Abstract

The propagation of a weak light beam through a quantum well in the vicinity of an excitonic resonance that is modulated harmonically in time at terahertz frequency is considered. It is found that the reflection probability of the light beam is considerably different in the cases of purely coherent versus Gaussian incoherent terahertz modulation, even in the limit of long coherence times.

© 1999 Optical Society of America

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References

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  1. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  2. J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
    [CrossRef]
  3. L. C. Andreani, Phys. Lett. A 192, 99 (1994).
    [CrossRef]
  4. D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
    [CrossRef]
  5. A. I. Larkin and K. A. Matveev, Sov. Phys. JETP 66, 580 (1987).
  6. L. I. Glazman and R. I. Shekhter, Sov. Phys. JETP 67, 163 (1988).
  7. Y. G. Rubo, JETP 77, 685 (1993).
  8. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1996).
  9. Note that for the central limit theorem to apply, we must have tave?tc, where tave is the time over which averages are performed.
  10. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1944).

1997 (1)

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

1994 (2)

L. C. Andreani, Phys. Lett. A 192, 99 (1994).
[CrossRef]

D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

1993 (1)

Y. G. Rubo, JETP 77, 685 (1993).

1988 (1)

L. I. Glazman and R. I. Shekhter, Sov. Phys. JETP 67, 163 (1988).

1987 (1)

A. I. Larkin and K. A. Matveev, Sov. Phys. JETP 66, 580 (1987).

Allen, S. J.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Andreani, L. C.

L. C. Andreani, Phys. Lett. A 192, 99 (1994).
[CrossRef]

Citrin, D. S.

D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

Glazman, L. I.

L. I. Glazman and R. I. Shekhter, Sov. Phys. JETP 67, 163 (1988).

Hashitsume, N.

R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1991).
[CrossRef]

Haug, H.

H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1996).

Inoshita, T.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Jauho, A.-P.

H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1996).

Kono, J.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Kubo, R.

R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1991).
[CrossRef]

Larkin, A. I.

A. I. Larkin and K. A. Matveev, Sov. Phys. JETP 66, 580 (1987).

Matveev, K. A.

A. I. Larkin and K. A. Matveev, Sov. Phys. JETP 66, 580 (1987).

Noda, T.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Rubo, Y. G.

Y. G. Rubo, JETP 77, 685 (1993).

Sakaki, H.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Shekhter, R. I.

L. I. Glazman and R. I. Shekhter, Sov. Phys. JETP 67, 163 (1988).

Sherwin, M. S.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Su, M. Y.

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Toda, M.

R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1991).
[CrossRef]

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1944).

JETP (1)

Y. G. Rubo, JETP 77, 685 (1993).

Phys. Lett. A (1)

L. C. Andreani, Phys. Lett. A 192, 99 (1994).
[CrossRef]

Phys. Rev. B (1)

D. S. Citrin, Phys. Rev. B 50, 5497 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, and H. Sakaki, Phys. Rev. Lett. 79, 1758 (1997).
[CrossRef]

Sov. Phys. JETP (2)

A. I. Larkin and K. A. Matveev, Sov. Phys. JETP 66, 580 (1987).

L. I. Glazman and R. I. Shekhter, Sov. Phys. JETP 67, 163 (1988).

Other (4)

H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1996).

Note that for the central limit theorem to apply, we must have tave?tc, where tave is the time over which averages are performed.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1944).

R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1991).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

A weak light beam of frequency ϵ is near resonance with the frequency difference ϵ0 between the ground state and the excited state. The upper-state frequency is modulated harmonically as ϵ1t=ϵ1cosω0t.

Fig. 2
Fig. 2

THz field with a long coherence time, tc2π/ω0. (a) An optical field, whose slowly varying envelope is shorter than tc, is incident upon the quantum well, and the experiment is described by Rtotcohϵ. (b) The optical envelope is much longer than tc; Rtotcohϵ is the applicable formula. In both cases we can choose the optical spectra as well as that of the THz to be as close to δ functions as desired.

Equations (7)

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

Rϵt=Γexp-iϵtwΔ,
Rϵϵ=-dtexpiϵtRϵt=ΓwΔδϵ-ϵ,
wϵ=0dtexpiϵtexp-i0tdtϵ1t,
Rϵ,ϵ=ω02π02π/ω0dt¯-dtexp-ϵtRϵt1Rϵt2=Γ2-dt0dt10dt2expiϵ-ϵt+ϵt1-ϵt2-ϵ0t1-t2-Γt1+t2×exp-i0t1dtϵ1texpit-t2tdtϵ1t,
Rtotϵ=ω02π02π/ω0dtRϵtRϵ*t=Γ2ΓRe wΔ,
Rtotcohϵ=Γ2ΓReiΔ1+2Δ2n=1Jn2nx1Δ2-nω02,
Rtotincohϵ=Γ2ΓReiΔ1+2 Δω0ne=1I2ne2nex2Δ2-2neω02×Δω0cosh2nex2+2nesinh2nex2+2 Δω0×no=1I2no-12no-1x2Δ2-2no-1ω022no-1×cosh2no-1x2-Δω0sinh2no-1x2,

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