Abstract

Traditional schemes for coherent population transfer or generation of coherent superposition states in multilevel atoms or molecules usually utilize two or more laser beams with radiation bandwidth smaller than the frequency interval between the working levels. We show the possibility of creation of the coherent superposition of three metastable states of a four-level atom with tripodlike level structure using a single short frequency-chirped laser pulse. The bandwidth of the pulse envelope (without chirp) must be comparable to or exceed the frequency distance between the two metastable levels. No appreciable excitation of the atom takes place during the creation of the coherent superposition state, thus diminishing significantly the effect of decoherence due to the spontaneous decay of the excited state. The proposed method of creation of superposition states is robust against variations in the laser pulse parameters. Since this method does not require maintaining steady resonance with the atomic transitions (owing to the frequency chirp of the laser pulse), it is effective both in homogeneously and inhomogeneously broadened media.

© 2008 Optical Society of America

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References

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  1. K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
    [CrossRef]
  2. R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, "Robust creation and phase-sensitive probing of superposition states via STIRAP with degenerate dark states," Opt. Commun. 155, 144-154 (1998).
    [CrossRef]
  3. H. Theuer, R. Unanyan, C. Habscheid, K. Klein, and K. Bergmann, "Novel laser controlled variable matter wave beamsplitter," Opt. Express 4, 77-83 (1999).
    [CrossRef] [PubMed]
  4. F. Vewinger, M. Heinz, R. G. Fernandez, N. V. Vitanov, and K. Bergmann, "Creation and measurement of a coherent superposition of quantum states," Phys. Rev. Lett. 91, 213001 (2003).
    [CrossRef] [PubMed]
  5. N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, "Preparation of coherent superposition in a three-state system by adiabatic passage," Phys. Rev. A 70, 013415 (2004).
    [CrossRef]
  6. L. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, "Creation of coherent superpositions using Stark-chirped rapid adiabatic passage," Opt. Commun. 204, 413-423 (2002).
    [CrossRef]
  7. G. P. Djotyan, J. S. Bakos, and Zs. Sörlei, "Coherent writing and reading of information using frequency-chirped short bichromatic laser pulses," Opt. Express 4, 113-120 (1999).
    [CrossRef] [PubMed]
  8. G. P. Djotyan, J. S. Bakos, and Zs. Sörlei, "Three-level Λ-atom in the field of frequency-chirped bichromatic laser pulses: writing and storage of optical phase information," Phys. Rev. A 64, 013408 (2001).
    [CrossRef]
  9. G. Djotyan, J. Bakos, Zs. Sörlei, J. Szigeti, P. Ignacz, and Z. Toth, "Interaction of a sequence of frequency-chirped bichromatic laser pulses with an ensemble of lambda-atoms: population trapping and coherent optical pumping," Laser Phys. 10, 355-359 (2000).
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  11. C. P. Williams and S. H. Clearwater, Explorations in Quantum Quantum Computing (Springer-Verlag, 1997).
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  14. M. Jain, Hui Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
    [CrossRef] [PubMed]
  15. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. F. Harris, "Raman generation by phased and antiphased molecular states," Phys. Rev. Lett. 85, 562-565 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
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  18. T. Rickes, J. P. Marangos, and T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. S. E. Harris, "Normal modes for electromagnetically induced transparency," Phys. Rev. Lett. 72, 52-55 (1994).
    [CrossRef] [PubMed]
  23. S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
    [CrossRef] [PubMed]
  24. S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  25. R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  30. L. Rippe, M. Nilsson, S. Kröll, R. Klieber, and D. Suter, "Experimental demonstration of efficient and selective population transfer and qubit distillation in a rare-earth-metal-ion-doped crystal," Phys. Rev. A 71, 062328 (2005).
    [CrossRef]
  31. G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, "Population transfer in three-level L atoms with Doppler-broadened transition lines by a single frequency-chirped short laser pulse," J. Opt. Soc. Am. B 17, 107-113 (2000).
    [CrossRef]
  32. G. P. Djotyan, J. S. Bakos, Zs. Sörlei, and J. Szigeti, "Coherent control of atomic quantum states by single frequency-chirped laser pulses," Phys. Rev. A 70, 063406 (2004).
    [CrossRef]
  33. X. Z. Zhang, Q. Z. Ma, and X. H. Li, "Coherent population transfer in Rydberg potassium atom by a single frequency-chirped laser pulse," Chin. Phys. 15, 1497-1501 (2006).
    [CrossRef]
  34. Z. Kis, A. Karpati, B. W. Shore, and V. V. Vitanov, "Stimulated Raman adiabatic passage among degenerate-level manifolds," Phys. Rev. A 70, 053405 (2004).
    [CrossRef]
  35. Z. Kis, N. V. Vitanov, A. Karpati, C. Barthel, and K. Bergmann, "Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage," Phys. Rev. A 72, 033403 (2005).
    [CrossRef]
  36. S. Menon and G. S. Agarwal, "Gain from cross talk among optical transitions," Phys. Rev. A 59, 740-749 (1999).
    [CrossRef]
  37. R. Unanyan, S. Guérin, B. W. Shore, and K. Bergmann, "Efficient population transfer by delayed pulses despite coupling ambiguity," Eur. Phys. J. D 8, 443-449 (2000).
    [CrossRef]
  38. B. W. Shore, K. Bergmann, A. Kuhn, S. Schiemann, J. Oreg, and J. H. Eberly, "Laser-induced population transfer in multistate systems: a comparative study," Phys. Rev. A 45, 5297-5300 (1992).
    [CrossRef] [PubMed]
  39. R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, "Adiabatic creation of coherent superposition states in atomic beams," Phys. Rev. A 70, 053404 (2004).
    [CrossRef]
  40. I. E. Mazets, "Adiabatic pulse propagation in coherent atomic media with the tripod level configuration," Phys. Rev. A 71, 023806 (2005).
    [CrossRef]
  41. A. Messiah, Quantum Mechanics (North-Holland, 1962), Vol. II.
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    [CrossRef] [PubMed]
  43. L. Jacak, P. Hawrylak, and A. Wójs, Quantum Dots (Springer, 1997).
  44. A. O. Orlov, I. Amlani, G. H. Bernstein, C. S. Lent, and G. L. Snider, "Realization of a functional cell for quantum-dot cellular automata," Science 277, 928-930 (1997).
    [CrossRef]

