Abstract

The timing jitter and frequency jitter of quantized optical pulses obey Heisenberg’s uncertainty principle. We show how one jitter may be reduced at the expense of the other, using dispersion and phase modulation.

© 2001 Optical Society of America

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References

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  1. L. S. Brown, Quantum Field Theory (Cambridge University Press, 1992).
  2. L. Knöll, W. Vogel, and D.-G. Welsch, “Action of passive, lossless optical systems in quantum optics,” Phys. Rev. A 36, 3803–3818 (1987).
    [Crossref] [PubMed]
  3. R. J. Glauber and M. Lewenstein, “Quantum optics of dielectic media,” Phys Rev. A 43, 467–491 (1991).
    [Crossref] [PubMed]
  4. H. Khosravi and R. Loudon, “Vacuum field fluctuations and spontaneous emission in a dielectric slab,” Proc. R. Soc. Lon don Ser. A 436, 373–389 (1992).
    [Crossref]
  5. P. D. Drummond, “Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics,” Phys. Rev. A 42, 6845–6857 (1990).
    [Crossref] [PubMed]
  6. B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett. 16, 177 (1991).
    [Crossref]
  7. P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42, 1991 (1995).
  8. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
    [Crossref] [PubMed]
  9. M. J. Potasek and B. Yurke, “Dissipative effects on squeezed light generated in systems governed by the nonlinear Schrödinger equation,” Phys. Rev. A 38, 1335–1348 (1988).
    [Crossref] [PubMed]
  10. L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
    [Crossref] [PubMed]
  11. M. Xiao, L. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 53, 278 (1987).
    [Crossref]
  12. M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Op. Lett. 12, 161 (1987).
    [Crossref]
  13. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
    [Crossref]
  14. M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
    [Crossref]
  15. F. Hong-Yi and J. VanderLinde, “Squeezed-state wave functions and their relation to classical phase-space maps,” Phys. Rev. A 40, 4785 (1989).
    [Crossref]
  16. D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699 (1991).
    [Crossref] [PubMed]
  17. F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
    [Crossref] [PubMed]
  18. A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulse widths and pulse shapes in CW mode-locked lasers,” IEEE J. Quantum Electron. 6, 212–215 (1970).
    [Crossref]
  19. D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26, 101–103 (1975).
    [Crossref]
  20. H. F. Taylor, “An electrooptic analog-to-digital converter-design and analysis,” IEEE J. Quantum. Electron. 15, 210–216 (1979).
    [Crossref]
  21. J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” Phot. Tech. Lett. 12, 1237–1239 (2000).
    [Crossref]
  22. H. A. Haus, “Steady-state quantum analysis of linear systems,” Proc. of the IEEE 58, 1599–1611 (1970).
    [Crossref]
  23. H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407 (1962).
    [Crossref]
  24. T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
    [Crossref]

2000 (1)

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” Phot. Tech. Lett. 12, 1237–1239 (2000).
[Crossref]

1999 (1)

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[Crossref]

1992 (2)

H. Khosravi and R. Loudon, “Vacuum field fluctuations and spontaneous emission in a dielectric slab,” Proc. R. Soc. Lon don Ser. A 436, 373–389 (1992).
[Crossref]

F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
[Crossref] [PubMed]

1991 (4)

D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699 (1991).
[Crossref] [PubMed]

R. J. Glauber and M. Lewenstein, “Quantum optics of dielectic media,” Phys Rev. A 43, 467–491 (1991).
[Crossref] [PubMed]

B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett. 16, 177 (1991).
[Crossref]

P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42, 1991 (1995).

