Abstract

A numerical analysis is presented of several potential pulsed-laser applications of adiabatic population inversion in atoms or molecules. A simple numerical method is demonstrated for evaluating adiabatic processes in multilevel systems for both swept-frequency and resonant, time-delayed pulses. Adiabatic inversion with time-delayed pulses is generalized to systems with any number of levels. The effect of Doppler broadening on time-delayed adiabatic pumping of a three-level system is investigated.

© 1992 Optical Society of America

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References

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  1. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).
  2. M. M. T. Loy, “Observation of population inversion by optical adiabatic rapid passage,” Phys. Rev. Lett. 32, 814–817 (1974).
    [Crossref]
  3. C. Liedenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep.178, 1–24 (1989);“Multiphoton excitation of molecules by single mode cw lasers,” Infrared Phys. 29, 397–409 (1989).
    [Crossref]
  4. A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
    [Crossref] [PubMed]
  5. J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690–697 (1984).
    [Crossref]
  6. R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
    [Crossref]
  7. C. E. Carroll and F. T. Hioe, “Analytic solutions for three-state systems with overlapping pulses,” Phys. Rev. A 42, 1522–1531 (1990);“Two-photon resonance in three-state model driven by two laser beams,” J. Phys. B 22, 2633–2647 (1989).
    [Crossref] [PubMed]
  8. U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
    [Crossref] [PubMed]
  9. F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000–3005 (1988).
    [Crossref] [PubMed]
  10. P. L. Knight and P. W. Milonni, “The Rabi frequency in optical spectra,” Phys. Rep.66, 21–107 (1980);C. Cohen-Tannoudji and S. Reynaud, “Dressed-atom description of resonance fluorescence and absorption spectra of a multilevel atom in an intense laser beam,” J. Phys. B 10, 345–363 (1977).
    [Crossref]
  11. C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696–702 (1932).
    [Crossref]
  12. C. E. Carroll and F. T. Hioe, “Further generalization of Landau–Zener calculation,” J. Opt. Soc. Am. B 2, 1355–1360 (1985).
    [Crossref]
  13. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
    [Crossref]
  14. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1980), Vol. II, p. 754.
  15. F. T. Hioe, “Exact solitary-wave solution of short different-wavelength optical pulses in many-level atomic absorbers,” Phys. Rev. A 26, 1466–1472 (1982);M. J. Konopnicki, P. D. Drummond, and J. H. Eberly, “Theory of lossless propagation of simultaneous different-wavelength optical pulses,” Opt. Commun. 36, 313–316 (1981);F. T. Hioe, “Lossless propagation of optical pulses through N-level systems with Gell-Mann symmetry,” J. Opt. Soc. Am. B 6, 1245–1252 (1989);M. J. Konopnicki and J. H. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Rev. A 24, 2567–2583 (1981).
    [Crossref]

1990 (1)

C. E. Carroll and F. T. Hioe, “Analytic solutions for three-state systems with overlapping pulses,” Phys. Rev. A 42, 1522–1531 (1990);“Two-photon resonance in three-state model driven by two laser beams,” J. Phys. B 22, 2633–2647 (1989).
[Crossref] [PubMed]

1988 (2)

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000–3005 (1988).
[Crossref] [PubMed]

1985 (2)

A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
[Crossref] [PubMed]

C. E. Carroll and F. T. Hioe, “Further generalization of Landau–Zener calculation,” J. Opt. Soc. Am. B 2, 1355–1360 (1985).
[Crossref]

1984 (1)

J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690–697 (1984).
[Crossref]

1982 (1)

F. T. Hioe, “Exact solitary-wave solution of short different-wavelength optical pulses in many-level atomic absorbers,” Phys. Rev. A 26, 1466–1472 (1982);M. J. Konopnicki, P. D. Drummond, and J. H. Eberly, “Theory of lossless propagation of simultaneous different-wavelength optical pulses,” Opt. Commun. 36, 313–316 (1981);F. T. Hioe, “Lossless propagation of optical pulses through N-level systems with Gell-Mann symmetry,” J. Opt. Soc. Am. B 6, 1245–1252 (1989);M. J. Konopnicki and J. H. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Rev. A 24, 2567–2583 (1981).
[Crossref]

1974 (1)

M. M. T. Loy, “Observation of population inversion by optical adiabatic rapid passage,” Phys. Rev. Lett. 32, 814–817 (1974).
[Crossref]

1957 (1)

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[Crossref]

1932 (1)

C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696–702 (1932).
[Crossref]

Adam, A. G.