2006 (1)

X. Z. Zhang, Q. Z. Ma, and X. H. Li, "Coherent population transfer in Rydberg potassium atom by a single frequency-chirped laser pulse," Chin. Phys. 15, 1497-1501 (2006).
[CrossRef]

2005 (3)

L. Rippe, M. Nilsson, S. Kröll, R. Klieber, and D. Suter, "Experimental demonstration of efficient and selective population transfer and qubit distillation in a rare-earth-metal-ion-doped crystal," Phys. Rev. A 71, 062328 (2005).
[CrossRef]

Z. Kis, N. V. Vitanov, A. Karpati, C. Barthel, and K. Bergmann, "Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage," Phys. Rev. A 72, 033403 (2005).
[CrossRef]

I. E. Mazets, "Adiabatic pulse propagation in coherent atomic media with the tripod level configuration," Phys. Rev. A 71, 023806 (2005).
[CrossRef]

2004 (4)

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, "Adiabatic creation of coherent superposition states in atomic beams," Phys. Rev. A 70, 053404 (2004).
[CrossRef]

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, "Preparation of coherent superposition in a three-state system by adiabatic passage," Phys. Rev. A 70, 013415 (2004).
[CrossRef]

G. P. Djotyan, J. S. Bakos, Zs. Sörlei, and J. Szigeti, "Coherent control of atomic quantum states by single frequency-chirped laser pulses," Phys. Rev. A 70, 063406 (2004).
[CrossRef]

Z. Kis, A. Karpati, B. W. Shore, and V. V. Vitanov, "Stimulated Raman adiabatic passage among degenerate-level manifolds," Phys. Rev. A 70, 053405 (2004).
[CrossRef]

2003 (3)

