Abstract

We demonstrate that appropriately time-ordered pulses of diode-laser light can provide efficient population transfer in a three-level cascade system. Laser-trapped Rb atoms are excited from the 5S ground state to the highly-excited 5D level (through the 5P intermediate level) with a transfer efficiency approaching 100%. Diode-laser light at 780 nm (5S5P) and 776 nm (5P5D) is switched with acousto-optic modulators to provide the excitation. The measured variation of transfer efficiency with relative delay between the two pulses is in reasonable agreement with theoretical predictions. However, the intensities needed for efficient transfer are significantly higher than expected. In general, optimum excitation occurs for the counterintuitive pulse ordering, i.e., when the upper transition is driven first.

© 1997 Optical Society of America

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  1. Special issue on the mechanical effects of light, P. Meystre and S. Stenholm, eds., J. Opt. Soc. Am. B 2 (11) (1985).
  2. Special issue on laser cooling and trapping of atoms, S. Chu and C. Wieman, eds., J. Opt. Soc. Am. B 6 (11) (1989).
  3. Special issue on laser cooling and trapping, V. Bagnato, N. Bigelow, A. Dykhne, J. Weiner, and Y. Yakovlev, eds. Laser Phys. 4 (5) (1994).
  4. H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203 (1994).
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  5. W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).
    [CrossRef]
  6. W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
    [CrossRef] [PubMed]
  7. U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
    [CrossRef]
  8. For a review of the subject see: K. Bergmann and B. W. Shore, in “Coherent population transfer,” Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping, H. L. Dai and R. W. Field, eds. (World Scientific, Singapore, 1995), pp. 315–373.
  9. P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
    [CrossRef] [PubMed]
  10. J. Lawall and M. Prentiss, “Demonstration of a novel atomic beam splitter,” Phys. Rev. Lett. 72, 993 (1994).
    [CrossRef] [PubMed]
  11. L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
    [CrossRef] [PubMed]
  12. M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563 (1994).
    [CrossRef] [PubMed]
  13. C. Liendenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep. 178, 1 (1989).
    [CrossRef]
  14. N. Dam, L. Oudejans, and J. Reuss, “Relaxation rates of ethylene obtained from their effect on coherent transients,” Chem. Phys. 140, 217 (1990).
    [CrossRef]
  15. B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
    [CrossRef] [PubMed]
  16. J. Oreg, F. T. Hioe, and J. H. Eberly, “Adiabatic following in multilevel systems,” Phys. Rev. A 29, 690 (1984).
    [CrossRef]
  17. 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 (1989).
    [CrossRef] [PubMed]
  18. G.-H. 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 (1990).
    [CrossRef]
  19. Y. B. Band and P. S. Julienne, “Density matrix calculation of population transfer between vibrational levels of Na2 by stimulated Raman scattering with temporally shifted laser beams,” J. Chem. Phys. 94, 5291 (1991).
    [CrossRef]
  20. A. V. Smith, “Numerical studies of adiabatic population inversion in multilevel systems,” J. Opt. Soc. Am. B 9, 1543 (1992).
    [CrossRef]
  21. B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
    [CrossRef] [PubMed]
  22. J. Martin, B. W. Shore, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis,” Phys. Rev. A 52, 583 (1995).
    [CrossRef] [PubMed]
  23. T. A. Laine and S. Stenholm, “Adiabatic processes in three-level systems,” Phys. Rev. A 53, 2501 (1996).
    [CrossRef] [PubMed]
  24. O. S. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am. 51, 1058 (1961).
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  25. J. K. Link, “Measurement of the radiative lifetimes of the first excited states of Na, K, Rb, and Cs by the phase-shift method,” J. Opt. Soc. Am. 56, 1195 (1966).
    [CrossRef]
  26. J. Javanainen, “Numerical experiments in semiclassical laser-cooling theory of multistate atoms,” Phys. Rev. A 46, 5819 (1992).
    [CrossRef] [PubMed]
  27. C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
    [CrossRef] [PubMed]
  28. T. P. Dinneen, C. D. Wallace, and P. L. Gould, “Narrow linewidth, highly stable, tunable diode laser system,” Opt. Commun. 92, 277 (1992).
    [CrossRef]
  29. T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
    [CrossRef]
  30. Owing to the finite speed of sound in the AOM crystal, there is a spatially dependent delay in the switching; i.e., different transverse portions of the beam switch at slightly different times. However, the resulting effective spread in delays (<5 ns over the FWHM of the atomic cloud) is small compared with both the pulse width (~33 ns) and the optimum delay (~20 ns).
  31. Zeeman splittings that are due to the magnetic field gradient and the finite extent of the atomic cloud are <1 MHz.
  32. We assume that the 5S1/2(F=3) atoms are uniformly distributed among the seven mF sublevels (mF=−3, …, +3) and use an average electric dipole moment for excitation with linearly polarized light (Δm=0 transitions for both S→P and P→D). This average is calculated from the A coefficients for the 5D5/2→5P3/2 (Ref. 24) and 5P3/2→5S1/2 (Ref. 25) transitions and the appropriate Clebsch–Gordan coefficients, yielding μ1=1.91 ea0 and μ3=0.537 ea0.
  33. G. W. Coulston and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses: analytical results for multilevel systems,” J. Chem. Phys. 96, 3467 (1992).
    [CrossRef]
  34. A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
    [CrossRef]
  35. S. R. Wilkinson, “Dynamical quantum coherence in multilevel atoms: experiment and theory,” Ph.D. dissertation (University of New Mexico, Albuquerque, New Mexico, 1995).

