Abstract

By solving the optical Bloch equations with the rate-equation approximation, we calculate the time dependence of the magnetic sublevel populations of Doppler-broadened atoms. With an increase of the left-circularly polarized pump intensity, the population fraction of a certain sublevel of the excited state almost reaches 0.3, resulting in anisotropy in the excited state, which is important to the optical filter based on circular birefringence and dichroism. Furthermore, numerical results show that the real saturation pump intensity for the moving atoms is much larger than that for the resting atoms.

© 2011 Optical Society of America

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References

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  1. N. Shigeru, “Doppler-free laser spectroscopic techniques with optical pumping in D1 lines of alkali atoms,” J. Opt. Soc. Am. B 2, 1431–1437 (1985).
    [CrossRef]
  2. M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
    [CrossRef]
  3. S. Chakrabati, B. Ray, and P. N. Glosh, “Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D2 lines of rubidium,” Eur. Phys. J. D 42, 359–368 (2007).
    [CrossRef]
  4. E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
    [CrossRef]
  5. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  6. C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65, 023806 (2002).
    [CrossRef]
  7. H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express 16, 12163–12170 (2008).
    [CrossRef] [PubMed]
  8. Z. He, Y. Zhang, H. Wu, P. Yuan, and S. Liu, “Theoretical model for an atomic optical filter based on optical anisotropy,” J. Opt. Soc. Am. B 26, 1755–1759 (2009).
    [CrossRef]
  9. Z. He, Y. Zhang, H. Wu, P. Yuan, and S. Liu, “Theory and experiment for atomic optical filter based on optical anisotropy in rubidium,” Opt. Commun. 282, 4548–4551 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. J. Gea-Banacloche, H. Wu, and M. Xiao, “Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime,” Phys. Rev. A 78, 023828 (2008).
    [CrossRef]

2009 (3)

2008 (3)

G. Moon, S. R. Shin, and H. Noh, “Analytic solutions for the populations of an optically-pumped multilevel atom,” J. Korean Phys. Soc. 53552–557 (2008).
[CrossRef]

J. Gea-Banacloche, H. Wu, and M. Xiao, “Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime,” Phys. Rev. A 78, 023828 (2008).
[CrossRef]

H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express 16, 12163–12170 (2008).
[CrossRef] [PubMed]

2007 (2)

Z. He, Y. Zhang, S. Liu, and P. Yuan, “Transmission characteristics of an excited-state induced dispersion optical of rubidium at 775.9 nm,” Chin. Opt. Lett. 5, 252–254 (2007).

S. Chakrabati, B. Ray, and P. N. Glosh, “Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D2 lines of rubidium,” Eur. Phys. J. D 42, 359–368 (2007).
[CrossRef]

2006 (1)

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

2002 (2)

L. D. Turner, V. Karaganov, P. J. O. Teubner, and R. E. Scholten, “Sub-Doppler bandwidth atomic optical filter,” Opt. Lett. 27, 500–502 (2002).
[CrossRef]

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65, 023806 (2002).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1996 (1)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

1995 (1)

1988 (1)

P. M. Farrell, W. R. MacGillivary, and M. C. Standage, “Quantum-electro dynamic calculation of hyperfine-state populations in atomic sodium,” Phys. Rev. A 37, 4240–4251(1988).
[CrossRef] [PubMed]

1985 (2)

J. J. McClelland and M. H. Kelley, “Detailed look at aspects of optical pumping in sodium,” Phys. Rev. A 31, 3704–3710(1985).
[CrossRef] [PubMed]

N. Shigeru, “Doppler-free laser spectroscopic techniques with optical pumping in D1 lines of alkali atoms,” J. Opt. Soc. Am. B 2, 1431–1437 (1985).
[CrossRef]

1980 (1)

V. I. Balykin, “Cyclic interaction of Na atoms with circularly polarized laser radiaton,” Opt. Commun. 33, 31–36 (1980).
[CrossRef]

Abad, M.

Adams, C. S.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Allocca, D. M.

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

Balykin, V. I.

V. I. Balykin, “Cyclic interaction of Na atoms with circularly polarized laser radiaton,” Opt. Commun. 33, 31–36 (1980).
[CrossRef]

Billmers, R. I.

Cere, A.

Chakrabati, S.

S. Chakrabati, B. Ray, and P. N. Glosh, “Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D2 lines of rubidium,” Eur. Phys. J. D 42, 359–368 (2007).
[CrossRef]

Contarino, V. M.

Cornish, S. L.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Farrell, P. M.

P. M. Farrell, W. R. MacGillivary, and M. C. Standage, “Quantum-electro dynamic calculation of hyperfine-state populations in atomic sodium,” Phys. Rev. A 37, 4240–4251(1988).
[CrossRef] [PubMed]

Gayen, S. K.

