Abstract

Using a two-photon correlated-spontaneous-emission laser (CEL) as an example, I show that a non-Lorentzian spectrum of squeezing is the result of fluctuation coupling and that the narrow peak at the center of the spectrum is a reflection of the fluctuations in the conjugate quadrature. More than 90% extracavity phase squeezing can be generated by the two-photon CEL near threshold with large one-photon detunings.

© 1991 Optical Society of America

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  1. B. Yurke, Phys. Rev. A 29, 408 (1984).
    [CrossRef]
  2. M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); C. W. Gardiner, M. J. Collett, Phys. Rev. A 31, 3761 (1985).
    [CrossRef] [PubMed]
  3. M. J. Collett, D. F. Walls, Phys. Rev. A 32, 2887 (1985).
    [CrossRef] [PubMed]
  4. C. M. Savage, D. F. Walls, Phys. Rev. A 33, 3282 (1986).
    [CrossRef] [PubMed]
  5. D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987).
    [CrossRef] [PubMed]
  6. H. J. Carmichael, J. Opt. Soc. Am. B 4, 1588 (1987).
    [CrossRef]
  7. J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
    [CrossRef] [PubMed]
  8. M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
    [CrossRef] [PubMed]
  9. N. Lu, S. Y. Zhu, Phys. Rev. A 40, 5735 (1989).
    [CrossRef] [PubMed]
  10. Y. Kano, J. Math. Phys. 6, 1913 (1965).
    [CrossRef]
  11. C. L. Mehta, E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
    [CrossRef]
  12. N. Lu, S. Y. Zhu, G. S. Agarwal, Phys. Rev. A 40, 258 (1989). In this reference one of Eqs. (3.3) should read DxyP− ⅛(Axy+ Ayx) = DxyQ+ ⅛(Axy+ Ayx) = DxyW; also, DxyW in Table III should be DxyW= ¼Im(Λ3+ Λ4).
    [CrossRef] [PubMed]
  13. N. Lu, F. X. Zhao, J. Bergou, Phys. Rev. A 39, 5189 (1989).
    [CrossRef] [PubMed]

1990 (1)

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

1989 (3)

N. Lu, S. Y. Zhu, Phys. Rev. A 40, 5735 (1989).
[CrossRef] [PubMed]

N. Lu, S. Y. Zhu, G. S. Agarwal, Phys. Rev. A 40, 258 (1989). In this reference one of Eqs. (3.3) should read DxyP− ⅛(Axy+ Ayx) = DxyQ+ ⅛(Axy+ Ayx) = DxyW; also, DxyW in Table III should be DxyW= ¼Im(Λ3+ Λ4).
[CrossRef] [PubMed]

N. Lu, F. X. Zhao, J. Bergou, Phys. Rev. A 39, 5189 (1989).
[CrossRef] [PubMed]

1988 (1)

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

1987 (2)

H. J. Carmichael, J. Opt. Soc. Am. B 4, 1588 (1987).
[CrossRef]

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987).
[CrossRef] [PubMed]

1986 (1)

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

1985 (1)

M. J. Collett, D. F. Walls, Phys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

1984 (2)

B. Yurke, Phys. Rev. A 29, 408 (1984).
[CrossRef]

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); C. W. Gardiner, M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

1965 (2)

Y. Kano, J. Math. Phys. 6, 1913 (1965).
[CrossRef]

C. L. Mehta, E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
[CrossRef]

Agarwal, G. S.

N. Lu, S. Y. Zhu, G. S. Agarwal, Phys. Rev. A 40, 258 (1989). In this reference one of Eqs. (3.3) should read DxyP− ⅛(Axy+ Ayx) = DxyQ+ ⅛(Axy+ Ayx) = DxyW; also, DxyW in Table III should be DxyW= ¼Im(Λ3+ Λ4).
[CrossRef] [PubMed]

Bergou, J.

N. Lu, F. X. Zhao, J. Bergou, Phys. Rev. A 39, 5189 (1989).
[CrossRef] [PubMed]

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

Carmichael, H. J.

Collett, M. J.

M. J. Collett, D. F. Walls, Phys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); C. W. Gardiner, M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

Gardiner, C. W.