E. Korsunsky, T. Halfmann, J. P. Marangos, M. Fleischhauer, and K. Bergmann, "Analytical study of four-wave mixing with large atomic coherence," Eur. Phys. J. D 23, 167-180 (2003).
[CrossRef]

T. Rickes, J. P. Marangos, and T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

F. Vewinger, M. Heinz, R. G. Fernandez, N. V. Vitanov, and K. Bergmann, "Creation and measurement of a coherent superposition of quantum states," Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

2002 (1)

L. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, "Creation of coherent superpositions using Stark-chirped rapid adiabatic passage," Opt. Commun. 204, 413-423 (2002).
[CrossRef]

2001 (1)

G. P. Djotyan, J. S. Bakos, and Zs. Sörlei, "Three-level Λ-atom in the field of frequency-chirped bichromatic laser pulses: writing and storage of optical phase information," Phys. Rev. A 64, 013408 (2001).
[CrossRef]

2000 (4)

G. Djotyan, J. Bakos, Zs. Sörlei, J. Szigeti, P. Ignacz, and Z. Toth, "Interaction of a sequence of frequency-chirped bichromatic laser pulses with an ensemble of lambda-atoms: population trapping and coherent optical pumping," Laser Phys. 10, 355-359 (2000).

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. F. Harris, "Raman generation by phased and antiphased molecular states," Phys. Rev. Lett. 85, 562-565 (2000).
[CrossRef] [PubMed]

R. Unanyan, S. Guérin, B. W. Shore, and K. Bergmann, "Efficient population transfer by delayed pulses despite coupling ambiguity," Eur. Phys. J. D 8, 443-449 (2000).
[CrossRef]

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, "Population transfer in three-level L atoms with Doppler-broadened transition lines by a single frequency-chirped short laser pulse," J. Opt. Soc. Am. B 17, 107-113 (2000).
[CrossRef]

1999 (3)

1998 (3)

K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
[CrossRef]

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, "Robust creation and phase-sensitive probing of superposition states via STIRAP with degenerate dark states," Opt. Commun. 155, 144-154 (1998).
[CrossRef]

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. Scully, "Resonant enhancement of parametric processes via radiative interference and induced coherence," Phys. Rev. Lett. 81, 2675-2678 (1998).
[CrossRef]

1997 (2)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

A. O. Orlov, I. Amlani, G. H. Bernstein, C. S. Lent, and G. L. Snider, "Realization of a functional cell for quantum-dot cellular automata," Science 277, 928-930 (1997).
[CrossRef]

1996 (2)

J. B. Watson, A. Saprera, X. Chen, and K. Burnett, "Harmonic generation from a coherent superposition of states," Phys. Rev. A 53, R1962-R1965 (1996).
[CrossRef] [PubMed]

M. Jain, Hui Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

1995 (2)

S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
[CrossRef] [PubMed]

J. Marangos, "Optics-focusing light with light," Nature 372, 679-680 (1995).
[CrossRef]

1994 (4)

S. E. Harris, "Normal modes for electromagnetically induced transparency," Phys. Rev. Lett. 72, 52-55 (1994).
[CrossRef] [PubMed]

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
[CrossRef] [PubMed]

F. T. Hioe and R. Grobe, "Matched optical solitary waves for three- and five-level systems," Phys. Rev. Lett. 73, 2559-2562 (1994).
[CrossRef] [PubMed]

J. H. Eberly, M. L. Pons, and H. R. Haq, "Dressed-field pulses in an absorbing medium," Phys. Rev. Lett. 72, 56-59 (1994).
[CrossRef] [PubMed]

1993 (2)

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, "Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence," Phys. Rev. Lett. 71, 3095-3098 (1993).
[CrossRef] [PubMed]

A. Nottelmann, C. Peters, and W. Lamge, "Inversionless amplification of picosecond pulses due to Zeeman coherence," Phys. Rev. Lett. 70, 1783-1786 (1993).
[CrossRef] [PubMed]

1992 (2)

