Abstract

Electromagnetically induced transparency (EIT) effect has been studied using an extremely thin cell (ETC) with the thickness of an Rb vapor column of the order of light wavelength λ(780nm) and varying in the range of 0.5λ2.5λ. Λ-systems on the D2 line of Rb85 and Rb87 have been studied experimentally. Along with EIT resonance, we study the peculiarities of velocity-selective optical pumping/saturation (VSOP) resonances, which accompany the EIT resonance and, as a rule, are spectrally broader. It is demonstrated that size-conditioned strongly anisotropic contribution of atoms with different velocities in an ETC causes several dramatic differences of the EIT and VSOP resonances formation in the ETC as compared with an ordinary 110cm long cell. Particularly, in the case of the ETC, the EIT linewidth and contrast dramatically depend on the coupling laser detuning from the exact atomic transition. A theoretical model taking into account the peculiarities of transmission spectra when L=nλ and L=(2n+1)λ2 (n is an integer) has been developed. The experimental transmission spectra are well described by the theoretical model developed. The possibility of EIT resonance formation when atomic column thickness is of the order of L=0.5λ and less is theoretically predicted.

© 2007 Optical Society of America

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  1. G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
    [CrossRef]
  2. E. Arimondo, "Coherent population trapping in laser spectroscopy," in Progress in Optics, Vol. 35, E.Wolf, ed. (Elsevier, 1996) pp. 257-354.
    [CrossRef]
  3. S. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  4. R. Wynands and A. Nagel, "Precision spectroscopy with coherent dark states," Appl. Phys. B 68, 1-25 (1999) and references therein.
    [CrossRef]
  5. E. B. Alexandrov, "Recent progress in optically pumped magnetometers," Phys. Scr., T 105, 27-30 (2003).
    [CrossRef]
  6. S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
    [CrossRef] [PubMed]
  7. D. Budker, V. Yashchuk, and M. Zolotorev, "Nonlinear magneto-optic effects with ultra narrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
    [CrossRef]
  8. D. Petrosyan and Yu. Malakyan, "Electromagnetically induced transparency in a thin vapor film," Phys. Rev. A 61, 053820 (2000).
    [CrossRef]
  9. A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
    [CrossRef]
  10. D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
    [CrossRef]
  11. E. A. Gazazyan, A. V. Papoyan, D. Sarkisyan, and A. Weis, "Laser frequency stabilization using selective reflection from a vapor cell with a half-wavelength thickness," submitted to Laser Phys. Lett.
  12. G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
    [CrossRef]
  13. G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, "Revising optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry-Perot microcavity effect," J. Opt. Soc. Am. B 20, 793-800 (2003).
    [CrossRef]
  14. D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
    [CrossRef]
  15. D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
    [CrossRef]
  16. J. H. Eberly, "Atomic relaxation in the presence of intense partially coherent radiation fields," Phys. Rev. Lett. 37, 1387-1390 (1976).
    [CrossRef]
  17. G. S. Agarwal, "Exact solution for the influence of laser temporal fluctuations on resonance fluorescence," Phys. Rev. Lett. 37, 1383-1386 (1976).
    [CrossRef]
  18. P. Zoller, "Fokker-Planck equation treatment of atomic relaxation and resonance fluorescence in phase-modulated laser light," J. Phys. B 10, L321-L324 (1977).
    [CrossRef]
  19. G. S. Agarwal, "Quantum statistical theory of optical-resonance phenomena in fluctuating laser fields," Phys. Rev. A 18, 1490-1506 (1978).
    [CrossRef]
  20. B. J. Dalton and P. L. Knight, "Population trapping and ultranarrow Raman lineshapes induced by phase-fluctuating fields," Opt. Commun. 42, 411-416 (1982).
    [CrossRef]
  21. G. Nikogosyan, D. Sarkisyan, and Yu. Malakyan, "Absorption of resonance radiation and fluorescence of a layer of an atomic gas with thickness of the order of a wavelength," J. Opt. Technol. 71, 602-607 (2004).
    [CrossRef]
  22. I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).
  23. A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
    [CrossRef]
  24. Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
    [CrossRef]
  25. J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
    [CrossRef]

