Abstract

We report excellent quantitative agreement between theoretical predictions and experimental observation of squeezing from a singly resonant second-harmonic-generating crystal. Limitations in the noise suppression imposed by the pump laser are explicitly modeled and confirmed by our measurements.

© 1995 Optical Society of America

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References

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  1. For a review seeC. Fabre, Phys. Rep. 219, 215 (1992).
    [CrossRef]
  2. E. S. Polzik, J. C. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
    [CrossRef] [PubMed]
  3. H. J. Kimble, Phys. Rep. 219, 227 (1992).
    [CrossRef]
  4. H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993); C. W. Gardiner, Phys. Rev. Lett. 70, 2269 (1993).
    [CrossRef] [PubMed]
  5. R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
    [CrossRef] [PubMed]
  6. S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
    [CrossRef] [PubMed]
  7. N. C. Wong, K. W. Leong, J. H. Shapiro, Opt. Lett. 15, 891 (1990).
    [CrossRef] [PubMed]
  8. T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
    [CrossRef] [PubMed]
  9. P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
    [CrossRef]
  10. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley-Interscience, New York, 1973).
  11. H. Haken, in Encyclopedia of Physics, S. Flügge, ed. (Springer-Verlag, Heidelberg, 1970), Vol. XXX/2c.
  12. P. D. Drummond, D. F. Walls, Phys. Rev. A 23, 2563 (1981).
    [CrossRef]
  13. C. W. Gardiner, M. J. Collett, Phys. Rev. A 31, 3761 (1985).
    [CrossRef] [PubMed]
  14. T. C. Ralph, C. M. Savage, Phys. Rev. A 44, 7809 (1991);T. C. Ralph, Ph.D. dissertation (Australian National University, Canberra, ACT, Australia, 1993).
    [CrossRef] [PubMed]
  15. Walter Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1988).
  16. I. Feitag, H. Welling, Appl. Phys. B 58, 537 (1994).
    [CrossRef]

1994 (2)

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

I. Feitag, H. Welling, Appl. Phys. B 58, 537 (1994).
[CrossRef]

1993 (1)

H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993); C. W. Gardiner, Phys. Rev. Lett. 70, 2269 (1993).
[CrossRef] [PubMed]

1992 (3)

For a review seeC. Fabre, Phys. Rep. 219, 215 (1992).
[CrossRef]

E. S. Polzik, J. C. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

H. J. Kimble, Phys. Rep. 219, 227 (1992).
[CrossRef]

1991 (1)

T. C. Ralph, C. M. Savage, Phys. Rev. A 44, 7809 (1991);T. C. Ralph, Ph.D. dissertation (Australian National University, Canberra, ACT, Australia, 1993).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

1988 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

1985 (1)

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

1981 (2)

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef]

P. D. Drummond, D. F. Walls, Phys. Rev. A 23, 2563 (1981).
[CrossRef]

Anderson, T. B.

T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

Bachor, H. A.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Carmichael, H. J.

H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993); C. W. Gardiner, Phys. Rev. Lett. 70, 2269 (1993).
[CrossRef] [PubMed]

Carri, J. C.

E. S. Polzik, J. C. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Collett, M.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Collett, M. J.

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

Drummond, P. D.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef]

P. D. Drummond, D. F. Walls, Phys. Rev. A 23, 2563 (1981).
[CrossRef]

Fabre, C.

For a review seeC. Fabre, Phys. Rep. 219, 215 (1992).
[CrossRef]

Feitag, I.

I. Feitag, H. Welling, Appl. Phys. B 58, 537 (1994).
[CrossRef]

Fiedler, K.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Gardiner, C. W.

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

Haken, H.

H. Haken, in Encyclopedia of Physics, S. Flügge, ed. (Springer-Verlag, Heidelberg, 1970), Vol. XXX/2c.

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Kennedy, T. A. B.

T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

Kimble, H. J.

E. S. Polzik, J. C. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

H. J. Kimble, Phys. Rep. 219, 227 (1992).
[CrossRef]

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Koechner, Walter

Walter Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1988).

Kürz, P.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Leong, K. W.

Louisell, W. H.

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley-Interscience, New York, 1973).

McNeil, K. J.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef]

Mlynek, J.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Paschotta, R.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Polzik, E. S.

E. S. Polzik, J. C. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Ralph, T. C.

T. C. Ralph, C. M. Savage, Phys. Rev. A 44, 7809 (1991);T. C. Ralph, Ph.D. dissertation (Australian National University, Canberra, ACT, Australia, 1993).
[CrossRef] [PubMed]

Savage, C. M.

T. C. Ralph, C. M. Savage, Phys. Rev. A 44, 7809 (1991);T. C. Ralph, Ph.D. dissertation (Australian National University, Canberra, ACT, Australia, 1993).
[CrossRef] [PubMed]

Shapiro, J. H.

Walls, D. F.

