Abstract

We present a fully quantum-mechanical theory of nondegenerate four-wave mixing processes in three-level cascades with a two-photon pump. The results are applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and tunings within the Rabi sidebands. We find good broadband squeezing for low pump intensities and tunings outside a small region around central tuning. Both cases avoid regions of significant spontaneous emission.

© 1988 Optical Society of America

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  1. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
    [CrossRef] [PubMed]
  2. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
    [CrossRef] [PubMed]
  3. M. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
    [CrossRef] [PubMed]
  4. L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
    [CrossRef] [PubMed]
  5. M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985).
    [CrossRef]
  6. D. A. Holm, M. Sargent, Phys. Rev. A 33, 1073 (1986).
    [CrossRef] [PubMed]
  7. C. M. Savage, D. F. Walls, Phys. Rev. A 33, 3282 (1986).
    [CrossRef] [PubMed]
  8. M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
    [CrossRef] [PubMed]
  9. R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
    [CrossRef] [PubMed]
  10. G. S. Agarwal, Phys. Rev. Lett. 57, 827 (1986).
    [CrossRef] [PubMed]
  11. D. A. Holm, M. Sargent, S. Stenholm, J. Opt. Soc. Am. B 2, 1456 (1985).
    [CrossRef]
  12. D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987). [Note: in Eq. (39) the term +χ1χ3 should be multiplied by C1* + C3*.]
    [CrossRef] [PubMed]

1987 (3)

M. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987). [Note: in Eq. (39) the term +χ1χ3 should be multiplied by C1* + C3*.]
[CrossRef] [PubMed]

1986 (5)

G. S. Agarwal, Phys. Rev. Lett. 57, 827 (1986).
[CrossRef] [PubMed]

D. A. Holm, M. Sargent, Phys. Rev. A 33, 1073 (1986).
[CrossRef] [PubMed]

C. M. Savage, D. F. Walls, Phys. Rev. A 33, 3282 (1986).
[CrossRef] [PubMed]

L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

1985 (4)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

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

M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

D. A. Holm, M. Sargent, S. Stenholm, J. Opt. Soc. Am. B 2, 1456 (1985).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. Lett. 57, 827 (1986).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

DeVoe, R. V.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Gauthier, D. J.

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

Hall, J. L.

L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Holm, D. A.

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987). [Note: in Eq. (39) the term +χ1χ3 should be multiplied by C1* + C3*.]
[CrossRef] [PubMed]

D. A. Holm, M. Sargent, Phys. Rev. A 33, 1073 (1986).
[CrossRef] [PubMed]

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

D. A. Holm, M. Sargent, S. Stenholm, J. Opt. Soc. Am. B 2, 1456 (1985).
[CrossRef]

Kimble, H. J.

L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Kumar, P.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Maeda, M.

Malcuit, M. S.

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Rzazewski, K.

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

Sargent, M.

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987). [Note: in Eq. (39) the term +χ1χ3 should be multiplied by C1* + C3*.]
[CrossRef] [PubMed]

D. A. Holm, M. Sargent, Phys. Rev. A 33, 1073 (1986).
[CrossRef] [PubMed]

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

D. A. Holm, M. Sargent, S. Stenholm, J. Opt. Soc. Am. B 2, 1456 (1985).
[CrossRef]

Savage, C. M.

C. M. Savage, D. F. Walls, Phys. Rev. A 33, 3282 (1986).
[CrossRef] [PubMed]

Shapiro, J. H.

Shelby, R. M.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Stenholm, S.

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Walls, D. F.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

C. M. Savage, D. F. Walls, Phys. Rev. A 33, 3282 (1986).
[CrossRef] [PubMed]

Wu, H.

L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Wu, L. A.

L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Yurke, B.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Zubairy, M. S.

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

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

Opt. Lett. (1)

Phys. Rev. A (5)

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

D. A. Holm, M. Sargent, Phys. Rev. A 33, 1073 (1986).
[CrossRef] [PubMed]

C. M. Savage, D. F. Walls, Phys. Rev. A 33, 3282 (1986).
[CrossRef] [PubMed]

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987). [Note: in Eq. (39) the term +χ1χ3 should be multiplied by C1* + C3*.]
[CrossRef] [PubMed]

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, K. Rzazewski, Phys. Rev. A 35, 1648 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

G. S. Agarwal, Phys. Rev. Lett. 57, 827 (1986).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Phys. Rev. Lett. 55, 1086 (1985).
[CrossRef] [PubMed]

L. A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. V. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Three-level cascade model with a two-photon pump.

Fig. 2
Fig. 2

Variance Δd12 versus Δ′ = (ωbcν2) − Δ for I2 = 0.5 and 150, C = 100, Δ2 = 0, Γa = 1, Γ1 = Γ3 = 1, and γ1 = γ2 = γ3 = 1. All frequencies are in units of γ2.

Fig. 3
Fig. 3

Variance Δd12 versus I2 for C = 100 and 1000, Δ′ = 0, and the other parameters the same as in Fig. 2.

Equations (9)

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ρ ˙ = A 1 ( ρ a 1 a 1 a 1 ρ a 1 ) ( B 1 + ν / 2 Q ) ( a 1 a 1 ρ a 1 ρ a 1 ) + A 3 ( ρ a 3 a 3 a 3 ρ a 3 ) ( B 3 + ν / 2 Q ) ( a 3 a 3 ρ a 3 ρ a 3 ) + C 3 ( a 3 a 1 ρ a 1 ρ a 3 ) + D 1 ( ρ a 3 a 1 a 1 ρ a 3 ) + adjoint ,
A 1 = g 1 2 D 1 1 + I 2 2 L 2 f a + I 2 2 D 3 * D 2 * / 4 T 1 T 2 1 + I 2 2 D 1 D 3 * / 4 T 1 T 2 ,
B 1 = g 1 2 D 1 1 + I 2 2 L 2 f b 1 + I 2 2 D 1 D 3 * / 4 T 1 T 2 ,
A 3 = g 3 2 D 3 1 + I 2 2 L 2 f b 1 + I 2 2 D 1 * D 3 / 4 T 1 T 2 ,
B 3 = g 3 2 D 3 1 + I 2 2 L 2 f c I 2 2 D 1 * D 2 * / 4 T 1 T 2 1 + I 2 2 D 1 * D 3 / 4 T 1 T 2 ,
C 3 = i g 3 2 D 3 1 + I 2 2 L 2 U 1 * U 3 * V 2 f a D 1 * + D 2 1 + I 2 2 D 1 * D 3 / 4 T 1 T 2 ,
D 1 = i g 1 2 D 1 1 + I 2 2 L 2 U 1 * U 3 * V 2 f c D 3 * D 2 1 + I 2 2 D 1 D 3 * / 4 T 1 T 2 ,
d = 2 1 / 2 ( a 1 e i θ + a 3 e i θ ) .
Δ d 1 2 = 1 4 + 1 4 ν Q ( S 12 + S 34 2 | S 13 | ) ,

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