1996 (1)

T. A. Laine and S. Stenholm, “Adiabatic processes in three-level systems,” Phys. Rev. A 53, 2501 (1996).
[CrossRef] [PubMed]

1995 (3)

B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
[CrossRef] [PubMed]

J. Martin, B. W. Shore, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis,” Phys. Rev. A 52, 583 (1995).
[CrossRef] [PubMed]

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

1994 (4)

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203 (1994).
[CrossRef]

J. Lawall and M. Prentiss, “Demonstration of a novel atomic beam splitter,” Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563 (1994).
[CrossRef] [PubMed]

1993 (2)

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
[CrossRef] [PubMed]

1992 (6)

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

A. V. Smith, “Numerical studies of adiabatic population inversion in multilevel systems,” J. Opt. Soc. Am. B 9, 1543 (1992).
[CrossRef]

G. W. Coulston and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses: analytical results for multilevel systems,” J. Chem. Phys. 96, 3467 (1992).
[CrossRef]

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

J. Javanainen, “Numerical experiments in semiclassical laser-cooling theory of multistate atoms,” Phys. Rev. A 46, 5819 (1992).
[CrossRef] [PubMed]

T. P. Dinneen, C. D. Wallace, and P. L. Gould, “Narrow linewidth, highly stable, tunable diode laser system,” Opt. Commun. 92, 277 (1992).
[CrossRef]

1991 (1)

Y. B. Band and P. S. Julienne, “Density matrix calculation of population transfer between vibrational levels of Na2 by stimulated Raman scattering with temporally shifted laser beams,” J. Chem. Phys. 94, 5291 (1991).
[CrossRef]

1990 (4)

G.-H. 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 (1990).
[CrossRef]

N. Dam, L. Oudejans, and J. Reuss, “Relaxation rates of ethylene obtained from their effect on coherent transients,” Chem. Phys. 140, 217 (1990).
[CrossRef]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

1989 (2)

C. Liendenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep. 178, 1 (1989).
[CrossRef]

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 (1989).
[CrossRef] [PubMed]

1984 (1)

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

1972 (1)

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

1966 (1)

1961 (1)

Band, Y. B.

Y. B. Band and P. S. Julienne, “Density matrix calculation of population transfer between vibrational levels of Na2 by stimulated Raman scattering with temporally shifted laser beams,” J. Chem. Phys. 94, 5291 (1991).
[CrossRef]

Bergmann, K.

J. Martin, B. W. Shore, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis,” Phys. Rev. A 52, 583 (1995).
[CrossRef] [PubMed]

B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
[CrossRef] [PubMed]

G. W. Coulston and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses: analytical results for multilevel systems,” J. Chem. Phys. 96, 3467 (1992).
[CrossRef]

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

G.-H. 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 (1990).
[CrossRef]

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 (1989).
[CrossRef] [PubMed]

Broers, B.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Chu, S.

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563 (1994).
[CrossRef] [PubMed]

Coulston, G. W.

G. W. Coulston and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses: analytical results for multilevel systems,” J. Chem. Phys. 96, 3467 (1992).
[CrossRef]

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

Dahleh, M.

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

Dam, N.