2006 (3)

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
[CrossRef]

2005 (1)

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

2004 (4)

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

G. Nikogosyan, D. Sarkisyan, and Yu. Malakyan, "Absorption of resonance radiation and fluorescence of a layer of an atomic gas with thickness of the order of a wavelength," J. Opt. Technol. 71, 602-607 (2004).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
[CrossRef] [PubMed]

2003 (3)

E. B. Alexandrov, "Recent progress in optically pumped magnetometers," Phys. Scr., T 105, 27-30 (2003).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, "Revising optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry-Perot microcavity effect," J. Opt. Soc. Am. B 20, 793-800 (2003).
[CrossRef]

2001 (1)

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
[CrossRef]

2000 (1)

D. Petrosyan and Yu. Malakyan, "Electromagnetically induced transparency in a thin vapor film," Phys. Rev. A 61, 053820 (2000).
[CrossRef]

1999 (1)

R. Wynands and A. Nagel, "Precision spectroscopy with coherent dark states," Appl. Phys. B 68, 1-25 (1999) and references therein.
[CrossRef]

1998 (1)

D. Budker, V. Yashchuk, and M. Zolotorev, "Nonlinear magneto-optic effects with ultra narrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
[CrossRef]

1982 (1)

B. J. Dalton and P. L. Knight, "Population trapping and ultranarrow Raman lineshapes induced by phase-fluctuating fields," Opt. Commun. 42, 411-416 (1982).
[CrossRef]

1978 (1)

G. S. Agarwal, "Quantum statistical theory of optical-resonance phenomena in fluctuating laser fields," Phys. Rev. A 18, 1490-1506 (1978).
[CrossRef]

1977 (1)

P. Zoller, "Fokker-Planck equation treatment of atomic relaxation and resonance fluorescence in phase-modulated laser light," J. Phys. B 10, L321-L324 (1977).
[CrossRef]

1976 (3)

J. H. Eberly, "Atomic relaxation in the presence of intense partially coherent radiation fields," Phys. Rev. Lett. 37, 1387-1390 (1976).
[CrossRef]

G. S. Agarwal, "Exact solution for the influence of laser temporal fluctuations on resonance fluorescence," Phys. Rev. Lett. 37, 1383-1386 (1976).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, "Quantum statistical theory of optical-resonance phenomena in fluctuating laser fields," Phys. Rev. A 18, 1490-1506 (1978).
[CrossRef]

G. S. Agarwal, "Exact solution for the influence of laser temporal fluctuations on resonance fluorescence," Phys. Rev. Lett. 37, 1383-1386 (1976).
[CrossRef]

Akulshin, A. M.

A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
[CrossRef]

Alexandrov, E. B.

E. B. Alexandrov, "Recent progress in optically pumped magnetometers," Phys. Scr., T 105, 27-30 (2003).
[CrossRef]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Arimondo, E.

E. Arimondo, "Coherent population trapping in laser spectroscopy," in Progress in Optics, Vol. 35, E.Wolf, ed. (Elsevier, 1996) pp. 257-354.
[CrossRef]

Bloch, D.

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, "Revising optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry-Perot microcavity effect," J. Opt. Soc. Am. B 20, 793-800 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
[CrossRef]

Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
[CrossRef]

Budker, D.

D. Budker, V. Yashchuk, and M. Zolotorev, "Nonlinear magneto-optic effects with ultra narrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
[CrossRef]

Dalton, B. J.

B. J. Dalton and P. L. Knight, "Population trapping and ultranarrow Raman lineshapes induced by phase-fluctuating fields," Opt. Commun. 42, 411-416 (1982).
[CrossRef]

Ducloy, M.

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, "Revising optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry-Perot microcavity effect," J. Opt. Soc. Am. B 20, 793-800 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
[CrossRef]

Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
[CrossRef]

Dutier, G.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, "Revising optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry-Perot microcavity effect," J. Opt. Soc. Am. B 20, 793-800 (2003).
[CrossRef]

Eberly, J. H.

