Abstract

We present calculations of the spontaneous-emission spectrum from a two-photon two-level system in the presence of an arbitrarily intense monochromatic field at half of the two-photon transition frequency. The single-photon counterpart to this is called resonance fluorescence. Because of the complexity of the two-photon two-level model, many effects arise that are absent in the one-photon problem. In particular, we show how the Rayleigh scattering from this system is markedly different and discuss the role of Stark shifts on the emission spectrum.

© 1985 Optical Society of America

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References

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  1. B. Podolsky, Proc. Nat. Acad. Sci. USA 14, 253 (1928).
  2. L. Spitzer, J. L. Greenstein, Astrophys. J. 114, 407 (1951).
  3. M. Takatsuji, Phys. Rev. A 4, 808 (1971).
  4. B. R. Mollow, Phys. Rev. A 4, 1666 (1971).
  5. M. Sargent, S. Ovadia, M. H. Lu, Phys. Rev. A (to be published).
  6. B. R. Mollow, Phys. Rev. 188, 1969 (1969).
  7. S. Stenholm, D. A. Holm, M. Sargent, Phys. Rev. A 31, 3124 (1985).
  8. M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).

1985 (2)

S. Stenholm, D. A. Holm, M. Sargent, Phys. Rev. A 31, 3124 (1985).

M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).

1971 (2)

M. Takatsuji, Phys. Rev. A 4, 808 (1971).

B. R. Mollow, Phys. Rev. A 4, 1666 (1971).

1969 (1)

B. R. Mollow, Phys. Rev. 188, 1969 (1969).

1951 (1)

L. Spitzer, J. L. Greenstein, Astrophys. J. 114, 407 (1951).

1928 (1)

B. Podolsky, Proc. Nat. Acad. Sci. USA 14, 253 (1928).

Greenstein, J. L.

L. Spitzer, J. L. Greenstein, Astrophys. J. 114, 407 (1951).

Holm, D. A.

S. Stenholm, D. A. Holm, M. Sargent, Phys. Rev. A 31, 3124 (1985).

M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).

Lu, M. H.

M. Sargent, S. Ovadia, M. H. Lu, Phys. Rev. A (to be published).

Mollow, B. R.

B. R. Mollow, Phys. Rev. A 4, 1666 (1971).

B. R. Mollow, Phys. Rev. 188, 1969 (1969).

Ovadia, S.

M. Sargent, S. Ovadia, M. H. Lu, Phys. Rev. A (to be published).

Podolsky, B.

B. Podolsky, Proc. Nat. Acad. Sci. USA 14, 253 (1928).

Sargent, M.

S. Stenholm, D. A. Holm, M. Sargent, Phys. Rev. A 31, 3124 (1985).

M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).

M. Sargent, S. Ovadia, M. H. Lu, Phys. Rev. A (to be published).

Spitzer, L.

L. Spitzer, J. L. Greenstein, Astrophys. J. 114, 407 (1951).

Stenholm, S.

S. Stenholm, D. A. Holm, M. Sargent, Phys. Rev. A 31, 3124 (1985).

Takatsuji, M.

M. Takatsuji, Phys. Rev. A 4, 808 (1971).

Zubairy, M. S.

M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).

Astrophys. J. (1)

L. Spitzer, J. L. Greenstein, Astrophys. J. 114, 407 (1951).

Phys. Rev. (1)

B. R. Mollow, Phys. Rev. 188, 1969 (1969).

Phys. Rev. A (4)

S. Stenholm, D. A. Holm, M. Sargent, Phys. Rev. A 31, 3124 (1985).

M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).

M. Takatsuji, Phys. Rev. A 4, 808 (1971).

B. R. Mollow, Phys. Rev. A 4, 1666 (1971).

Proc. Nat. Acad. Sci. USA (1)

B. Podolsky, Proc. Nat. Acad. Sci. USA 14, 253 (1928).

Other (1)

M. Sargent, S. Ovadia, M. H. Lu, Phys. Rev. A (to be published).

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Figures (4)

Fig. 1
Fig. 1

Two-photon two-level model considered in this Letter.

Fig. 2
Fig. 2

Centrally tuned, two-photon resonant-fluorescence spectrum versus ΔT1 = (ν2ν1)T2 for I2 = 10, T2 = 2T1, and ωs = 0.

Fig. 3
Fig. 3

Two-peaked spectrum versus ΔT1 for I2 = 10, T2 = 2T1, ωsI2 = 5/T1, and ω − 2ν2 = −5/T 1.

Fig. 4
Fig. 4

Intensity of Rayleigh scattering versus detuning Δ2 = ω − 2ν2 for I2 = 10, k21 = 5k22 = 5k11.

Equations (13)

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H = H sc + H f + H int .
H sc = Ω + V 2 j σ 2 + V j 1 σ 1 + V j 2 σ 2 + V i j σ 1 ,
Ω = [ ω 2 0 0 0 ω 1 0 0 0 ω j ] ,             σ 2 = [ 0 0 1 0 0 0 0 0 0 ] ,             σ 1 = [ 0 0 0 0 0 0 0 1 0 ]
V 2 j = - μ 2 j 2 [ E 2 exp ( - i ν 2 t ) + E 2 * exp ( i ν 2 t ) ] ,
V j 1 = - μ j 1 2 [ E 2 exp ( - i ν 2 t ) + E 2 * exp ( i ν 2 t ) ,
H f = ν 1 a a ,
H int = - [ μ 2 j 2 ( σ 2 + σ 2 ) + μ j 1 2 ( σ 1 + σ 1 ) ] × ( E 1 a + E 1 * a ) .
ρ ˙ = - i [ H , ρ ] + Γ ( ρ ) ,
Γ = - [ Γ ρ 22 γ ρ 21 γ 2 j ρ 2 j γ ρ 12 - Γ ρ 22 γ j 1 ρ 1 j γ 2 j ρ j 2 γ j 1 ρ j 1 0 ] .
( d / d t ) n 1 = A 1 + A 1 * .
A 1 = k 21 E 1 2 2 ( 1 + I 2 2 L 2 ) { γ Γ I 2 D 1 ( 2 f 2 + i γ Γ I 2 D 2 k 11 / k 21 ) + 2 i ( k 22 + f 2 + k 11 + f 1 ) k 21 - I 2 2 F γ Γ γ I 2 D 1 - i ω s / Γ 1 + I 2 2 F γ 2 ( D 1 + D 3 * ) × [ D 1 f 2 - D 2 * 2 + i γ Γ I 2 k 22 D 2 * D 3 * + k 11 D 1 D 2 2 k 21 - i ( k 11 f 1 - k 22 k 2 ) γ Γ I 2 k 21 ] + γ Γ I 2 D 2 * / 2 + i ( k 22 f 2 + k 11 f 1 ) / k 21 i Δ [ I 2 F ( γ Γ I 2 D 1 - i ω s ) 1 + I 2 2 F γ 2 ( D 1 + D 3 * ) - i γ Γ I 2 ( k 22 + k 11 ) k 21 ] } .
ω s = k 11 - k 22 k 21 γ Γ ,
A EI = 2 π γ Γ I 2 E 1 2 ( 1 + I 2 2 L 2 ) 2 [ ( k 22 f 2 + k 11 f 1 ) 2 k 21 + k 21 Γ f 2 2 γ + ( k 22 f 2 + k 11 f 1 ) I 2 L 2 ( γ Γ ) 1 / 2 Δ 2 γ 2 ] δ ( Δ ) ,

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