N. Dam, L. Oudejans, and J. Reuss, “Relaxation rates of ethylene obtained from their effect on coherent transients,” Chem. Phys. 140, 217 (1990).
[CrossRef]

Dinneen, T. P.

T. P. Dinneen, C. D. Wallace, and P. L. Gould, “Narrow linewidth, highly stable, tunable diode laser system,” Opt. Commun. 92, 277 (1992).
[CrossRef]

Duncan, B. C.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

Eberly, J. H.

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

Fewell, M. P.

B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
[CrossRef] [PubMed]

Gaubatz, U.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

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 (1989).
[CrossRef] [PubMed]

Gerz, C.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

Goldner, L. S.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

Gould, P. L.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

T. P. Dinneen, C. D. Wallace, and P. L. Gould, “Narrow linewidth, highly stable, tunable diode laser system,” Opt. Commun. 92, 277 (1992).
[CrossRef]

Grove, T. T.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

Happer, W.

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

He, G. Z.

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

He, G.-H.

Heavens, O. S.

Hioe, F. T.

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 (1989).
[CrossRef] [PubMed]

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

Javanainen, J.

J. Javanainen, “Numerical experiments in semiclassical laser-cooling theory of multistate atoms,” Phys. Rev. A 46, 5819 (1992).
[CrossRef] [PubMed]

Julienne, P. S.

Y. B. Band and P. S. Julienne, “Density matrix calculation of population transfer between vibrational levels of Na2 by stimulated Raman scattering with temporally shifted laser beams,” J. Chem. Phys. 94, 5291 (1991).
[CrossRef]

Kuhn, A.

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

G.-H. 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 (1990).
[CrossRef]

Kuklinski, J. R.

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 (1989).
[CrossRef] [PubMed]

Laine, T. A.

T. A. Laine and S. Stenholm, “Adiabatic processes in three-level systems,” Phys. Rev. A 53, 2501 (1996).
[CrossRef] [PubMed]

Lawall, J.

J. Lawall and M. Prentiss, “Demonstration of a novel atomic beam splitter,” Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

Liendenbaum, C.

C. Liendenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep. 178, 1 (1989).
[CrossRef]

Link, J. K.

Maleki, S.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

Marte, P.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

Martin, J.

J. Martin, B. W. Shore, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis,” Phys. Rev. A 52, 583 (1995).
[CrossRef] [PubMed]

B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
[CrossRef] [PubMed]

Metcalf, H.

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203 (1994).
[CrossRef]

Monroe, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Noordam, L. D.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Oreg, J.

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

Oudejans, L.

N. Dam, L. Oudejans, and J. Reuss, “Relaxation rates of ethylene obtained from their effect on coherent transients,” Chem. Phys. 140, 217 (1990).
[CrossRef]

Phillips, W. D.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

Pillet, P.

P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
[CrossRef] [PubMed]

Prentiss, M.

J. Lawall and M. Prentiss, “Demonstration of a novel atomic beam splitter,” Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

Rabitz, H.

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

Reuss, J.

N. Dam, L. Oudejans, and J. Reuss, “Relaxation rates of ethylene obtained from their effect on coherent transients,” Chem. Phys. 140, 217 (1990).
[CrossRef]

C. Liendenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep. 178, 1 (1989).
[CrossRef]

Robinson, H.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Rolston, S. L.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

Rudecki, P.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Sanchez-Villicana, V.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

Schiemann, S.

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

G.-H. 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 (1990).
[CrossRef]

Shore, B. W.

B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
[CrossRef] [PubMed]

J. Martin, B. W. Shore, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis,” Phys. Rev. A 52, 583 (1995).
[CrossRef] [PubMed]

Smith, A. V.

Spreeuw, R. J. C.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
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T. A. Laine and S. Stenholm, “Adiabatic processes in three-level systems,” Phys. Rev. A 53, 2501 (1996).
[CrossRef] [PubMed]

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C. Liendenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep. 178, 1 (1989).
[CrossRef]

Swann, W.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Valentin, C.

P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
[CrossRef] [PubMed]

van der Straten, P.

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203 (1994).
[CrossRef]

van Linden van den Heuvell, H. B.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Wallace, C. D.

T. P. Dinneen, C. D. Wallace, and P. L. Gould, “Narrow linewidth, highly stable, tunable diode laser system,” Opt. Commun. 92, 277 (1992).
[CrossRef]

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W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

Weitz, M.

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563 (1994).
[CrossRef] [PubMed]

Westbrook, C. I.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

Wieman, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Young, B. C.