A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
[Crossref] [PubMed]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Becker, M.

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

Bergmann, K.

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

Blum, K.

K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
[Crossref]

Carroll, C. E.

C. E. Carroll and F. T. Hioe, “Analytic solutions for three-state systems with overlapping pulses,” Phys. Rev. A 42, 1522–1531 (1990);“Two-photon resonance in three-state model driven by two laser beams,” J. Phys. B 22, 2633–2647 (1989).
[Crossref] [PubMed]

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000–3005 (1988).
[Crossref] [PubMed]

C. E. Carroll and F. T. Hioe, “Further generalization of Landau–Zener calculation,” J. Opt. Soc. Am. B 2, 1355–1360 (1985).
[Crossref]

Eberly, J. H.

J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690–697 (1984).
[Crossref]

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Feynman, R. P.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[Crossref]

Gaubatz, U.

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

Gough, T. E.

A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
[Crossref] [PubMed]

Hellwarth, R. W.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[Crossref]

Hioe, F. T.

C. E. Carroll and F. T. Hioe, “Analytic solutions for three-state systems with overlapping pulses,” Phys. Rev. A 42, 1522–1531 (1990);“Two-photon resonance in three-state model driven by two laser beams,” J. Phys. B 22, 2633–2647 (1989).
[Crossref] [PubMed]

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000–3005 (1988).
[Crossref] [PubMed]

C. E. Carroll and F. T. Hioe, “Further generalization of Landau–Zener calculation,” J. Opt. Soc. Am. B 2, 1355–1360 (1985).
[Crossref]

J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690–697 (1984).
[Crossref]

F. T. Hioe, “Exact solitary-wave solution of short different-wavelength optical pulses in many-level atomic absorbers,” Phys. Rev. A 26, 1466–1472 (1982);M. J. Konopnicki, P. D. Drummond, and J. H. Eberly, “Theory of lossless propagation of simultaneous different-wavelength optical pulses,” Opt. Commun. 36, 313–316 (1981);F. T. Hioe, “Lossless propagation of optical pulses through N-level systems with Gell-Mann symmetry,” J. Opt. Soc. Am. B 6, 1245–1252 (1989);M. J. Konopnicki and J. H. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Rev. A 24, 2567–2583 (1981).
[Crossref]

Isenor, N. R.

A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
[Crossref] [PubMed]

Kluz, M.

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

Knight, P. L.

P. L. Knight and P. W. Milonni, “The Rabi frequency in optical spectra,” Phys. Rep.66, 21–107 (1980);C. Cohen-Tannoudji and S. Reynaud, “Dressed-atom description of resonance fluorescence and absorption spectra of a multilevel atom in an intense laser beam,” J. Phys. B 10, 345–363 (1977).
[Crossref]

Liedenbaum, C.

C. Liedenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep.178, 1–24 (1989);“Multiphoton excitation of molecules by single mode cw lasers,” Infrared Phys. 29, 397–409 (1989).
[Crossref]

Loy, M. M. T.

M. M. T. Loy, “Observation of population inversion by optical adiabatic rapid passage,” Phys. Rev. Lett. 32, 814–817 (1974).
[Crossref]

Messiah, A.

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1980), Vol. II, p. 754.

Milonni, P. W.

P. L. Knight and P. W. Milonni, “The Rabi frequency in optical spectra,” Phys. Rep.66, 21–107 (1980);C. Cohen-Tannoudji and S. Reynaud, “Dressed-atom description of resonance fluorescence and absorption spectra of a multilevel atom in an intense laser beam,” J. Phys. B 10, 345–363 (1977).
[Crossref]

Oreg, J.

J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690–697 (1984).
[Crossref]

Reuss, J.

C. Liedenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep.178, 1–24 (1989);“Multiphoton excitation of molecules by single mode cw lasers,” Infrared Phys. 29, 397–409 (1989).
[Crossref]

Rudecki, P.

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

Schiemann, S.

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

Scoles, G.

A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
[Crossref] [PubMed]

Stolte, S.

C. Liedenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep.178, 1–24 (1989);“Multiphoton excitation of molecules by single mode cw lasers,” Infrared Phys. 29, 397–409 (1989).
[Crossref]

Vernon, F. L.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[Crossref]

Zener, C.

C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696–702 (1932).
[Crossref]

Chem. Phys. Lett. (1)

U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kluz, and K. Bergmann, “Population switching between vibrational levels in molecular beams,” Chem. Phys. Lett. 149, 463–468 (1988);J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40, 6741–6744 (1989);U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990);G. He, A. Kuhn, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study,” J. Opt. Soc. Am. B 7, 1960–1969 (1990).
[Crossref] [PubMed]

J. Appl. Phys. (1)

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[Crossref]

J. Opt. Soc. Am. B (1)

Phys. Rev. A (5)

F. T. Hioe, “Exact solitary-wave solution of short different-wavelength optical pulses in many-level atomic absorbers,” Phys. Rev. A 26, 1466–1472 (1982);M. J. Konopnicki, P. D. Drummond, and J. H. Eberly, “Theory of lossless propagation of simultaneous different-wavelength optical pulses,” Opt. Commun. 36, 313–316 (1981);F. T. Hioe, “Lossless propagation of optical pulses through N-level systems with Gell-Mann symmetry,” J. Opt. Soc. Am. B 6, 1245–1252 (1989);M. J. Konopnicki and J. H. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Rev. A 24, 2567–2583 (1981).
[Crossref]

C. E. Carroll and F. T. Hioe, “Analytic solutions for three-state systems with overlapping pulses,” Phys. Rev. A 42, 1522–1531 (1990);“Two-photon resonance in three-state model driven by two laser beams,” J. Phys. B 22, 2633–2647 (1989).
[Crossref] [PubMed]

F. T. Hioe and C. E. Carroll, “Coherent population trapping in N-level quantum systems,” Phys. Rev. A 37, 3000–3005 (1988).
[Crossref] [PubMed]

A. G. Adam, T. E. Gough, N. R. Isenor, and G. Scoles, “Rabi oscillations and rapid-passage effects in the molecular-beam CO2-laser Stark spectroscopy of Ch3F,” Phys. Rev. A 32, 1451–1457 (1985).
[Crossref] [PubMed]

J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690–697 (1984).
[Crossref]

Phys. Rev. Lett. (1)

M. M. T. Loy, “Observation of population inversion by optical adiabatic rapid passage,” Phys. Rev. Lett. 32, 814–817 (1974).
[Crossref]

Proc. R. Soc. London Ser. A (1)

C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696–702 (1932).
[Crossref]

Other (5)

K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
[Crossref]

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1980), Vol. II, p. 754.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

C. Liedenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep.178, 1–24 (1989);“Multiphoton excitation of molecules by single mode cw lasers,” Infrared Phys. 29, 397–409 (1989).
[Crossref]

P. L. Knight and P. W. Milonni, “The Rabi frequency in optical spectra,” Phys. Rep.66, 21–107 (1980);C. Cohen-Tannoudji and S. Reynaud, “Dressed-atom description of resonance fluorescence and absorption spectra of a multilevel atom in an intense laser beam,” J. Phys. B 10, 345–363 (1977).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Adiabatic energy levels for a two-level system as a function of the detuning Δ of the driving radiation from resonance.

Fig. 2
Fig. 2

(a) Adiabatic energy levels as a function of time for a 5-ns FWHM driving pulse frequency swept to the blue at 200 MHz/ns with a pulse area of 6π. Curve I is the time profile of the drive pulse plotted in arbitrary units. Curve D is explained in the text, (b) Population in the upper and lower levels as a function of time for the same conditions as in (a).

Fig. 3
Fig. 3

(a) Adiabatic energy levels as a function of time for 5-ns FWHM synchronous drive pulses frequency swept to the red at 200 MHz/ns for both transitions with pulse areas of 12π. D is the diabatic term defined in the text, (b) Populations as a function of time for the same conditions as in (a).

Fig. 4
Fig. 4

(a) Adiabatic energy levels as a function of time for 5-ns FWHM synchronous drive pulses of area 12π frequency swept to the blue at 400 MHz/ns for the lower transition and to the red at 400 MHz/ns for the upper transition, with the lower transition reaching resonance first. D is the diabatic term defined in the text, (b) Populations as a function of time for the same conditions as in (a).