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); C. W. Gardiner, M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

Gea-Banacloche, J.

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

Holm, D. A.

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987).
[CrossRef] [PubMed]

Kano, Y.

Y. Kano, J. Math. Phys. 6, 1913 (1965).
[CrossRef]

Lu, N.

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

N. Lu, S. Y. Zhu, Phys. Rev. A 40, 5735 (1989).
[CrossRef] [PubMed]

N. Lu, F. X. Zhao, J. Bergou, Phys. Rev. A 39, 5189 (1989).
[CrossRef] [PubMed]

N. Lu, S. Y. Zhu, G. S. Agarwal, Phys. Rev. A 40, 258 (1989). In this reference one of Eqs. (3.3) should read DxyP− ⅛(Axy+ Ayx) = DxyQ+ ⅛(Axy+ Ayx) = DxyW; also, DxyW in Table III should be DxyW= ¼Im(Λ3+ Λ4).
[CrossRef] [PubMed]

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

Mehta, C. L.

C. L. Mehta, E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
[CrossRef]

Meyer ter Vehn, J.

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

Pedrotti, L. M.

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

Prasad, S.

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

Sargent, M.

D. A. Holm, M. Sargent, Phys. Rev. A 35, 2150 (1987).
[CrossRef] [PubMed]

Savage, C. M.

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

Scully, M. O.

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

Sudarshan, E. C. G.

C. L. Mehta, E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
[CrossRef]

Walls, D. F.

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

M. J. Collett, D. F. Walls, Phys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

Wódkiewicz, K.

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

Yurke, B.

B. Yurke, Phys. Rev. A 29, 408 (1984).
[CrossRef]

Zhao, F. X.

N. Lu, F. X. Zhao, J. Bergou, Phys. Rev. A 39, 5189 (1989).
[CrossRef] [PubMed]

Zhu, S. Y.

N. Lu, S. Y. Zhu, Phys. Rev. A 40, 5735 (1989).
[CrossRef] [PubMed]

N. Lu, S. Y. Zhu, G. S. Agarwal, Phys. Rev. A 40, 258 (1989). In this reference one of Eqs. (3.3) should read DxyP− ⅛(Axy+ Ayx) = DxyQ+ ⅛(Axy+ Ayx) = DxyW; also, DxyW in Table III should be DxyW= ¼Im(Λ3+ Λ4).
[CrossRef] [PubMed]

Zubairy, M. S.

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

J. Math. Phys. (1)

Y. Kano, J. Math. Phys. 6, 1913 (1965).
[CrossRef]

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

Phys. Rev. (1)

C. L. Mehta, E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
[CrossRef]

Phys. Rev. A (9)

N. Lu, S. Y. Zhu, G. S. Agarwal, Phys. Rev. A 40, 258 (1989). In this reference one of Eqs. (3.3) should read DxyP− ⅛(Axy+ Ayx) = DxyQ+ ⅛(Axy+ Ayx) = DxyW; also, DxyW in Table III should be DxyW= ¼Im(Λ3+ Λ4).
[CrossRef] [PubMed]

N. Lu, F. X. Zhao, J. Bergou, Phys. Rev. A 39, 5189 (1989).
[CrossRef] [PubMed]

B. Yurke, Phys. Rev. A 29, 408 (1984).
[CrossRef]

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); C. W. Gardiner, M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

M. J. Collett, D. F. Walls, Phys. Rev. A 32, 2887 (1985).
[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).
[CrossRef] [PubMed]

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wódkiewicz, Phys. Rev. A 41, 369, 381 (1990).
[CrossRef] [PubMed]

N. Lu, S. Y. Zhu, Phys. Rev. A 40, 5735 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. O. Scully, K. Wódkiewicz, M. S. Zubairy, J. Bergou, N. Lu, J. Meyer ter Vehn, Phys. Rev. Lett. 60, 1832 (1988).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Phase-quadrature spectrum of squeezing at different laser intensities (N0′) for ρaa = 0.2 and (a) |δ| = 10, (b) |δ| = 5. The relations ρcc = 1 − ρaa and | ρ ¯ a c| = (ρaaρcc)1/2 were used. From bottom to top, N0′ is 0.001 (solid curve), 0.01 (dashed curve), 0.05 (dotted–dashed curve), and 0.1 (dotted curve).