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563 (1994).
[CrossRef] [PubMed]

Yu, J.

P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
[CrossRef] [PubMed]

Yuan, R.-L.

P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
[CrossRef] [PubMed]

Zoller, P.

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
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U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Y. B. Band and P. S. Julienne, “Density matrix calculation of population transfer between vibrational levels of Na2 by stimulated Raman scattering with temporally shifted laser beams,” J. Chem. Phys. 94, 5291 (1991).
[CrossRef]

G. W. Coulston and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses: analytical results for multilevel systems,” J. Chem. Phys. 96, 3467 (1992).
[CrossRef]

A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, and K. Bergmann, “Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light,” J. Chem. Phys. 96, 4215 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

T. P. Dinneen, C. D. Wallace, and P. L. Gould, “Narrow linewidth, highly stable, tunable diode laser system,” Opt. Commun. 92, 277 (1992).
[CrossRef]

Phys. Rep. (2)

C. Liendenbaum, S. Stolte, and J. Reuss, “Inversion produced and reversed by adiabatic passage,” Phys. Rep. 178, 1 (1989).
[CrossRef]

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203 (1994).
[CrossRef]

Phys. Rev. A (7)

P. Pillet, C. Valentin, R.-L. Yuan, and J. Yu, “Transfer by adiabatic following in a multilevel system,” Phys. Rev. A 48, 845 (1993).
[CrossRef] [PubMed]

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

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 (1989).
[CrossRef] [PubMed]

B. W. Shore, J. Martin, M. P. Fewell, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. I. Numerical studies,” Phys. Rev. A 52, 566 (1995).
[CrossRef] [PubMed]

J. Martin, B. W. Shore, and K. Bergmann, “Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis,” Phys. Rev. A 52, 583 (1995).
[CrossRef] [PubMed]

T. A. Laine and S. Stenholm, “Adiabatic processes in three-level systems,” Phys. Rev. A 53, 2501 (1996).
[CrossRef] [PubMed]

J. Javanainen, “Numerical experiments in semiclassical laser-cooling theory of multistate atoms,” Phys. Rev. A 46, 5819 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

J. Lawall and M. Prentiss, “Demonstration of a novel atomic beam splitter,” Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

L. S. Goldner, C. Gerz, R. J. C. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, “Momentum transfer in laser-cooled cesium by adiabatic passage in a light field,” Phys. Rev. Lett. 72, 997 (1994).
[CrossRef] [PubMed]

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563 (1994).
[CrossRef] [PubMed]

Phys. Scr. (1)

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, “Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state,” Phys. Scr. 52, 271 (1995).
[CrossRef]

Rev. Mod. Phys. (1)

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Science (1)

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

Other (8)

Special issue on the mechanical effects of light, P. Meystre and S. Stenholm, eds., J. Opt. Soc. Am. B 2 (11) (1985).

Special issue on laser cooling and trapping of atoms, S. Chu and C. Wieman, eds., J. Opt. Soc. Am. B 6 (11) (1989).

Special issue on laser cooling and trapping, V. Bagnato, N. Bigelow, A. Dykhne, J. Weiner, and Y. Yakovlev, eds. Laser Phys. 4 (5) (1994).

For a review of the subject see: K. Bergmann and B. W. Shore, in “Coherent population transfer,” Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping, H. L. Dai and R. W. Field, eds. (World Scientific, Singapore, 1995), pp. 315–373.

Owing to the finite speed of sound in the AOM crystal, there is a spatially dependent delay in the switching; i.e., different transverse portions of the beam switch at slightly different times. However, the resulting effective spread in delays (<5 ns over the FWHM of the atomic cloud) is small compared with both the pulse width (~33 ns) and the optimum delay (~20 ns).

Zeeman splittings that are due to the magnetic field gradient and the finite extent of the atomic cloud are <1 MHz.

We assume that the 5S1/2(F=3) atoms are uniformly distributed among the seven mF sublevels (mF=−3, …, +3) and use an average electric dipole moment for excitation with linearly polarized light (Δm=0 transitions for both S→P and P→D). This average is calculated from the A coefficients for the 5D5/2→5P3/2 (Ref. 24) and 5P3/2→5S1/2 (Ref. 25) transitions and the appropriate Clebsch–Gordan coefficients, yielding μ1=1.91 ea0 and μ3=0.537 ea0.