Fig. 5
Fig. 5

(a) Adiabatic energy levels as a function of time for 5-ns FWHM synchronous drive pulses of area 18π, with the lower drive frequency swept at 250 MHz/ns to the blue and the upper drive frequency fixed at 600 MHz blue. D is the diabatic term defined in the text, (b) Populations as a function of time for the same conditions as in (a).

Fig. 6
Fig. 6

(a) Adiabatic energy levels as a function of time for 5-ns FWHM asynchronous, resonant drive pulses of area 18π. The time delay is 6 ns, with the upper transition (I2) driven first. D is the diabatic term defined in the text, (b) Populations as a function of time for the same conditions as in (a).

Fig. 7
Fig. 7

(a) Adiabatic energy levels of a five-level system as a function of time for 5-ns FWHM asynchronous, resonant drive pulses of area 36π. The time delay is 6 ns, the even-numbered transitions (I2,4) are driven first, followed by the odd transitions. D is the diabatic factor defined in the text, (b) Populations as a function of time for the same conditions as in (a).

Fig. 8
Fig. 8

(a) Adiabatic energy levels of a four-level system as a function of time for 5-ns FWHM asynchronous drive pulses of area 18π. The pulses are centered at 17, 15, 13 ns. The lowest transition is driven by 500-MHz blue-shifted light, the middle transition is driven by resonant light, and the upper transition is driven by 500-MHz red-shifted light. D is the diabatic term defined in the text, (b) Populations as a function of time for the same conditions as in (a).

Fig. 9
Fig. 9

Some examples of non-cascade-coupled systems.

Fig. 10
Fig. 10

(a) Adiabatic energy level of a three-level system as a function of time for 5-ns FWHM asynchronous, resonant drive pulses of area 18π. The time delay is 6ns, the Doppler shift of the lower transition is −450 MHz, and the Doppler shift of the upper transition is −270 MHz. (b) Populations as a function of the Doppler shift of the lower transition. The Doppler profile for the lower transition has a FWHM of 1.66 GHz. The Doppler shift of the upper transition is 0.6 of the shift of the lower transition.

Fig. 11
Fig. 11

(a) Adiabatic energy level of a three-level system as a function of time for 5-ns FWHM asynchronous, resonant drive pulses of area 18π. The time delay is 6 ns, the Doppler shift of the lower transition is −900 MHz, and the Doppler shift of the upper transition is +480 MHz. (b) Populations as a function of the Doppler shift of the lower transition. The Doppler profile for the lower transition has a FWHM of 1.66 GHz. The Doppler shift of the upper transition is 0.6 of the shift of the lower transition.

Equations (11)

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H = [ Δ Ω / 2 Ω / 2 0 ] ,
d ρ / d t = ( i / ) [ H , ρ ] ,
D = n [ ( d Ψ 1 | / d t ) | Ψ n e 1 e n ] 2 1 ,
d Δ / d t 2 ( Ω 2 + Δ 2 ) 3 / 2 Ω .
H = [ Δ 1 Ω 1 / 2 0 Ω 1 / 2 0 Ω 2 / 2 0 Ω 2 / 2 Δ 2 ] ,
Ψ 0 = ( Ω 2 | 1 Ω 1 | 3 ) / ( Ω 1 2 + Ω 2 2 ) 1 / 2 .
Ψ 0 = Ω 2 Ω 4 | 1 Ω 1 Ω 4 | 3 + Ω 1 Ω 3 | 5 N ,
Ψ 0 = Ω 2 Ω 4 Ω 6 | 1 Ω 1 Ω 4 Ω 6 | 3 + Ω 1 Ω 3 Ω 6 | 5 Ω 1 Ω 3 Ω 5 | 7 N .
H = [ Δ 1 Ω 1 / 2 0 0 Ω 1 / 2 0 Ω 2 / 2 Ω 3 / 2 0 Ω 2 / 2 Δ 2 0 0 Ω 3 / 2 0 Δ 3 ] .
d ρ i j / d t = γ i j ρ i j ( i / ) [ H , ρ ] i j , γ 13 = γ 12 + γ 23 , γ 12 = γ 23 .
η = 0.333 + 0.667 exp ( 4.3 × 10 9 γ 12 ) .

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