Gea-Banacloche, J.

J. Gea-Banacloche, H. Wu, and M. Xiao, “Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime,” Phys. Rev. A 78, 023828 (2008).
[CrossRef]

Glosh, P. N.

S. Chakrabati, B. Ray, and P. N. Glosh, “Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D2 lines of rubidium,” Eur. Phys. J. D 42, 359–368 (2007).
[CrossRef]

Harris, M. L.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

He, Z.

Herczfeld, P. R.

Hughes, I. G.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Karaganov, V.

Kelley, M. H.

J. J. McClelland and M. H. Kelley, “Detailed look at aspects of optical pumping in sodium,” Phys. Rev. A 31, 3704–3710(1985).
[CrossRef] [PubMed]

Kim, J. B.

Lee, L.

Liu, S.

London, R.

R. London, The Quantum Theory of Light, 2nd ed. (Oxford University, 1983).

MacGillivary, W. R.

P. M. Farrell, W. R. MacGillivary, and M. C. Standage, “Quantum-electro dynamic calculation of hyperfine-state populations in atomic sodium,” Phys. Rev. A 37, 4240–4251(1988).
[CrossRef] [PubMed]

McClelland, J. J.

J. J. McClelland and M. H. Kelley, “Detailed look at aspects of optical pumping in sodium,” Phys. Rev. A 31, 3704–3710(1985).
[CrossRef] [PubMed]

Mcleod, I. C.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Meystre, P.

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
[CrossRef]

Mitchell, M. W.

Moon, G.

G. Moon, S. R. Shin, and H. Noh, “Analytic solutions for the populations of an optically-pumped multilevel atom,” J. Korean Phys. Soc. 53552–557 (2008).
[CrossRef]

Moon, H. S.

Noh, H.

G. Moon, S. R. Shin, and H. Noh, “Analytic solutions for the populations of an optically-pumped multilevel atom,” J. Korean Phys. Soc. 53552–557 (2008).
[CrossRef]

Parigi, V.

Predojevic, A.

Ray, B.

S. Chakrabati, B. Ray, and P. N. Glosh, “Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D2 lines of rubidium,” Eur. Phys. J. D 42, 359–368 (2007).
[CrossRef]

Sargent, M.

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
[CrossRef]

Scharpf, W. J.

Scholten, R. E.

Shigeru, N.

Shin, S. R.

G. Moon, S. R. Shin, and H. Noh, “Analytic solutions for the populations of an optically-pumped multilevel atom,” J. Korean Phys. Soc. 53552–557 (2008).
[CrossRef]

Squicciarini, M. F.

Standage, M. C.

P. M. Farrell, W. R. MacGillivary, and M. C. Standage, “Quantum-electro dynamic calculation of hyperfine-state populations in atomic sodium,” Phys. Rev. A 37, 4240–4251(1988).
[CrossRef] [PubMed]

Tarleton, E.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Teubner, P. J. O.

Turner, L. D.

Wolfgramm, F.

Wu, H.

Z. He, Y. Zhang, H. Wu, P. Yuan, and S. Liu, “Theoretical model for an atomic optical filter based on optical anisotropy,” J. Opt. Soc. Am. B 26, 1755–1759 (2009).
[CrossRef]

Z. He, Y. Zhang, H. Wu, P. Yuan, and S. Liu, “Theory and experiment for atomic optical filter based on optical anisotropy in rubidium,” Opt. Commun. 282, 4548–4551 (2009).
[CrossRef]

J. Gea-Banacloche, H. Wu, and M. Xiao, “Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime,” Phys. Rev. A 78, 023828 (2008).
[CrossRef]

Xiao, M.

J. Gea-Banacloche, H. Wu, and M. Xiao, “Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime,” Phys. Rev. A 78, 023828 (2008).
[CrossRef]

Yang, G.

Ye, C. Y.

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65, 023806 (2002).
[CrossRef]

Yuan, P.

Zhang, Y.

Zibrov, A. S.