T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef]

P. D. Drummond, D. F. Walls, Phys. Rev. A 23, 2563 (1981).
[CrossRef]

Welling, H.

I. Feitag, H. Welling, Appl. Phys. B 58, 537 (1994).
[CrossRef]

Wong, N. C.

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Appl. Phys. B (1)

I. Feitag, H. Welling, Appl. Phys. B 58, 537 (1994).
[CrossRef]

Opt. Acta (1)

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (2)

For a review seeC. Fabre, Phys. Rep. 219, 215 (1992).
[CrossRef]

H. J. Kimble, Phys. Rep. 219, 227 (1992).
[CrossRef]

Phys. Rev. A (5)

T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

P. D. Drummond, D. F. Walls, Phys. Rev. A 23, 2563 (1981).
[CrossRef]

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

T. C. Ralph, C. M. Savage, Phys. Rev. A 44, 7809 (1991);T. C. Ralph, Ph.D. dissertation (Australian National University, Canberra, ACT, Australia, 1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993); C. W. Gardiner, Phys. Rev. Lett. 70, 2269 (1993).
[CrossRef] [PubMed]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. Mlynek, Phys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

E. S. Polzik, J. C. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Other (3)

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley-Interscience, New York, 1973).

H. Haken, in Encyclopedia of Physics, S. Flügge, ed. (Springer-Verlag, Heidelberg, 1970), Vol. XXX/2c.

Walter Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1988).

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of the experimental setup. A diode-pumped Nd:YAG laser (Lightwave 122) drives the monolithic doubler. A Faraday isolator prevents significant backreflection entering the laser. A half-wave plate (λ/2) permits variable attenuation. The electro-optic modulator (EOM) phase modulates the driving field at 88 MHz. An error signal for locking the laser is derived from the 88-MHz signal driving the EOM and the fundamental light reflected from the monolith by use of a double-balanced mixer. The second-harmonic beam exits the front face of the monolith, where it is separated from the fundamental by use of two dichroic beam splitters. It is then incident upon a balanced detector, the summed and differenced outputs of the which are monitored with an HP8568B spectrum analyzer.

Fig. 2
Fig. 2

Comparison of experimental and theoretical noise spectra of the green light produced by the SHG crystal. The experimental traces are obtained with a resolution bandwidth of 300 kHz and a video bandwidth of 100 Hz. They are averages of ten sweeps and have been corrected for electronic noise and the overall detector efficiency. The detected green power is 30 mW. The parameters used to obtain the theoretical traces are g2N/γp = σs/2 = 6.7 × 1011 s−1, where σs is the stimulated emission cross section for Nd:YAG and ρ is the density of Nd atoms; γ23 = 4.3 × 103 s−1; γ12 = 3.3 × 107 s−1; κa + κal = 1.4 × 108 s−1; Γ = 8.3 s−1; N = 4.23 × 10 12 s - 1; κbf = 1.1 × 107 s−1; κbb = 3.2 × 106 s−1; κbl = 6.7 × 106 s−1; κc = 2.58 × 109 s−1; and κa = 1.54 × 107 s−1. W.R.T, with respect to.

Fig. 3
Fig. 3

Comparison of squeezing spectra with (solid curve) and without (dashed curve) pump noise. Parameters are the same as in Fig. 2 except that, for the dashed curve, pumping is achieved by means of a coherent field of equal intensity to the laser output.

Equations (3)

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H ^ l = i g ( a ^ J ^ 23 - - a ^ J ^ 23 + ) ,
H ^ S = i 2 ( b ^ 2 c ^ - b ^ 2 c ^ ) ,
d d t ρ ^ = 1 i ( H ^ l , ρ ^ ) + 1 i ( H ^ s , ρ ^ ) + 1 2 ( γ 12 L 12 + γ 23 L 23 ) ρ ^ + Γ 2 ( L 13 ρ ) + 1 4 γ p [ 2 ( J ^ 3 - J ^ 2 ) ρ ^ ( J ^ 3 - J ^ 2 ) - ( J ^ 3 - J ^ 2 ) 2 ρ ^ - ρ ^ ( J ^ 3 - J ^ 2 ) 2 ] + ( κ a + κ a l ) ( 2 a ^ ρ ^ a ^ - a ^ a ^ ρ ^ - ρ ^ a ^ a ^ ) + ( κ b f + κ b b + κ b l ) ( 2 b ^ ρ ^ b ^ - b ^ b ^ ρ ^ - ρ ^ b ^ b ^ ) + κ c ( 2 c ^ ρ ^ c ^ - c ^ c ^ ρ ^ - ρ ^ c ^ c ^ ) + 2 κ a κ b f ( a ^ ρ ^ b ^ + b ^ ρ ^ a ^ - ρ ^ a ^ b ^ - b ^ ρ ^ a ^ ) , L i j ρ ^ = ( 2 J ^ i j - ρ ^ J ^ i j + - J ^ i j + J ^ i j - ρ ^ - ρ ^ J ^ i j + J ^ i j - ) .

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