Abstract

We investigate effects of inhomogeneous broadening of excitons on normal mode oscillation in semiconductor microcavities using a coupled oscillator model. We show that inhomogeneous broadening can drastically alter the coherent oscillatory energy exchange process even in regimes where normal mode splitting remains nearly unchanged. The depth, frequency, and phase of normal mode oscillations of excitons at a given energy within the inhomogeneous distribution depend strongly on the energy separation between the exciton and the normal mode resonance. In addition, for an inhomogeneous broadened system, pronounced oscillations in the intensity of the optical field or the total induced optical polarization no longer imply a similar oscillatory coherent energy exchange between excitons and cavity photons.

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References

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  1. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, "Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity," Phys. Rev. Lett. 69, 3314 (1992).
    [CrossRef] [PubMed]
  2. T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, C. Weisbuch, "Time-resolved vacuum Rabi oscillations in a semiconductor quantum microcavity," Phys. Rev. B 50, 14663 (1994).
    [CrossRef]
  3. J. Jacobson, S. Pau, H. Cao, G. Bjork, Y. Yamamoto, "Observation of exciton-polariton oscillating emission in a single-quantum-well semiconductor microcavity," Phys. Rev. A 51 2542 (1995).
    [CrossRef] [PubMed]
  4. Hailin Wang, Jagdeep Shah, T. C. Damen, W. Y. Jan, J. E. Cunningham, M. H. Hong, and J. P. Mannaerts, "Coherent oscillations in semiconductor microcavities," Phys. Rev. B 51, 14713 (1995).
    [CrossRef]
  5. D. Bogavarapu, D. McAlister, A. Anderson, M. Munroe, M. G. Raymer, G. Khitrova, and H. M. Gibbs, "Ultrafast photon statistics of normal mode coupling in a semiconductor microcavity," Quantum Electronics and Laser Science Conference, OSA Technical Digest 9, 33 (1996).
  6. S. Pau, G. Bjork, H. Cao, E. Hanamura, and Y. Yamamoto, "Theory of inhomogeneous microcavity polariton splitting," Solid State Commun. 98, 781 (1996).
    [CrossRef]
  7. F. Jahnke, M. Ruopp, M. Kira, and S. W. Koch, "Ultrafast pulse propagation and excitonic nonlinearities in semiconductor microcavities," Adv. in Solid State Phys. 37, accepted for publication (1997).
  8. H. J. Carmichael , "Quantum fluctuations in absorptive bistability without adiabatic elimination," Phys. Rev. A 33, 3262 (1986).
    [CrossRef] [PubMed]
  9. Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, Vacuum Rabi splitting as a feature of linear dispersion theory, Phys. Rev. Lett. 64, 2499 (1990).
    [CrossRef] [PubMed]
  10. M. Kira, F. Jahnke, S. W. Koch, "Ultrashort pulse propagation effects in semiconductor microcavities," Solid State Commun. 102, 703 (1997).
    [CrossRef]
  11. R. Zimmermann and E. Runge, "Exciton lineshape in semiconductor quantum structures with interface roughness," J. Lumin. 60&61, 320 (1994).
    [CrossRef]
  12. D.M. Whittaker, P. Kinsler, T.A. Fisher, M.S. Skolnick, A. Armitage, A.M. Afshar, M.D. Sturge, and J.S. Roberts, "Motional narrowing in semiconductor microcavities," Phys. Rev. Lett. 77, 4792 (1996).
    [CrossRef] [PubMed]
  13. V. Savona, C. Piermarocchi, A. Quattropani, F. Tassone, and P. Schwendimann, "Microscopic theory of motional narrowing of microcavity polaritons in a disordered potential," Phys. Rev. Lett. 78, 4470 (1997).
    [CrossRef]
  14. Different line width for lower and upper cavity-polaritons can also be obtained by using the simple coupled-oscillator model and an asymmetric inhomogeneous lineshape.