J. H. Eberly, "Atomic relaxation in the presence of intense partially coherent radiation fields," Phys. Rev. Lett. 37, 1387-1390 (1976).
[CrossRef]

Fichet, M.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Gazazyan, E. A.

E. A. Gazazyan, A. V. Papoyan, D. Sarkisyan, and A. Weis, "Laser frequency stabilization using selective reflection from a vapor cell with a half-wavelength thickness," submitted to Laser Phys. Lett.

Gorza, M.-P.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Hamdi, I.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Harris, S.

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

Hollberg, L.

Juncar, P.

Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
[CrossRef]

Kitching, J.

Knappe, S.

Knight, P. L.

B. J. Dalton and P. L. Knight, "Population trapping and ultranarrow Raman lineshapes induced by phase-fluctuating fields," Opt. Commun. 42, 411-416 (1982).
[CrossRef]

Lezama, A.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Li, Y.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Liu, T.

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

Liu, Z. D.

Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
[CrossRef]

Malakyan, Yu.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Nikogosyan, D. Sarkisyan, and Yu. Malakyan, "Absorption of resonance radiation and fluorescence of a layer of an atomic gas with thickness of the order of a wavelength," J. Opt. Technol. 71, 602-607 (2004).
[CrossRef]

D. Petrosyan and Yu. Malakyan, "Electromagnetically induced transparency in a thin vapor film," Phys. Rev. A 61, 053820 (2000).
[CrossRef]

Maurin, I.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Nagel, A.

R. Wynands and A. Nagel, "Precision spectroscopy with coherent dark states," Appl. Phys. B 68, 1-25 (1999) and references therein.
[CrossRef]

Nikogosyan, G.

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Papoyan, A.

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
[CrossRef]

Papoyan, A. V.

E. A. Gazazyan, A. V. Papoyan, D. Sarkisyan, and A. Weis, "Laser frequency stabilization using selective reflection from a vapor cell with a half-wavelength thickness," submitted to Laser Phys. Lett.

Petrosyan, D.

D. Petrosyan and Yu. Malakyan, "Electromagnetically induced transparency in a thin vapor film," Phys. Rev. A 61, 053820 (2000).
[CrossRef]

Saltiel, S.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, "Revising optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry-Perot microcavity effect," J. Opt. Soc. Am. B 20, 793-800 (2003).
[CrossRef]

Sargsyan, A.

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
[CrossRef]

Sarkisyan, A.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Sarkisyan, D.

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
[CrossRef]

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Nikogosyan, D. Sarkisyan, and Yu. Malakyan, "Absorption of resonance radiation and fluorescence of a layer of an atomic gas with thickness of the order of a wavelength," J. Opt. Technol. 71, 602-607 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
[CrossRef]

E. A. Gazazyan, A. V. Papoyan, D. Sarkisyan, and A. Weis, "Laser frequency stabilization using selective reflection from a vapor cell with a half-wavelength thickness," submitted to Laser Phys. Lett.

Staedter, D.

A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
[CrossRef]

Todorov, P.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Varzhapetyan, T.

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Wang, J.

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

Wang, Y.

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

Weis, A.

E. A. Gazazyan, A. V. Papoyan, D. Sarkisyan, and A. Weis, "Laser frequency stabilization using selective reflection from a vapor cell with a half-wavelength thickness," submitted to Laser Phys. Lett.

Wynands, R.

R. Wynands and A. Nagel, "Precision spectroscopy with coherent dark states," Appl. Phys. B 68, 1-25 (1999) and references therein.
[CrossRef]

Yan, S.

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

Yarovitski, A.

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

Yashchuk, V.

D. Budker, V. Yashchuk, and M. Zolotorev, "Nonlinear magneto-optic effects with ultra narrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
[CrossRef]

Zhang, T.

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

Zoller, P.

P. Zoller, "Fokker-Planck equation treatment of atomic relaxation and resonance fluorescence in phase-modulated laser light," J. Phys. B 10, L321-L324 (1977).
[CrossRef]

Zolotorev, M.

