rev. B 50, 15099 (1994).
[CrossRef]

Appl. Phys. Lett. (1)

H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S. D. Brorson, and E. P. Ippen, Appl. Phys. Lett. 57, 2814 (1990);T. Yamauchi, Y. Arakawa, and M. Nishioka, Appl. Phys. Lett. 58, 2339 (1991);Y. Yamamoto, S. Machida, and G. Björk, Surf. Sci. 267, 605 (1992).
[CrossRef]

J. Chem. Phys. (1)

R. M. Hochstrasser and J. D. Whiteman, J. Chem. Phys. 56, 5945 (1972).
[CrossRef]

Nuovo Cimento D (2)

T. B. Norris, J.-K. Rhee, D. S. Citrin, M. Nishioka, and Y. Arakawa, Nuovo Cimento D 17, 1295 (1995);R. Houdré, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, Phys. Rev. B 52, 7810 (1995);A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, and F. Bassani, Phys. Rev. A 54, 3493 (1996).
[CrossRef] [PubMed]

F. Tassone, F. Bassani, and L. C. Andreani, Nuovo Cimento D 12, 1673 (1990);L. C. Andreani, Phys. Lett. A 192, 99 (1994);D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

Phys. Lett. A (1)

V. M. Agranovich and S. Mukamel, Phys. Lett. A 147, 155 (1990).
[CrossRef]

Phys. Rev. A (1)

This may lead to an additional luminescence band between the Raby split lines [see also the discussion in R. Houdre, R. P. Stanley, and M. Ilegems, Phys. Rev. A 53, 2711 (1996)]. A dark state partially activated by mixing with an optically active one may also be responsible for the so called weak-coupling component observed in resonant Raman scattering [ A. Fainstein, B. Jusserand, and V. Thierry-Mieg, Phys. Rev. Lett. 78, 1576 (1997)].
[CrossRef]

Phys. Rev. B (6)

Here we assume that the structural quality is high enough to preclude such a localization along the cavity axis. See also the discussion in H. Cao, S. Pau, Y. Yamamoto, and G. Bjork, Phys. Rev. B 54, 8083 (1996).
[CrossRef]

F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 7642 (1996).
[CrossRef]

V. Savona, F. Tassone, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Phys. Rev. B 53, 13051 (1996).
[CrossRef]

D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
[CrossRef]

D. A. Kleinman, Phys. Rev. B 28, 871 (1983).
[CrossRef]

T. B. Norris, J.-K. Rhee, C.-Y. Sung, Y. Arakawa, M. Nishioka, and C. Weisbuch, Phys. Rev. B 50, 14663 (1994);J. Jacobson, S. Pau, H. Cao, G. Björk, and Y. Yamamoto, Phys. Rev. A 51, 2542 (1995);S. Long, B. Sermage, I. Abram, J. Bloch, R. Planel, and V. Thierry-Mieg, Nuovo Cimento D 17, 1601 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

A. L. Ivanov and H. Haug, Phys. Rev. Lett. 74, 438 (1995);A. L. Ivanov and H. Haug, Nuovo Cimento D 17, 1255 (1995).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992);R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Phys. Rev. Lett. 73, 2043 (1994).
[CrossRef] [PubMed]

A discussion of this issue, also in relation to the motional narrowing considered in D. M. Whittaker, P. Kinsler, T. A. Fisher, M. S. Skolnick, A. Armitage, A. M. Afshar, M. D. Sturge, and J. S. Roberts, Phys. Rev. Lett. 77, 4792 (1996), will be given elsewhere [V. M. Agranovich, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. (to be published)].
[CrossRef] [PubMed]

Solid State Commun. (2)

V. M. Agranovich, H. Benisty, and C. Weisbuch, Solid State Commun. 102, 631 (1997).
[CrossRef]

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, Solid State Commun. 93, 733 (1995).
[CrossRef]

Other (6)

E. Burstein and C. Weisbuch, eds., Confined Electrons and Photons: New Physics and Applications (Plenum, New York, 1995); H. Yokoyama and K. Ujihara, eds., Spontaneous Emission and Laser Oscillations in Microcavities (CRC, Boca Raton, 1995); and references therein.

For polarization along the growth direction, the fundamental mode of the cavity has the same dispersion as a free photon, and a situation similar to that of Ref. 7 would result.

If the distance of the wells from the cavity center is comparable to the wavelength, appropriate phase factors should be included in all following expressions (for instance, in the definition of the exciton state coupled to light, b1k). For the sake of simplicity we have avoided their introduction, which does not alter any of the physically significant effects.

Short-wavelength phonons as well as interface and confined-phonon modes associated with the multiple-quantum-well structure may lead to a partial mixing of the b states because they are coupled to excitons in different wells.

It would be interesting to calculate the biexciton properties in the presence of the cavity along the lines followed in Ref. 7 for a free quantum well.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory (Pergamon, London, 1958), Sect. 45, pp. 153–156; B. Simon, Ann. Phys. (N.Y.) 97, 279 (1976).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of cavity quasi particles and biexciton luminescence in the strong-coupling regime: The solid curve gives the biexciton dispersion, the long-dashed, short-dashed, and dotted curves give, respectively, the upper-cavity polariton, lower-cavity polariton, and dark-exciton dispersion (note that the energy scale is broken and the wave vector scale is logarithmic; the broadenings are not indicated and numerical values are representative of GaAs-based microcavities). The vertical arrows indicate transitions that possibly lead to cavity-biexciton luminescence, when the conditions discussed in the text are fulfilled.

