Abstract

Ground state sublevels are assigned distinct labels to correct angular momentum matrix element notation.

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References

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  1. S. C. Rand, “Quantum theory of coherent transverse optical magnetism,” J. Opt. Soc. Am. B 26, B120 (2009);
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  2. S. Rand, “Erratum,” J. Opt. Soc. Am. B 27, 1983 (2010).
    [CrossRef]

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2009

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Equations (4)

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μ 12 ( m ) μ 13 ( m ) , ρ 12 ( m ) ρ 13 ( m ) , Γ 12 ( m ) Γ 13 ( m ) , 1 | L y | 2 1 | L y | 3 , 2 | V ± ( m ) | 1 3 | V ± ( m ) | 1 = ( ) l 3 m 3 1 2 { B ± α 3 l 3 m 3 μ ( m ) α 1 l 1 m 1 + c . c . } ( l 3 1 l 1 m 3 q m 1 ) .
μ ¯ ( m ) = y ^ 1 | μ ( m ) | 3 ρ 32 ( m ) ( t ) ρ ˜ 21 ( e ) + h . c . = y ^ 1 | μ ( m ) | 3 ρ 31 ( m ) ( t ) ρ ˜ 21 ( e ) + h . c . , ρ 13 ( t ) = ρ ˜ 13 ( m ) * ( ω ) ρ ˜ 12 ( e ) ( ω ) + ρ ˜ 13 ( m ) ( ω ) ρ ˜ 12 ( e ) ( ω ) e 2 i ϕ = ρ ˜ 13 ( ω = 0 ) + ρ ˜ 13 ( 2 ω ) e 2 i ϕ , ρ 13 ( m ) = 1 2 { [ Ω + ( m ) + Ω ( m ) ] 13 ( ω φ + i Γ 13 ( m ) ) e i ω t + [ Ω + ( m ) + Ω ( m ) ] 13 ( Δ 2 + i Γ 13 ( m ) ) e i ω t } ( ρ 11 ( 0 ) ρ 22 ( 0 ) ) .
M ¯ ( t ) = N y ^ 3 | μ ( m ) ( t ) | 1 ρ 12 ( e ) ( t ) ρ 13 ( m ) ( t ) + h . c . = y ^ ( N e 2 m ) { 1 2 [ 3 | L y | 1 [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 13 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 13 ( m ) ) e i ω t + 3 | L y | 1 [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 13 ( Δ 1 + i Γ 12 ( e ) ) ( ω φ + i Γ 13 ( m ) ) e i ω t ] + h . c . } ( ρ 11 ρ 22 ) ,
P ¯ ( t ) = N z ^ ( μ 31 ( e ) ρ 12 ( e ) ρ 13 ( m ) ( t ) + h . c . ) = N z ^ { ( 1 2 μ 31 ( e ) [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 13 ( Δ 1 + i Γ 12 ( e ) ) ( ω φ + i Γ 13 ( m ) ) + h . c . ) + ( 1 2 μ 31 ( e ) [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 13 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 13 ( m ) ) e 2 i ω t + h . c . ) } ( ρ 11 ρ 22 ) .

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