B. W. Shore, K. Bergmann, A. Kuhn, S. Schiemann, J. Oreg, and J. H. Eberly, "Laser-induced population transfer in multistate systems: a comparative study," Phys. Rev. A 45, 5297-5300 (1992).
[CrossRef] [PubMed]

P. Brumer and M. Shapiro, "Laser control of molecular processes," Annu. Rev. Phys. Chem. 43, 257-282 (1992).
[CrossRef] [PubMed]

1991 (2)

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

P. Brumer and M. Shapiro, "Laser control of molecular processes," Annu. Rev. Phys. Chem. 43, 257-282 (1992).
[CrossRef] [PubMed]

Chin. Phys. (1)

X. Z. Zhang, Q. Z. Ma, and X. H. Li, "Coherent population transfer in Rydberg potassium atom by a single frequency-chirped laser pulse," Chin. Phys. 15, 1497-1501 (2006).
[CrossRef]

Eur. Phys. J. D (2)

R. Unanyan, S. Guérin, B. W. Shore, and K. Bergmann, "Efficient population transfer by delayed pulses despite coupling ambiguity," Eur. Phys. J. D 8, 443-449 (2000).
[CrossRef]

E. Korsunsky, T. Halfmann, J. P. Marangos, M. Fleischhauer, and K. Bergmann, "Analytical study of four-wave mixing with large atomic coherence," Eur. Phys. J. D 23, 167-180 (2003).
[CrossRef]

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

Laser Phys. (1)

G. Djotyan, J. Bakos, Zs. Sörlei, J. Szigeti, P. Ignacz, and Z. Toth, "Interaction of a sequence of frequency-chirped bichromatic laser pulses with an ensemble of lambda-atoms: population trapping and coherent optical pumping," Laser Phys. 10, 355-359 (2000).

Nature (1)

J. Marangos, "Optics-focusing light with light," Nature 372, 679-680 (1995).
[CrossRef]

Opt. Commun. (3)

T. Rickes, J. P. Marangos, and T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

L. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, "Creation of coherent superpositions using Stark-chirped rapid adiabatic passage," Opt. Commun. 204, 413-423 (2002).
[CrossRef]

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, "Robust creation and phase-sensitive probing of superposition states via STIRAP with degenerate dark states," Opt. Commun. 155, 144-154 (1998).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (12)

G. P. Djotyan, J. S. Bakos, and Zs. Sörlei, "Three-level Λ-atom in the field of frequency-chirped bichromatic laser pulses: writing and storage of optical phase information," Phys. Rev. A 64, 013408 (2001).
[CrossRef]

N. Sangouard, S. Guérin, L. P. Yatsenko, and T. Halfmann, "Preparation of coherent superposition in a three-state system by adiabatic passage," Phys. Rev. A 70, 013415 (2004).
[CrossRef]

S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
[CrossRef] [PubMed]

J. B. Watson, A. Saprera, X. Chen, and K. Burnett, "Harmonic generation from a coherent superposition of states," Phys. Rev. A 53, R1962-R1965 (1996).
[CrossRef] [PubMed]

Z. Kis, A. Karpati, B. W. Shore, and V. V. Vitanov, "Stimulated Raman adiabatic passage among degenerate-level manifolds," Phys. Rev. A 70, 053405 (2004).
[CrossRef]

Z. Kis, N. V. Vitanov, A. Karpati, C. Barthel, and K. Bergmann, "Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage," Phys. Rev. A 72, 033403 (2005).
[CrossRef]

S. Menon and G. S. Agarwal, "Gain from cross talk among optical transitions," Phys. Rev. A 59, 740-749 (1999).
[CrossRef]

B. W. Shore, K. Bergmann, A. Kuhn, S. Schiemann, J. Oreg, and J. H. Eberly, "Laser-induced population transfer in multistate systems: a comparative study," Phys. Rev. A 45, 5297-5300 (1992).
[CrossRef] [PubMed]

R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann, "Adiabatic creation of coherent superposition states in atomic beams," Phys. Rev. A 70, 053404 (2004).
[CrossRef]

I. E. Mazets, "Adiabatic pulse propagation in coherent atomic media with the tripod level configuration," Phys. Rev. A 71, 023806 (2005).
[CrossRef]

