Abstract

It is often desirable in laser spectroscopy and isotope separation to extract as much as possible of an atomic or molecular population that is distributed among a number of ground-state sublevels and low-lying metastable levels. We describe a form of coherent trapping that occurs when multiple resonant laser beams are used to couple the various ground states to a common upper level. This effect prevents the extraction of the entire population. We then study the effect with two dye lasers and an atomic beam and suggest possible ways to maximize the pumping efficiency.

© 1978 Optical Society of America

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References

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  1. E. Arimondo, G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Nuovo Cimento Lett. 17, 333 (1976).
    [CrossRef]
  2. R. Whitley, “Double Optical Resonance,” doctoral dissertation (University of Rochester, Rochester, N.Y., 1977); see also B. W. Shore, .
  3. G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

1976 (2)

E. Arimondo, G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Nuovo Cimento Lett. 17, 333 (1976).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

Arimondo, E.

E. Arimondo, G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Nuovo Cimento Lett. 17, 333 (1976).
[CrossRef]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

E. Arimondo, G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Nuovo Cimento Lett. 17, 333 (1976).
[CrossRef]

Whitley, R.

R. Whitley, “Double Optical Resonance,” doctoral dissertation (University of Rochester, Rochester, N.Y., 1977); see also B. W. Shore, .

Nuovo Cimento (1)

G. Alzetta, A. Gozzini, L. Moi, G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento 36B, 5 (1976).

Nuovo Cimento Lett. (1)

E. Arimondo, G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Nuovo Cimento Lett. 17, 333 (1976).
[CrossRef]

Other (1)

R. Whitley, “Double Optical Resonance,” doctoral dissertation (University of Rochester, Rochester, N.Y., 1977); see also B. W. Shore, .

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Figures (3)

Fig. 1
Fig. 1

Energy-level configuration. E1 and E3 are nondegenerate sublevels of the ground state. E2 is a common excited state. Two monochromatic lasers of frequency ωa and ωb are tuned δa and δb off resonance.

Fig. 2
Fig. 2

(a) Experimentally observed excited-state population σ22. The fixed-frequency laser is at exact resonance, δa = 0, with an intensity of 23 mW/cm2. The second laser is detuned δb from exact resonance, with an intensity of 54 mW/cm2. (b) Theoretical prediction of excited-state population σ22. The fixed-frequency laser is at exact resonance, δa = 0. The second laser is detuned δb from exact resonance.

Fig. 3
Fig. 3

Off-resonance spectra. The experimentally observed excited-state population for δa = 0, −12, −24, −36, and −48 MHz detuning from exact resonance.

Equations (17)

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ψ ( r , t ) = a 1 ( t ) exp ( - i ω 1 t ) ψ 1 ( r ) + a 2 ( t ) exp ( - i ω 2 t ) ψ 2 ( r ) + a 3 ( t ) exp ( - i ω 3 t ) ψ 3 ( r ) ,
a ˙ 1 = ( i μ 1 a / ) exp ( i δ a t ) a 2 ,
a ˙ 2 = ( i μ 1 a / ) exp ( - i δ a t ) a 1 + ( i μ 2 b / ) exp ( - i δ b t ) a 3 ,
a ˙ 3 = ( i μ 2 b / ) exp ( i δ b t ) a 2 ,
E ( t ) = a exp ( - i ω a t ) + b exp ( - i ω b t ) + c . c . ,
r ( t ) = a 1 ( t ) cos θ - a 3 ( t ) sin θ ,
s ( t ) = a 1 ( t ) sin θ + a 3 ( t ) cos θ ,
tan θ = ( μ 1 a / μ 2 b ) .
r ˙ ( t ) = 0 ,
s ˙ ( t ) = i R exp ( i δ t ) a 2 ( t ) ,
R = ( 1 / ) [ ( μ 1 a ) 2 + ( μ 2 b ) 2 ] 1 / 2 .
r ( 0 ) = a 1 ( 0 ) cos θ - a 3 ( 0 ) sin θ ,
lim t ψ ( r , t ) = cos θ exp ( - i ω 1 t ) ψ 1 ( r ) - sin θ exp ( - i ω 3 t ) ψ 3 ( r ) .
σ 22 = N 22 / D ,
N 22 = 4 α 2 β 2 ( Γ a + Γ b ) ( δ a - δ b ) 2 ,
D = ( δ a - δ b ) 2 { 8 α 2 β 2 ( Γ a + Γ b ) + 16 α 2 Γ b [ ( Γ a + Γ b ) 2 + δ b 2 ] + 16 β 2 Γ a [ ( Γ a + Γ b ) 2 + δ a 2 ] } + 8 ( δ a - δ b ) ( α 4 δ b Γ b - β 4 δ a Γ a ) + ( α 2 Γ b + β 2 Γ a ) ( α 2 + β 2 ) 2 ,
FWHM = ( α 2 + β 2 ) / 2 ( Γ a + Γ b ) .

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