D. Budker, V. Yashchuk, and M. Zolotorev, "Nonlinear magneto-optic effects with ultra narrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
[CrossRef]

Appl. Phys. B (1)

R. Wynands and A. Nagel, "Precision spectroscopy with coherent dark states," Appl. Phys. B 68, 1-25 (1999) and references therein.
[CrossRef]

Appl. Phys. B: Lasers Opt. (1)

J. Wang, Y. Wang, S. Yan, T. Liu, and T. Zhang, "Observation of sub-Doppler absorption in the Λ-type three-level Doppler-broadened cesium system," Appl. Phys. B: Lasers Opt. 78, 217-220 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

Z. D. Liu, P. Juncar, D. Bloch, and M. Ducloy, "Raman polarization-selective feedback schemes for all-optical microwave frequency standards," Appl. Phys. Lett. 69, 2318-2320 (1996).
[CrossRef]

Europhys. Lett. (1)

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, "Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy," Europhys. Lett. 63, 35-41 (2003).
[CrossRef]

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

J. Opt. Technol. (1)

J. Phys. B (1)

P. Zoller, "Fokker-Planck equation treatment of atomic relaxation and resonance fluorescence in phase-modulated laser light," J. Phys. B 10, L321-L324 (1977).
[CrossRef]

Laser Phys. (1)

I. Hamdi, P. Todorov, A. Yarovitski, G. Dutier, I. Maurin, S. Saltiel, Y. Li, A. Lezama, T. Varzhapetyan, D. Sarkisyan, M.-P. Gorza, M. Fichet, D. Bloch, and M. Ducloy, "Laser spectroscopy with nanometric gas cells: distance dependence of atom-surface interaction and collisions under confinement," Laser Phys. 15, 987-996 (2005).

Nuovo Cimento Soc. Ital. Fis., B (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of the RF transition and laser beat resonance in oriented Na vapour," in Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Opt. Commun. (2)

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, "Sub-Doppler spectroscopy by submicron thin Cs-vapor layer," Opt. Commun. 200, 201-208 (2001).
[CrossRef]

B. J. Dalton and P. L. Knight, "Population trapping and ultranarrow Raman lineshapes induced by phase-fluctuating fields," Opt. Commun. 42, 411-416 (1982).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

A. Sargsyan, D. Sarkisyan, D. Staedter, and A. M. Akulshin, "Doppler-free satellites of resonances of electromagnetically induced transparency and absorption on the D2 lines of alkali metals," Opt. Spectrosc. 101, 762-768 (2006).
[CrossRef]

Phys. Rev. A (4)

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, "Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques," Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. S. Agarwal, "Quantum statistical theory of optical-resonance phenomena in fluctuating laser fields," Phys. Rev. A 18, 1490-1506 (1978).
[CrossRef]

D. Petrosyan and Yu. Malakyan, "Electromagnetically induced transparency in a thin vapor film," Phys. Rev. A 61, 053820 (2000).
[CrossRef]

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

D. Budker, V. Yashchuk, and M. Zolotorev, "Nonlinear magneto-optic effects with ultra narrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
[CrossRef]

J. H. Eberly, "Atomic relaxation in the presence of intense partially coherent radiation fields," Phys. Rev. Lett. 37, 1387-1390 (1976).
[CrossRef]

G. S. Agarwal, "Exact solution for the influence of laser temporal fluctuations on resonance fluorescence," Phys. Rev. Lett. 37, 1383-1386 (1976).
[CrossRef]

Phys. Scr., T (1)

E. B. Alexandrov, "Recent progress in optically pumped magnetometers," Phys. Scr., T 105, 27-30 (2003).
[CrossRef]

Phys. Today (1)

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

Proc. SPIE (1)

D. Sarkisyan, T. Varzhapetyan, A. Papoyan, D. Bloch, and M. Ducloy, "Absorption and fluorescence in atomic submicron cell: high laser intensity case," in ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, S. N. Bagayev, A. Chikishev, A. Dmitriev, M. Ducloy, Y. Heinz, V. Letokhov, A. Shkurinov, and H. Takahashi, eds., Proc. SPIE 6257, 625701 (2006).
[CrossRef]

Other (2)

E. A. Gazazyan, A. V. Papoyan, D. Sarkisyan, and A. Weis, "Laser frequency stabilization using selective reflection from a vapor cell with a half-wavelength thickness," submitted to Laser Phys. Lett.