L. Rippe, M. Nilsson, S. Kröll, R. Klieber, and D. Suter, "Experimental demonstration of efficient and selective population transfer and qubit distillation in a rare-earth-metal-ion-doped crystal," Phys. Rev. A 71, 062328 (2005).
[CrossRef]

G. P. Djotyan, J. S. Bakos, Zs. Sörlei, and J. Szigeti, "Coherent control of atomic quantum states by single frequency-chirped laser pulses," Phys. Rev. A 70, 063406 (2004).
[CrossRef]

Phys. Rev. Lett. (12)

A. Nottelmann, C. Peters, and W. Lamge, "Inversionless amplification of picosecond pulses due to Zeeman coherence," Phys. Rev. Lett. 70, 1783-1786 (1993).
[CrossRef] [PubMed]

R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of shape-preserving pulses in a nonlinear adiabatically integrable system," Phys. Rev. Lett. 73, 3183-3186 (1994).
[CrossRef] [PubMed]

F. T. Hioe and R. Grobe, "Matched optical solitary waves for three- and five-level systems," Phys. Rev. Lett. 73, 2559-2562 (1994).
[CrossRef] [PubMed]

J. H. Eberly, M. L. Pons, and H. R. Haq, "Dressed-field pulses in an absorbing medium," Phys. Rev. Lett. 72, 56-59 (1994).
[CrossRef] [PubMed]

M. Jain, Hui Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. F. Harris, "Raman generation by phased and antiphased molecular states," Phys. Rev. Lett. 85, 562-565 (2000).
[CrossRef] [PubMed]

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. Scully, "Resonant enhancement of parametric processes via radiative interference and induced coherence," Phys. Rev. Lett. 81, 2675-2678 (1998).
[CrossRef]

A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, "Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence," Phys. Rev. Lett. 71, 3095-3098 (1993).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

S. E. Harris, "Normal modes for electromagnetically induced transparency," Phys. Rev. Lett. 72, 52-55 (1994).
[CrossRef] [PubMed]

F. Vewinger, M. Heinz, R. G. Fernandez, N. V. Vitanov, and K. Bergmann, "Creation and measurement of a coherent superposition of quantum states," Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
[CrossRef]

Science (1)

A. O. Orlov, I. Amlani, G. H. Bernstein, C. S. Lent, and G. L. Snider, "Realization of a functional cell for quantum-dot cellular automata," Science 277, 928-930 (1997).
[CrossRef]

Other (5)

C. P. Williams and S. H. Clearwater, Explorations in Quantum Quantum Computing (Springer-Verlag, 1997).

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer-Verlag, 2000).
[PubMed]

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

L. Jacak, P. Hawrylak, and A. Wójs, Quantum Dots (Springer, 1997).

A. Messiah, Quantum Mechanics (North-Holland, 1962), Vol. II.

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Figures (6)

Fig. 1
Fig. 1

Scheme of the tripod-linkage atom levels. Levels ∣1⟩ and ∣3⟩ are the close levels, and level ∣2⟩ represents the far level.

Fig. 2
Fig. 2

(a) Population dynamics of the states of the tripod-linkage atom during action of the frequency-chirped laser pulse. Parameters applied are duration of the pulse τ p = 15 ns , Rabi frequency for transitions from the metastable states to the excited state (the dipole moments for the allowed transitions are assumed equal to each other for simplicity) is Ω 10 = Ω 20 = Ω 30 = 15 GHz , and the speed of the frequency chirp β = 3 GHz ns , the distance Δ ω 31 between the close levels is equal to 10 MHz and the distance between the close and the far levels is equal to 1 GHz . (b) Population of the excited state. (c) Evolution of the phase of the Raman coherence between states ∣1⟩ and ∣3⟩ in units of π.

Fig. 3
Fig. 3

Structure of the quantum states of the equivalent-linkage atom with one of the ground states, d b being a superposition of the close metastable states of the tripod atom.