Fig. 2
Fig. 2

Schematic diagram of cavity quasi particles and biexciton luminescence in the weak-coupling regime: the solid curve gives the biexciton dispersion, the long-dashed and dotted curves give, respectively, the cavity mode and exciton dispersion (note that the energy scale is broken and the wave vector scale is logarithmic; the broadenings are not indicated; numerical values are representative of GaAs-based microcavities). The vertical arrows indicate transitions possibly leading to cavity-biexciton luminescence when the conditions discussed in the text are fulfilled.

Fig. 3
Fig. 3

Dispersion relations and broadenings in the (a) strong-, (b) semistrong-, and (c) weak-coupling regimes. On the left of the vertical axes the corresponding densities of states at k0 are also shown.

Fig. 4
Fig. 4

Schematic diagram of the cavity-mode energy ωc(0) as a function of the effective cavity thickness L (solid line); also indicated are the exciton energy ωe(0) (long-dashed line) and the exciton energy minus the biexciton binding energy Ebo (short-dashed line). The arrows mark the thickness Lo at which the exciton-cavity detuning vanishes and the thickness Lo at which the cavity-biexciton luminescence at low temperature is resonantly enhanced (see text; numerical values are representative of II–VI semiconductor-based microcavities).

Equations (44)

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ωc(k)=ωc(0)1+(kL/π)2,
ωe(k)=ωe(0)+2k22M,
Ho=kωc(k)akak+αωe(k)BαkBαk-δ2 α(Bαkak+Bαkak),
Hee=1A α,k,q,QVQBαkBαqBαk-QBαq+Q,
bjk=αBαkTα,j,α, j=1,2N,
Ho=kωc(k)akak+ωe(k)b1kb1k-Δ2 (b1kak+b1kak)+j>1ωe(k)bjkbjk,
b1k=F1b(k)p1k+F2b(k)p2k,
ak=F1a(k)p1k+F2a(k)p2k,
[ωe(k)-ωpj(k)]Fjb(k)-Δ2 Fja(k)
=0=[ωc(k)-ωpj(k)]Fja(k)-Δ2 Fjb(k),
ωp1,2(k)=ωe(k)+ωc(k)2±12 [ωe(k)-ωc(k)]2+Δ2/2.
Ho=kωp1(k)p1kp1k+ωp2(k)p2kp2k+j>1ωe(k)bjkbjk.
Bαk=j=1NTα,jbjk=1N [F1b(k)p1k+F2b(k)p2k]+j=2NTα,jbjk.
c1kp1k,c2kp2k,
cjkb(j-1)k,j=3, 4N+1,
Sα,1(k)Tα,1F1b(k),Sα,2(k)Tα,1F2b(k),
Sα,j(k)Tα,j-1,j=3, 4N+1,
E1(k)ωp1(k),E2(k)ωp2(k),
Ej(k)ωe(k),j=3, 4N+1.
H=Ho+Hee=i=1N+1kEi(k)cikcik+i,j,m,n=1N+1k,q,QVk,q,Qijmncikcjqcmk-Qcnq+Q,
Vk,q,Qijmn=1A αVQSα,i(k)Sα,j(q)×Sα,m(k-Q)Sα,n(q+Q)=Vq,k,-Qjinm.
Hep=α,k,q,qzWk,q,qzBαkBαk-q(dq,qz+d-q,qz),
Hep=i,j=1N+1k,q,qzWk,q,qzcikcjk-q(dq,qz+d-q,qz)×αSα,i(k)Sα,j(k-q).
αSα,i(k)Sα,j(k-q)=αTα,i-1Tα,j-1=δij,
αSα,i(k)Sα,j(k-q)=α 1N Fib(k)Tα,j-1=0.
Hed=α,k,qUk,q(α)BαkBαq=i,j=1N+1k,qMij(k, q)cikcjq,
Mij(k, q)=αUk,q(α)Sα,i(k)Sα,j(q).
M22(k, q)=αUk,q(α)Sα,2(k)Sα,2(q)=F2b(k)F2b(q) 1N αUk,q(α).
U(α)(r)U(β)(0)=U02 exp(-r2/l02)δα,β;
1N αU(α)(r) 1N βU(β)(0)
=1N U(α)(r)U(α)(0).
|Φχ=ijQΦχij(Q)ci(χ/2+Q)cj(χ/2-Q)|0,
[Ei(|χ/2+Q|)+Ej(|χ/2-Q|)-E(χ)]Φχij(Q)
=-2mnqVχ/2+Q,χ/2-Q,Q-qijmnΦχmn(q).
ωp2(k)=ω0-Δ2+2k24M+ω0 k2L24π2+O(k4)=ω0-Δ2+2k22mp+O(k4),
[2ωp2(k)-(2ωp2(0)-Ebp2)]Φ(k)
=-2qVk,-k,k-q2222Φ(q).
2k2mp+Ebp2Φ(k)-2qΦ(q)1A αVk-qSα,2(k)×Sα,2(-k)Sα,2(q)Sα,2(-q)=-2qΦ(q) 1AN Vk-q[F2b(k)]2×[F2b(q)]2-12AN qVk-qΦ(q).
Ebp22mpa2 exp-22/mp|V(r)|rdrMmp exp(-4M/mp)Eb0Eb0,
abp2exp(2M/mp)ab0ab0.
ω=ωe(0)-2χ24M-Ebo,
ω=2ωe-Ebo-E2ωo+Δ/2-Ebo,
ω=2ωe-Ebo-E1ωo-Δ/2-Ebo;
ω=2ωe-Ebo-Ej>2ωo-Ebo.

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