E. Arimondo, "Coherent population trapping in laser spectroscopy," in Progress in Optics, Vol. 35, E.Wolf, ed. (Elsevier, 1996) pp. 257-354.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Energy level diagram of the six-level model.

Fig. 2
Fig. 2

Transmission spectra of the probe laser scanned across Rb 87 F g = 1 F e = 0 , 1 , 2 transitions (the relevant energy levels of Rb 87 are presented in the upper-left inset), when the coupling laser is resonant with F g = 2 F e = 2 transition. The cell thickness L = λ ( 780 nm ) , γ L = 5 MHz . (a) Experimental results. The upper inset presents results of the fitting by Lorentzian profiles. FWHM of the EIT and VSOP resonances are 12 and 30 MHz , correspondingly. (b) Numerical simulation, all the parameters are the same as in (a), and Ω c = 1.5 Γ , Ω p = 0.35 Γ . FWHM of the EIT and VSOP resonances are 12 and 20 MHz , correspondingly.

Fig. 3
Fig. 3

Transmission spectra of the probe laser scanned across Rb 87 F g = 1 F e = 0 , 1 , 2 transitions when the coupling laser is red detuned by 48 MHz from the F g = 2 F e = 2 transition. The cell thickness is L = 2 λ ( 1560 nm ) . (a) Experiment, γ L = 5 MHz . The middle curve is the case when the coupling laser is blocked (the curve is vertically shifted for convenience). The lower curve (dotted) presents the transmission spectra of the reference ETC1, L = λ . (b) Theoretical curve, all the parameters are the same as in (a). The Rabi frequencies of the couple and the probe lasers are Ω c = 2 Γ and Ω p = 0.3 Γ , correspondingly. The arrow shows the EIT resonance accompanied by the VSOP resonances. The lower curve is the case when the couple is blocked.

Fig. 4
Fig. 4

Transmission spectra of the probe laser scanned across Rb 85 F g = 2 F e = 1 , 2 , 3 transitions; the couple is resonant with F g = 3 F e = 3 transition (the relevant energy levels are presented in the inset). The cell thickness L = λ ( 780 nm ) , γ L = 5 MHz . (a) Experiment. Only the EIT resonance (pointed with the arrow on the upper curve) is present, while the VSOP resonances are absent due to a strong repumping. The lower curve presents the case when the couple is blocked (the curve is vertically shifted for convenience). (b) Numerical calculations with all the parameters are the same as in (a), Ω c = 1 Γ and Ω p = 0.26 Γ , correspondingly. (c) Transmission spectra of the probe laser under the same conditions as in (a).

Fig. 5
Fig. 5

Transmission spectra of the probe laser scanned across Rb 85 F g = 2 F e = 1 , 2 , 3 transitions. (1) and (2) refer to the coupling laser blue detuned by 15 MHz from F g = 3 F e = 3 transition; the cell thickness is L = 2.5 λ . The pointing arrows show the EIT resonances: (1) experiment and (2) numerical calculations. (3) and (4) refer to the case where the couple is resonant with F g = 3 F e = 3 transition, the cell thickness L = 1.5 λ : (3) experiment and (4) numerical calculations. (5) The transmission spectrum of the reference ETC1, L = λ .

Fig. 6
Fig. 6

Calculated linewidth of the EIT resonance as a function of the laser radiation spectral width (couple and probe are assumed to have the same linewidth). The coupling laser is resonant with Rb 87 F g = 2 F e = 2 transition, cell thickness L = λ ( 780 nm ) , Ω c = 1.5 Γ , Ω p = 0.35 Γ .

Fig. 7
Fig. 7

Calculated transmission spectra of the probe field for the cell thickness L = λ 2 ( 390 nm ) when the couple is resonant Rb 85 F g = 3 F e = 3 transition (the relevant energy levels are presented in the inset); γ L = 1 MHz, Ω c = 1 Γ , Ω p = 0.3 Γ . (1) the couple beam is blocked, (2) the couple is on. EIT resonance on curve (2) is marked by an arrow. A possibility to observe EIT resonance at the cell thickness L = λ 2 is a remarkable result (see the text). Also on curve (2), the increase of absorption on VSOP resonances on F g = 2 F e = 1 , 2 transitions is observable [compare with curve (1)].