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65, 023806 (2002).
[CrossRef]

Chin. Opt. Lett. (1)

Eur. Phys. J. D (1)

S. Chakrabati, B. Ray, and P. N. Glosh, “Velocity selective optical pumping and repumping effects with counter and copropagating laser radiations for D2 lines of rubidium,” Eur. Phys. J. D 42, 359–368 (2007).
[CrossRef]

J. Korean Phys. Soc. (1)

G. Moon, S. R. Shin, and H. Noh, “Analytic solutions for the populations of an optically-pumped multilevel atom,” J. Korean Phys. Soc. 53552–557 (2008).
[CrossRef]

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

Opt. Commun. (2)

Z. He, Y. Zhang, H. Wu, P. Yuan, and S. Liu, “Theory and experiment for atomic optical filter based on optical anisotropy in rubidium,” Opt. Commun. 282, 4548–4551 (2009).
[CrossRef]

V. I. Balykin, “Cyclic interaction of Na atoms with circularly polarized laser radiaton,” Opt. Commun. 33, 31–36 (1980).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (5)

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65, 023806 (2002).
[CrossRef]

J. Gea-Banacloche, H. Wu, and M. Xiao, “Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime,” Phys. Rev. A 78, 023828 (2008).
[CrossRef]

J. J. McClelland and M. H. Kelley, “Detailed look at aspects of optical pumping in sodium,” Phys. Rev. A 31, 3704–3710(1985).
[CrossRef] [PubMed]

P. M. Farrell, W. R. MacGillivary, and M. C. Standage, “Quantum-electro dynamic calculation of hyperfine-state populations in atomic sodium,” Phys. Rev. A 37, 4240–4251(1988).
[CrossRef] [PubMed]

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. Mcleod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Prog. Opt. (1)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

Other (2)

R. London, The Quantum Theory of Light, 2nd ed. (Oxford University, 1983).

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Hyperfine structure of Rb 87 D 2 transition.

Fig. 2
Fig. 2

Saturation intensity of the 5 S 1 / 2 ( F = 2 , m F = + 2 ) 5 P 3 / 2 ( F = 3 , m F = + 3 ) transition as a function of the pump detuning in two cases: resting atoms (dashed curve) and moving atoms (solid curve).

Fig. 3
Fig. 3

Time evolution of the magnetic sublevel populations after the pump laser is on. The pump laser is on the resonance of the 5 S 1 / 2 ( F = 2 ) to 5 P 3 / 2 ( F = 3 ) transition. Atoms in the ground state 5 S 1 / 2 ( F = 2 ) can also be pumped into 5 P 3 / 2 ( F = 2 ) resulting from the pump power broadening and the Doppler effect. The pump drives the σ + transition and has an intensity of 100 I sat : (a) ground state 5 S 1 / 2 , (b) excited state 5 P 3 / 2 ( F = 2 ) , and (c) excited state 5 P 3 / 2 ( F = 3 ) . Vertical axes represent the population fraction of atoms in each sublevel.

Fig. 4
Fig. 4

The population fractions of 5 S 1 / 2 ( F = 2 , m F = + 2 ) and 5 P 3 / 2 ( F = 3 , m F = + 3 ) in the steady state as a function of pump intensity.

Equations (7)

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ρ ˙ a a = i Ω p 2 ( ρ a b ρ b a ) + Γ ρ b b , ρ ˙ a b = i Ω p 2 ( ρ b b ρ a a ) ( i Δ + γ b a ) ρ a b , ρ ˙ b b = i Ω p 2 ( ρ a b ρ b a ) Γ ρ b b .
ρ ˙ a a = Γ 2 I I sat ρ b b 1 + 4 Δ 2 / Γ 2 Γ 2 I I sat ρ a a 1 + 4 Δ 2 / Γ 2 + Γ ρ b b , ρ ˙ b b = Γ 2 I I sat ρ b b 1 + 4 Δ 2 / Γ 2 + Γ 2 I I sat ρ a a 1 + 4 Δ 2 / Γ 2 Γ ρ b b .
d P F , m F d t = F = F 1 F = F + 1 C F , m F F , m F + 1 Γ 2 I I sat ( P F , m F Q F , m F + 1 ) 1 + 4 Δ 2 / Γ 2 + m F = m F 1 m F = m F + 1 F = F 1 F = F + 1 C F , m F F , m F + 1 Γ Q F , m F .
d Q F , m F d t = F = F 1 F = F + 1 C F , m F 1 F , m F Γ 2 I I sat ( P F , m F 1 Q F , m F ) 1 + 4 Δ 2 / Γ 2 m F = m F 1 m F = m F + 1 F = F 1 F = F + 1 C F , m F F , m F Γ Q F , m F .
C F , m F F , m F + 1 = ( 2 L + 1 ) ( 2 J + 1 ) ( 2 J + 1 ) ( 2 F + 1 ) ( 2 F + 1 ) [ { L J J L S 1 } { J F F J I 1 } ( F m F 1 1 F m F ) ] 2 .
I sat = c ε 0 2 ( 4 Δ 2 + Γ 2 ) 4 μ 2 .
I sat = 1 π u c ε 0 2 ( 4 ( Δ + k υ ) 2 + Γ 2 ) 4 μ 2 e υ 2 u 2 d υ .

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