Fig. 4
Fig. 4

Evolution of the quasienergies of the equivalent Λ-linkage atom during the action of the frequency-chirped laser pulse corresponding to the case of the quantum states population dynamics shown in Fig. 2. Dashed lines are the diabatic lines. Time is normalized by τ p .

Fig. 5
Fig. 5

Population dynamics in the tripod-linkage atom for two atoms moving with different velocities (different values of the Doppler shift of the transition lines). The central frequency of the laser pulse has Doppler shift (a) ω D = 2 β τ p ; (b) ω D = 2 β τ p .

Fig. 6
Fig. 6

Energy scheme of the J = 1 J 1 = 0 transition of a Sm atom in a magnetic field with additionally applied nonresonant π-polarized laser field performing Stark shift of the sublevels with m = 0 . The electric strength vector E of the frequency-chirped laser pulse is shown in the right part of the figure with σ and π components. The quantizing magnetic field is directed along the Z axis.

Equations (24)

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Ψ ( t ) = exp [ i E 1 t ] { a 0 ( t ) exp [ i ω L ( t ) t ] 0 + a 1 ( t ) 1 + a 2 ( t ) 2 + a 3 ( t ) 3 } ,
a ̇ 0 i a 0 ε 1 ( t ) = i 2 A ( t ) [ a 1 d 10 + a 2 d 20 + a 3 d 30 ] ,
a ̇ 1 = i 2 A ( t ) d 01 a 0 ,
a ̇ 2 + i Δ ω 21 a 2 = i 2 A ( t ) a 0 d 02 ,
a ̇ 3 + i Δ ω 31 a 3 = i 2 A ( t ) a 0 d 03 ,
Δ ω L Δ ω 13 ,
Δ ω L < Δ ω 12 .
d b = 1 1 + γ 31 2 ( 1 + γ 31 3 ) , d d = 1 1 + γ 31 2 ( γ 31 1 3 ) ,
d ̇ b = i 2 a 0 F 1 , a ̇ 2 + i Δ ω 21 a 2 = i 2 a 0 F 2 , d ̇ d = 0 ,
a ̇ 0 i a 0 ε 1 = i 2 [ d b F 1 * + a 2 F 2 * ] ,
i d d t c ̱ = H ̂ b c ̱ ,
H ̂ b = [ 0 F 1 2 0 F 1 * 2 ε 1 F 2 * 2 0 F 2 2 Δ ω 21 ] .
c ̱ ( t ) = k r k ( t ) b ̱ ( k ) ( t ) exp [ i t w k ( t ) d t ] ,
c ̱ ( ) = k r k ( ) b ̱ ( k ) ( ) ,
H ̂ b b ̱ ( k ) = w k b ̱ ( k ) .
w 3 + w 2 [ Δ ω 21 ε 1 ] w 2 [ ε 1 Δ ω 21 + ( F 1 2 + F 2 2 ) ] 3 F 1 2 Δ ω 21 = 0 ,
b 1 ( k ) = F 1 ( w k + Δ ω 21 ) N , b 2 ( k ) = w k ( w k + Δ ω 21 ) N , b 3 ( k ) = F 2 w k N ,
N = F 1 2 2 ( w k + Δ ω 21 ) 2 + w k 2 ( w k + Δ ω 21 ) 2 + F 2 2 2 w k 2 .
0 w 1 Δ ω 21 .
b ̱ ( 1 ) ( t ) = b 1 ( 1 ) ( 1 0 0 ) T + b 2 ( 1 ) ( 0 1 0 ) T + b 3 ( 1 ) ( 0 0 1 ) T
b 2 ( k ) b 1 ( k ) = w k F 1 , b 3 ( k ) b 1 ( k ) = F 2 w k F 1 ( w k Δ ω 21 ) ( k = 1 , 2 , 3 ) .
w 1 d 01 2 + d 03 2 d 01 2 + d 03 2 + d 02 2 Δ ω 21 ,
F 1 2 + F 2 2 ε 1 Δ ω 21 , F 1 Δ ω 21 .
Ψ ( ) = γ 31 2 1 + γ 31 2 1 + 1 1 + γ 31 2 2 γ 31 1 + γ 31 2 3 .

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