Abstract
By the use of a bosonization transformation and group-theoretical arguments, the Hamiltonian of an electron–hole–photon system in a laser-excited direct two-band semiconductor is transcribed into that of an exciton–photon system with the particle spins rigorously taken into consideration. It is shown that the third-order optical nonlinearities in the spectral region below the band edge have their microscopic origin in two-exciton correlations, which are expressed in terms of the effective exciton–exciton and anharmonic exciton–photon interactions. The dependence of the interparticle interactions on the spin states of quasiparticles is behind the polarization dependence of the semiconductor nonlinear optical response. On the example of the system of heavy hole excitons in quantum wells, grown from compounds with the zinc blende type of symmetry, it is demonstrated that the effective exciton–exciton interaction in two-exciton states with nonzero total spin is repulsive, while in zero-spin states it is attractive, which may result in the biexciton formation. The derived Heisenberg equations of motion for the exciton and biexciton operators form the basis for a theoretical study of the coherent four-wave-mixing in GaAs and ZnSe quantum wells. It is readily apparent from the equations that in different polarization configurations the coherent four-wave-mixing is generated by different ingredients of two-exciton Coulomb correlations: in the co-circular configuration, it is the interexciton repulsion, in the cross-linear configuration, the formation of the biexciton and its coupling to excitons, and in the collinear configuration, both of them jointly. The obtained expressions for the time-resolved and frequency-resolved four-wave-mixing signals adequately describe the main characteristics and various details of wave mixing phenomena, including a biexciton signature in the appropriate polarization configurations. Results of the work clarify the microscopic mechanism of the polarization dependence in coherent four-wave-mixing spectroscopy in semiconductor quantum wells.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Weisbuch, in: R. Dingle (ed.), Semiconductors and Semimetals, Academic Press, New York (1987), Vol. 24.
M. Lindberg and S. W. Koch, Phys. Rev. B, 38, 3342 (1988).
W. Sch¨afer, in: F. Henneberger, S. Schmitt-Rink and E. O. G¨ obel (eds.), Optics of Semiconductor Nanostructures, Akademie Verlag, Berlin (1993).
M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Sch¨afer, Phys. Rev. A, 42, 5675 (1990).
R. Eccleston, J. Kuhn, Bennhard, and P. Thomas, Solid State Commun., 86, 93 (1993).
H. Wang, K. B. Ferrio, D. G. Steel, et al., Phys. Rev. Lett., 71, 1261 (1993).
H. H. Yaffe, Y. Prior, J. P. Harbison, and L. T. Florez, J. Opt. Soc. Am. B, 10, 578 (1993).
Y. Z. Hu, R. Binder, S. W. Koch, et al., Phys. Rev. B, 49, 14 382 (1994).
T. Saiki, M. Kuwata-Gonokami, T. Matsusue, and H. Sakaki, Phys. Rev. B, 49, 7817 (1994).
D. J. Lovering, R. T. Phillips, G. J. Denton, and G. W. Smith, Phys. Rev. Lett., 68, 1880 (1992).
E. J. Mayer, G. O. Smith, V. Heuckeroth, et al., Phys. Rev. B, 50, 14 730 (1994)
K. Bott, O. Heller, D. Bennhardt, et al., Phys. Rev. B, 48, 17 418 (1993).
H. P. Wagner, A. Sch¨atz, W. Langbein, et al., Phys. Rev. B, 60, 4454 (1999).
J. Ishi, H. Kunugita, K. Ema, et al., Phys. Rev. B, 63, 073303 (2001).
V. M. Axt and A. Stahl, Z. Phys. B, 93, 175 (1994).
M. Linberg, Y. Z. Hu, R. Binder, and S. W. Koch, Phys. Rev. B, 50, 18060 (1994).
W. Sch¨afer, D. S. Kim, J. Shah, et al., Phys. Rev. B, 53, 16 429 (1996).
E. Hanamura, J. Phys. Soc. Jpn., 29, 50 (1970); 37, 1545 (1974).
T. Usui, Progr. Theor. Phys., 23, 787 (1960).
M. I. Sheboul and W. Ekardt, Phys. Status Solidi B, 73, 165 (1976).
H. Stolz, R. Zimmermann, and G. Ropke, Phys. Status Solidi B, 105, 585 (1981).
T. Hiroshima, Phys. Rev. B, 40, 3862 (1989).
G. Rochat, C. Ciuti, V. Savona, et al., Phys. Rev. B, 61, 13 856 (2000).
A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton (1957).
L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, Pergamon, New York (1965), Vol. 3.
Hoang Ngoc Cam, Phys. Rev. B, 55, 10 487 (1997).
J. R. Kuklinski and S. Mukamel, Phys. Rev. B, 42, 2959 (1990).
D. S. Kim, J. Shah, T. S. Damen, et al., Phys. Rev. B, 50, 15 086 (1994).
A. I. Bobrysheva, V. T. Zyukov, and S. I. Beryl, Phys. Status Solidi B, 101, 69 (1980).
S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Phys. Rev. B, 32, 6601 (1985).
A. I. Bobrysheva, S. I. Beryl, S. A. Moskalenko, and E. P. Pokatylov, Phys. Status Solidi B, 100, 281 (1980).
F. Henneberger and J. Voigt, Phys. Status Solidi B, 76, 313 (1976).
P. I. Khadzhi, S. A. Moskalenko, and S. N. Belkin, Pis'ma Zh. ´ Eksp. Teor. Fiz., 29, 223 (1979) [Sov. Phys.-JETP Lett., 29, 200 (1979)].
A. L. Ivanov, L. V. Keldysh, and V. V. Panashenko, Zh. ´ Eksp. Teor. Fiz., 99, 641 (1991) [Sov. Phys.-JETP, 72, 359 (1991)].
A. Mysyrowicz, D. Hulin, A. Antonetti, et al., Phys. Rev. Lett., 56, 2748 (1986); A. von Lehmen, D. S. Chemla, J. E. Zucker, and J. P. Heritage, Optics Lett., 11, 609 (1986).
D. Hulin and M. Joffre, Phys. Rev. Lett., 65, 3425 (1990).
R. Shimano and M. Kuwata-Gonokami, Phys. Rev. Lett., 72, 530 (1994).
G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the Thirty-Two Point Groups, MIT, Cambridge (1963).
S. A. Moskalenko, Introduction to the Theory of High-Density Exciton Systems [in Russian], Shtiintsa, Kishinev (1983).
L. V. Keldysh, in: Problems in Theoretical Physics [in Russian], Nauka, Moscow (1972), p. 433.
V. F. Elesin and Yu. V. Kopaev, Zh. ´ Eksp. Teor. Fiz., 63, 1447 (1972) [Sov. Phys.-JETP, 36, 767 (1973)].
A. I. Bobrysheva, S. A. Moskalenko, and Hoang Ngoc Cam, Zh. ´ Eksp. Teor. Fiz., 103, 301 (1993) [Sov. Phys.-JETP, 76, 163 (1993)].
T. Yajima and Y. Taira, J. Phys. Soc. Jpn., 47, 1620 (1979).
B. Birkedal, V. G. Lyssenko, J. Erland, et al., Phys. Rev. Lett., 76, 672 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ngoc Cam, H. Exciton-Boson Formalism in the Theory of Laser-Excited Semiconductors and Its Application in Coherent Four-Wave-Mixing Spectroscopy. Journal of Russian Laser Research 25, 412–439 (2004). https://doi.org/10.1023/B:JORR.0000043731.28809.95
Issue Date:
DOI: https://doi.org/10.1023/B:JORR.0000043731.28809.95