Other (14)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, "Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity," Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

T. B. Norris, J. K. Rhee, C. Y. Sung, Y. Arakawa, M. Nishioka, C. Weisbuch, "Time-resolved vacuum Rabi oscillations in a semiconductor quantum microcavity," Phys. Rev. B 50, 14663 (1994).
[CrossRef]

J. Jacobson, S. Pau, H. Cao, G. Bjork, Y. Yamamoto, "Observation of exciton-polariton oscillating emission in a single-quantum-well semiconductor microcavity," Phys. Rev. A 51 2542 (1995).
[CrossRef] [PubMed]

Hailin Wang, Jagdeep Shah, T. C. Damen, W. Y. Jan, J. E. Cunningham, M. H. Hong, and J. P. Mannaerts, "Coherent oscillations in semiconductor microcavities," Phys. Rev. B 51, 14713 (1995).
[CrossRef]

D. Bogavarapu, D. McAlister, A. Anderson, M. Munroe, M. G. Raymer, G. Khitrova, and H. M. Gibbs, "Ultrafast photon statistics of normal mode coupling in a semiconductor microcavity," Quantum Electronics and Laser Science Conference, OSA Technical Digest 9, 33 (1996).

S. Pau, G. Bjork, H. Cao, E. Hanamura, and Y. Yamamoto, "Theory of inhomogeneous microcavity polariton splitting," Solid State Commun. 98, 781 (1996).
[CrossRef]

F. Jahnke, M. Ruopp, M. Kira, and S. W. Koch, "Ultrafast pulse propagation and excitonic nonlinearities in semiconductor microcavities," Adv. in Solid State Phys. 37, accepted for publication (1997).

H. J. Carmichael , "Quantum fluctuations in absorptive bistability without adiabatic elimination," Phys. Rev. A 33, 3262 (1986).
[CrossRef] [PubMed]

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, Vacuum Rabi splitting as a feature of linear dispersion theory, Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

M. Kira, F. Jahnke, S. W. Koch, "Ultrashort pulse propagation effects in semiconductor microcavities," Solid State Commun. 102, 703 (1997).
[CrossRef]

R. Zimmermann and E. Runge, "Exciton lineshape in semiconductor quantum structures with interface roughness," J. Lumin. 60&61, 320 (1994).
[CrossRef]

D.M. Whittaker, P. Kinsler, T.A. Fisher, M.S. Skolnick, A. Armitage, A.M. Afshar, M.D. Sturge, and J.S. Roberts, "Motional narrowing in semiconductor microcavities," Phys. Rev. Lett. 77, 4792 (1996).
[CrossRef] [PubMed]

V. Savona, C. Piermarocchi, A. Quattropani, F. Tassone, and P. Schwendimann, "Microscopic theory of motional narrowing of microcavity polaritons in a disordered potential," Phys. Rev. Lett. 78, 4470 (1997).
[CrossRef]

Different line width for lower and upper cavity-polaritons can also be obtained by using the simple coupled-oscillator model and an asymmetric inhomogeneous lineshape.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Transmission spectra (normalized) for composite exciton-cavity systems. All parameters are normalized to Ω (taken to be 1 ps-1 or 3.4 Å). For the black curve (inhomogeneously broadened), Γinh=κ=0.5 and γ=0.05. For the red curve (homogeneously broadened), γ=κ=0.5 and Γinh=0.01. (b) The inhomogeneous distribution used in calculating the black curve in (a).

Fig. 2.
Fig. 2.

(a) Normal mode oscillation for an inhomogeneously broadened system in the intensity of the field (black curve) and polarization (red curve). (b) Normal mode oscillation in the total exciton population. Γ=2γ and other parameters used are the same as in Fig. 1.

Fig. 3.
Fig. 3.

Normal mode oscillation in the intensity of the polarization (a) and in the exciton population (b). The top figures show the oscillation in the total polarization and population shown in Fig. 2. The bottom figures are for an exciton within the inhomogeneous distribution. The wavelength used (from bottom to top) is 800, 800.03, 800.07, 800.1, 800.14, 800.17, and 800.27 nm, respectively. Successive curves are displaced by half a decade in the log plot.

Fig. 4.
Fig. 4.

Normal mode oscillation in the total exciton population in microcavities with κ=0.5 and γ =0.05 and with Γinh=0.2, 0.3, 0.4, 0.5 (from green to red).

Equations (3)

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α ˙ = ( i ω c + κ ) α + Ω dωf ( ω ) β ( ω ) + κε ( t ) ( 1 )
β ˙ ( ω ) = ( + γ ) β ( ω ) Ω α
n ˙ ( ω ) = Γ n ( ω ) Ω [ α * f ( ω ) β ( ω ) + c . c . ]

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