Fig. 8
Fig. 8

Calculated probe field transmission spectra as a function of the blue detuning of the couple field frequency from the Rb 87 , F g = 2 F e = 2 transition. The cell thickness L = λ ( 780 nm ) , γ L = 1 MHz , Ω c = 1.5 Γ , Ω p = 0.35 Γ , Γ = 6 MHz . (1) dashed curve, coupling laser is blocked, (2) coupling laser is resonant with F g = 2 F e = 2 transition, (3) couple laser is blue detuned by 3 Γ , (4) by 6 Γ , (5) by 10 Γ . γ E I T =12, 16, 25, and 36 MHz for (2), (3), (4), and (5), correspondingly; γ V S O P 18 MHz for all cases (2)–(5).

Fig. 9
Fig. 9

Transmission spectrum of the probe laser (upper curve), when the coupling laser is resonant with the Rb 85 F g = 3 F e = 2 transition, while the probe laser is scanned across F g = 2 F e = 1 , 2 , 3 transitions. The cell length is 1 cm , and the temperature is 40 ° C . In the upper curve, the EIT resonance (with the linewidth of 2 3 MHz and mentioned by the pointing arrow) is seen together with seven VSOP resonances. The lower curve is the transmission spectrum of the ETC1 for the L = λ and serves as a reference for the calibration of the frequency scale.

Equations (32)

