Abstract

We present a time-resolved technique to measure optical excitation processes with a time resolution shorter than the oscillation period of the exciting light. Our terahertz (THz) experiments fully resolve the polarization dynamics of electrons in semiconductor heterostructures when they are excited by a THz pulse. The time resolution of the polarization enables us to deduce the population dynamics of the excited state, which includes the dynamics of a virtual population in the case of off-resonant excitation.

© 2000 Optical Society of America

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  1. P. Meystre and M. Sargent, Elements of Quantum Optics (Springer, New York, 1998).
  2. R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
    [Crossref]
  3. R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972); N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964); G. B. Hocker and C. L. Tang, Phys. Rev. Lett. 21, 591 (1968).
    [Crossref]
  4. D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
    [Crossref]
  5. R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
    [Crossref]
  6. W. Kohn, Phys. Rev. 123, 1242 (1961).
    [Crossref]
  7. L. Brey, F. Johnson, and B. I. Halperin, Phys. Rev. B 40, 10647 (1989).
    [Crossref]
  8. R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
    [Crossref]
  9. J. N. Heyman, R. Kersting, and K. Unterrainer, Appl. Phys. Lett. 72, 644 (1998).
    [Crossref]
  10. K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
    [Crossref]

1998 (1)

J. N. Heyman, R. Kersting, and K. Unterrainer, Appl. Phys. Lett. 72, 644 (1998).
[Crossref]

1997 (1)

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

1996 (1)

K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
[Crossref]

1989 (1)

L. Brey, F. Johnson, and B. I. Halperin, Phys. Rev. B 40, 10647 (1989).
[Crossref]

1984 (1)

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[Crossref]

1978 (1)

R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
[Crossref]

1972 (1)

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972); N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964); G. B. Hocker and C. L. Tang, Phys. Rev. Lett. 21, 591 (1968).
[Crossref]

1961 (1)

W. Kohn, Phys. Rev. 123, 1242 (1961).
[Crossref]

1957 (1)

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
[Crossref]

Auston, D. H.

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[Crossref]

Brewer, R. G.

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972); N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964); G. B. Hocker and C. L. Tang, Phys. Rev. Lett. 21, 591 (1968).
[Crossref]

Brey, L.

L. Brey, F. Johnson, and B. I. Halperin, Phys. Rev. B 40, 10647 (1989).
[Crossref]

Campman, K. L.

K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
[Crossref]

Cheung, K. P.

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[Crossref]

Dingle, R.

R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
[Crossref]

Feynman, R. P.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
[Crossref]

Gornik, E.

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

Gossard, A. C.

K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
[Crossref]

R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
[Crossref]

Halperin, B. I.

L. Brey, F. Johnson, and B. I. Halperin, Phys. Rev. B 40, 10647 (1989).
[Crossref]

Hellwarth, R. W.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
[Crossref]

Heyman, J. N.

J. N. Heyman, R. Kersting, and K. Unterrainer, Appl. Phys. Lett. 72, 644 (1998).
[Crossref]

Imamoglu, A.

K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
[Crossref]

Johnson, F.

L. Brey, F. Johnson, and B. I. Halperin, Phys. Rev. B 40, 10647 (1989).
[Crossref]

Kauffmann, H. F.

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

Kersting, R.

J. N. Heyman, R. Kersting, and K. Unterrainer, Appl. Phys. Lett. 72, 644 (1998).
[Crossref]

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

Kohn, W.

W. Kohn, Phys. Rev. 123, 1242 (1961).
[Crossref]

Meystre, P.

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer, New York, 1998).

Sargent, M.

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer, New York, 1998).

Schmidt, H.

K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
[Crossref]

Shoemaker, R. L.

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972); N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964); G. B. Hocker and C. L. Tang, Phys. Rev. Lett. 21, 591 (1968).
[Crossref]

Smith, P. R.

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[Crossref]

Störmer, H. L.

R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
[Crossref]

Strasser, G.

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

Unterrainer, K.

J. N. Heyman, R. Kersting, and K. Unterrainer, Appl. Phys. Lett. 72, 644 (1998).
[Crossref]

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

Vernon, F. L.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
[Crossref]

Wiegman, W.

R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
[Crossref]

Appl. Phys. Lett. (4)

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[Crossref]

R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 655 (1978).
[Crossref]

J. N. Heyman, R. Kersting, and K. Unterrainer, Appl. Phys. Lett. 72, 644 (1998).
[Crossref]

K. L. Campman, H. Schmidt, A. Imamoglu, and A. C. Gossard, Appl. Phys. Lett. 69, 2554 (1996).
[Crossref]

J. Appl. Phys. (1)

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
[Crossref]

Phys. Rev. (1)

W. Kohn, Phys. Rev. 123, 1242 (1961).
[Crossref]

Phys. Rev. A (1)

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972); N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964); G. B. Hocker and C. L. Tang, Phys. Rev. Lett. 21, 591 (1968).
[Crossref]

Phys. Rev. B (1)

L. Brey, F. Johnson, and B. I. Halperin, Phys. Rev. B 40, 10647 (1989).
[Crossref]

Phys. Rev. Lett. (1)

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, Phys. Rev. Lett. 79, 3038 (1997).
[Crossref]

Other (1)

P. Meystre and M. Sargent, Elements of Quantum Optics (Springer, New York, 1998).

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Figures (4)

Fig. 1
Fig. 1

(a) Band structure of the PQW. Electrons are excited from the lowest subband to the second subband by absorption of a few-cycle THz pulse. (b) Experimental setup.

Fig. 2
Fig. 2

(a) Schematic of an intersubband transition with an eigenfrequency of 2.2 THz driven nearly resonantly by a THz wave with a center frequency of 2.0 THz. (b) Transient of the exciting THz pulse (dotted curve) and modulation signal (solid curve), showing the motion of the electrons.

Fig. 3
Fig. 3

(a) Band diagram of an intersubband transition at 3.0 THz that is driven by an off-resonant 1.6-THz pulse. (b) Driving THz pulse (dotted curve) and response of the electrons (solid curve). The oscillation times T1 and T2 indicate the change of the oscillation frequency. (c) Fourier spectra of the exciting THz pulse and the transmission change, as measured by modulation spectroscopy.

Fig. 4
Fig. 4

(a) Model calculation of the polarization and the experimental data for the off-resonant case. (b) Probability of occupation of the upper level, as deduced from the results of the model calculation.

Equations (2)

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iddtρ=Hint,ρ,
pt=ρ12μ21+c.c.,

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