Fig. 2
Fig. 2

Same as in Fig. 1 but for ρaa = 0.5. In (a) the values of S22(0) at the center of the spectra are 1.00, 0.85, 0.47, and 0.30 for N0′ values of 0.001, 0.01, 0.05, and 0.1, respectively; in (b) the values of S22(0) are 1.04, 0.95, 0.67, and 0.49 for N0′ values of 0.001, 0.01, 0.05, and 0.1, respectively.

Equations (15)

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V = g ( a b + b c ) a + H . c . ,
G ( N 0 , 0 ) α δ ( ρ a a - ρ c c ) ( N 0 + δ - 1 ) + 2 ρ ¯ a c 1 + ( N 0 + δ - 1 ) 2 = γ .
t Q ( E 1 , E 2 , t ) = j , k = 1 2 ( - A j k E j δ E k + D j k Q 2 E j E k ) Q ( E 1 , E 2 , t ) ,
A 11 = - α N 0 δ × ( ρ c c - ρ a a ) [ 1 - ( N 0 + δ - 1 ) 2 ] + 4 ( N 0 + δ - 1 ) ρ ¯ a c [ 1 + ( N 0 + δ - 1 ) 2 ] 2
A 12 = 0 ,
A 21 = 4 α N 0 ( ρ a a + ρ c c ) sgn δ ( δ + δ - 1 + 4 N 0 ) 2 0 ,
A 22 = - 2 α ρ ¯ a c δ + δ - 1 + 4 N 0 < 0 ;
D 11 Q = γ 4 + α 8 δ × { ρ a a ( 3 N 0 + δ - 1 ) + ρ c c ( N 0 + 3 δ - 1 ) - 2 ρ ¯ a c 1 + ( N 0 + δ - 1 ) 2 - ρ a a + ρ c c δ + δ - 1 + 4 N 0 + 4 N 0 [ 2 ρ ¯ a c ( N 0 + δ - 1 ) + ρ c c - ρ a a ] [ 1 + ( N 0 + δ - 1 ) 2 ] 2 } ,
D 22 Q = γ 8 + α [ 2 ρ ¯ a c + ( ρ a a + ρ c c ) ( 2 N 0 + ½ δ - 1 ) ] 4 ( δ + δ - 1 + 4 N 0 ) ,
D 12 Q = α sgn δ 8 { ρ a a - ρ c c - 2 ρ ¯ a c δ - 1 δ [ 1 + ( N 0 + δ - 1 ) 2 ] + ρ c c - ρ a a δ + δ - 1 + 4 N 0 - 4 ( ρ a a + ρ c c ) N 0 ( δ + δ - 1 + 4 N 0 ) 2 - 2 N 0 [ 2 ρ ¯ a c + ( ρ a a - ρ c c ) ( N 0 + δ - 1 ) ] δ [ 1 + ( N 0 + δ - 1 ) 2 ] 2 } ,
D P = D Q + ¼ ( A + A T ) ,
: S j k ( δ ω ) : = γ - exp ( - i δ ω t ) : Δ a j ( t ) Δ a k ( 0 ) : d t .
: S ( δ ω ) : = 2 γ ( A - i δ ω ) - 1 D P ( A T + i δ ω ) - 1 ,
S j j ( δ ω ) = 1 4 + : S j j ( δ ω ) : = 1 4 + 2 γ { D j j Q - ½ A j j A j j 2 + ( δ ω ) 2 + δ j 2 A 21 ( 2 A 11 D 12 Q + A 21 D 11 Q ) [ A 11 2 + ( δ ω ) 2 ] [ A 22 2 + ( δ ω ) 2 ] } .
( S 22 ) min 1 4 + 2 γ A 22 ( D 22 Q A 22 - 1 2 ) = ( ½ δ - 1 + 2 N 0 ) ( ρ a a + ρ c c ) 4 ρ ¯ a c ,             N 0 , δ - 1 1 ,

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