S. R. Wilkinson, “Dynamical quantum coherence in multilevel atoms: experiment and theory,” Ph.D. dissertation (University of New Mexico, Albuquerque, New Mexico, 1995).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of the Rb three-level (cascade) system. The two lasers, with Rabi rates Ω1 and Ω3, are two-photon resonant with the |1〉→|3〉 transition but detuned from the intermediate state by Δ, shown here as positive. The decay rates are Γ1 =3.7×107 s-1 and Γ3=4.1×106 s-1. (b) Schematic of the delayed pulses, shown here in the counterintuitive order (delay less than 0).

Fig. 2
Fig. 2

Time evolution of the populations under the influence of (a) pulses in the counterintuitive order (delay -20 ns) and (b) overlapping pulses. The dotted curves corresponds to the 5S population, the dashed curves to the 5P, and the solid curves to the 5D. The insets show the timing of the pulses (dashed curve for Ω3 and solid curve for Ω1). Parameters are Ω1=6Γ, Ω3 =6Γ, Δ=+7.5Γ, and pulse width 33 ns (FWHM of Gaussian intensity profile), where we define Γ≡Γ1.

Fig. 3
Fig. 3

Fluorescence at 420 nm (dashed curve) and 780 nm (dotted curve) as functions of delay between the pulses. A negative delay corresponds to the counterintuitive pulse ordering. The 420-nm fluorescence is proportional to the number of 5D atoms, and the 780-nm fluorescence is proportional to the total number of atoms. The relative excitation efficiency (solid curve) is obtained by dividing the dashed curve by the dotted curve. Parameters are I1=7.9 W/cm2, I3=9.3 W/cm2, Δ =+2π(44MHz)=+7.5Γ, and pulse width 33 ns.

Fig. 4
Fig. 4

(a) Measured and (b) calculated 5D excitation efficiencies as functions of delay between the pulses. The different curves are for different attenuations of Ω3, as indicated. The highest intensity in (a) is I3=9.3 W/cm2, and I1=7.9 W/cm2 for all curves. The highest intensity in (b) corresponds to Ω3 =4.0Γ, and Ω1 is fixed at 5.25Γ. Other parameters are Δ =+7.5Γ and pulse width 33 ns.

Fig. 5
Fig. 5

(a) Measured and (b) calculated 5D excitation efficiencies versus delay for different attenuations of Ω1. The highest intensity in (a) is I1=7.9 W/cm2, and I3=9.3 W/cm2 for all curves. The highest intensity in (b) corresponds to Ω1=5.25Γ, and Ω3 is fixed at 4.0Γ. Other parameters are the same as in Fig. 4.

Fig. 6
Fig. 6

Contour plots showing calculated excitation efficiency versus Ω3 and Ω1 for three fixed delays: (a) -20 ns (counterintuitive order), (b) zero delay, and (c) +20 ns (intuitive order). The detuning is Δ=+7.5Γ, and the pulse width is 33 ns. Each contour represents an increment of 10% in the excitation efficiency; the darkest region corresponds to 0%→10% and the highest region to 90%→100%. Maximum intensities used in the experiment define a point, according to Eq. (4), at Ω3/Γ=9.74 and Ω1/Γ=32.0. However, the best match of (a) to the data yields maximum Rabi rates of Ω3/Γ=4.0 and Ω1/Γ=5.25.

Fig. 7
Fig. 7

Efficiency at a fixed counterintuitive delay (-20 ns) as a function of (a) Ω3 and (b) Ω1. The solid curves are calculated results, and the points are experimental measurements. The scaling of horizontal and vertical axes for the data is discussed in the text. Other parameters are the same as in Fig. 6.

Fig. 8
Fig. 8

Rb 5D excitation in a room-temperature vapor cell as a function of delay between the pulses. Curves are shown for various intensities I1 driving the lower (5S5P) transition. Parameters are I1,max=32 W/cm2, I3=37 W/cm2, Δ=0, pulse width 33 ns, and repetition rate 1 MHz. The signal resulting from continuous excitation at the maximum intensity is 135 on this scale.

Equations (5)

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H=-20Ω1t0Ω1t2ΔΩ3t0Ω3t0.
|ψ0(t)=cos θ(t)|1-sin θ(t)|3,
Ω1,3=μ1,3E1,3=μ1,3(2I1,30c)1/2.
Ω1Γ=0.360I1mWcm21/2,
Ω3Γ=0.101I3mWcm21/2.

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