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Δ p 1 , 2 , 3 = ω i 1 ω p ± k p v z ( i = 3 , 4 , 5 ) ,
Δ c 4 , 5 , 6 = ω i 2 ω c ± k c v z ( i = 4 , 5 , 6 ) ,
d ρ d t = i [ H , ρ ] + Λ ρ .
P ( z ) = N j = 3 5 μ j 1 ( ρ j 1 + + ρ j 1 ) ,
ρ ̇ 31 = i Ω 1 ( ρ 11 ρ 33 ) i Ω 2 ρ 34 i Ω 3 ρ 35 [ i Δ p 1 + Γ 31 ] ρ 31 ,
ρ ̇ 41 = i Ω 2 ( ρ 11 ρ 44 ) + i Ω 4 ρ 21 i Ω 1 ρ 43 i Ω 3 ρ 45 [ i Δ p 2 + Γ 41 ] ρ 41 ,
ρ 51 ̇ = i Ω 3 ( ρ 11 ρ 55 ) + i Ω 5 ρ 21 i Ω 1 ρ 51 i Ω 2 ρ 54 [ i Δ p 3 + Γ 51 ] ρ 51 .
1 E p 2 A = 4 π ω p N t 2 2 t 1 c u u 1 E p F 2 0 e v z 2 u 2 v z d v z 0 L v d t × Im { i = 3 5 μ i 1 [ ρ i 1 + ( t , Δ + , E p 0 ( v z t ) ) ( 1 r 1 e 2 i k p v z t ) + ρ i 1 ( t , Δ , E p 0 ( L v z t ) ) ( 1 r 1 e 2 i k p ( L v z t ) ) ] } .
E p 0 ( z ) = E p t 1 F [ 1 r 2 e 2 i k ( L z ) ] ,
ρ ̇ 11 = 2 Im ( Ω 1 * ρ 31 ) 2 Im ( Ω 2 * ρ 41 ) 2 Im ( Ω 3 * ρ 51 ) + γ 31 ρ 33 + γ 41 ρ 44 + γ 51 ρ 55 ,
ρ ̇ 22 = 2 Im ( Ω 4 * ρ 42 ) 2 Im ( Ω 5 * ρ 52 ) 2 Im ( Ω 6 * ρ 62 ) + γ 42 ρ 44 + γ 52 ρ 55 + γ 62 ρ 66 ,
ρ ̇ 33 = 2 Im ( Ω 1 * ρ 31 ) Γ 33 ρ 33 ,
ρ ̇ 44 = 2 Im ( Ω 2 * ρ 41 ) + 2 Im ( Ω 4 * ρ 42 ) Γ 44 ρ 44 ,
ρ ̇ 55 = 2 Im ( Ω 3 * ρ 51 ) + 2 Im ( Ω 5 * ρ 52 ) Γ 55 ρ 55 ,
ρ ̇ 66 = 2 Im ( Ω 6 * ρ 62 ) Γ 66 ρ 66 ,
ρ ̇ 62 = i Ω 6 ( ρ 22 ρ 66 ) i Ω 4 ρ 64 i Ω 5 ρ 65 ( i Δ 6 c + Γ 62 ) ρ 62 ,
ρ ̇ 52 = i Ω 5 ( ρ 22 ρ 55 ) + i Ω 3 ρ 12 i Ω 4 ρ 54 i Ω 6 ρ 56 ( i Δ 5 c + Γ 52 ) ρ 52 ,
ρ ̇ 42 = i Ω 4 ( ρ 22 ρ 44 ) + i Ω 2 ρ 12 i Ω 5 ρ 45 i Ω 6 ρ 46 ( i Δ 4 c + Γ 42 ) ρ 42 ,
ρ ̇ 32 = i Ω 1 ρ 12 i Ω 4 ρ 34 i Ω 5 ρ 35 i Ω 6 ρ 36 [ i ( Δ 5 c δ 1 δ 2 ) + Γ 32 ] ρ 32 ,
ρ ̇ 61 = i Ω 6 ρ 21 i Ω 2 ρ 64 i Ω 3 ρ 65 i Ω 1 ρ 63 [ i ( Δ 6 c + Δ R ) + Γ 61 ] ρ 61 ,
ρ ̇ 51 = i Ω 3 ( ρ 11 ρ 55 ) + i Ω 5 ρ 21 i Ω 1 ρ 53 i Ω 2 ρ 54 [ i Δ 3 p + Γ 51 ] ρ 51 ,
ρ ̇ 41 = i Ω 2 ( ρ 11 ρ 44 ) + i Ω 4 ρ 21 i Ω 1 ρ 43 i Ω 3 ρ 45 [ i Δ 2 p + Γ 41 ] ρ 41 ,
ρ ̇ 31 = i Ω 1 ( ρ 11 ρ 33 ) i Ω 2 ρ 34 i Ω 3 ρ 35 [ i Δ 1 p + Γ 31 ] ρ 31 ,
ρ ̇ 65 = i Ω 3 * ρ 61 + i Ω 6 ρ 25 i Ω 5 * ρ 62 [ i δ 3 + Γ 65 ] ρ 65 ,
ρ ̇ 64 = i Ω 2 * ρ 61 + i Ω 6 ρ 24 i Ω 4 * ρ 62 [ i ( δ 2 + δ 3 ) + Γ 64 ] ρ 64 ,
ρ ̇ 63 = i Ω 1 * ρ 61 + i Ω 6 ρ 23 [ i ( δ 1 + δ 2 + δ 3 ) + Γ 63 ] ρ 63 ,
ρ ̇ 54 = i Ω 3 ρ 14 + i Ω 2 * ρ 51 + i Ω 5 ρ 24 i Ω 4 * ρ 52 [ i δ 2 + Γ 54 ] ρ 54 ,
ρ ̇ 53 = i Ω 3 ρ 13 i Ω 1 * ρ 51 + i Ω 5 ρ 23 [ i ( δ 1 + δ 2 ) + Γ 53 ] ρ 53 ,
ρ ̇ 43 = i Ω 2 ρ 31 * i Ω 1 * ρ 41 + [ i δ 1 + Γ 43 ] ρ 43 ,
ρ ̇ 21 = i Ω 1 ρ 32 * + i Ω 4 * ρ 41 i Ω 2 ρ 42 * + i Ω 5 * ρ 51 i Ω 3 ρ 52 * + i Ω 6 * ρ 61 [ i Δ R + Γ 21 ] ρ 21 ,
Γ i i = i j γ i j ( i = 3 , 4 , 5 , 6 ; j = 1 , 2 )
Γ i j = 1 2 ( k γ i k + l γ j l )

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