1990 (2)

P. D. Drummond, “Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics,” Phys. Rev. A 42, 6845–6857 (1990).
[Crossref] [PubMed]

M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
[Crossref]

1989 (1)

F. Hong-Yi and J. VanderLinde, “Squeezed-state wave functions and their relation to classical phase-space maps,” Phys. Rev. A 40, 4785 (1989).
[Crossref]

1988 (1)

M. J. Potasek and B. Yurke, “Dissipative effects on squeezed light generated in systems governed by the nonlinear Schrödinger equation,” Phys. Rev. A 38, 1335–1348 (1988).
[Crossref] [PubMed]

1987 (3)

L. Knöll, W. Vogel, and D.-G. Welsch, “Action of passive, lossless optical systems in quantum optics,” Phys. Rev. A 36, 3803–3818 (1987).
[Crossref] [PubMed]

M. Xiao, L. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 53, 278 (1987).
[Crossref]

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Op. Lett. 12, 161 (1987).
[Crossref]

1986 (2)

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[Crossref] [PubMed]

1985 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

1979 (1)

H. F. Taylor, “An electrooptic analog-to-digital converter-design and analysis,” IEEE J. Quantum. Electron. 15, 210–216 (1979).
[Crossref]

1975 (1)

D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26, 101–103 (1975).
[Crossref]

1970 (2)

A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulse widths and pulse shapes in CW mode-locked lasers,” IEEE J. Quantum Electron. 6, 212–215 (1970).
[Crossref]

H. A. Haus, “Steady-state quantum analysis of linear systems,” Proc. of the IEEE 58, 1599–1611 (1970).
[Crossref]

1962 (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407 (1962).
[Crossref]

Auston, D. H.

D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26, 101–103 (1975).
[Crossref]

Barnett, S. M.

B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett. 16, 177 (1991).
[Crossref]

Baumberg, J. J.

B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett. 16, 177 (1991).
[Crossref]

Boyce, K. R.

F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
[Crossref] [PubMed]

Brown, L. S.

L. S. Brown, Quantum Field Theory (Cambridge University Press, 1992).

Carruthers, T. F.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[Crossref]

Clark, T. R.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[Crossref]

DeVoe, R. G.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

DiFilippo, F.

F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
[Crossref] [PubMed]

Drummond, P. D.

P. D. Drummond, “Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics,” Phys. Rev. A 42, 6845–6857 (1990).
[Crossref] [PubMed]

Duling III, I. N.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[Crossref]

Glauber, R. J.

R. J. Glauber and M. Lewenstein, “Quantum optics of dielectic media,” Phys Rev. A 43, 467–491 (1991).
[Crossref] [PubMed]

Grutter, P.

D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699 (1991).
[Crossref] [PubMed]

Hall, J. L.

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[Crossref] [PubMed]

Haus, H. A.

M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
[Crossref]

H. A. Haus, “Steady-state quantum analysis of linear systems,” Proc. of the IEEE 58, 1599–1611 (1970).
[Crossref]

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407 (1962).
[Crossref]

Helkey, R.

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” Phot. Tech. Lett. 12, 1237–1239 (2000).
[Crossref]

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Hong-Yi, F.

F. Hong-Yi and J. VanderLinde, “Squeezed-state wave functions and their relation to classical phase-space maps,” Phys. Rev. A 40, 4785 (1989).
[Crossref]

Huttner, B.

B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett. 16, 177 (1991).
[Crossref]

Khosravi, H.

H. Khosravi and R. Loudon, “Vacuum field fluctuations and spontaneous emission in a dielectric slab,” Proc. R. Soc. Lon don Ser. A 436, 373–389 (1992).
[Crossref]

Kimble, H. J.

M. Xiao, L. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 53, 278 (1987).
[Crossref]

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[Crossref] [PubMed]

Knöll, L.

L. Knöll, W. Vogel, and D.-G. Welsch, “Action of passive, lossless optical systems in quantum optics,” Phys. Rev. A 36, 3803–3818 (1987).
[Crossref] [PubMed]

Kuizenga, D. J.

A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulse widths and pulse shapes in CW mode-locked lasers,” IEEE J. Quantum Electron. 6, 212–215 (1970).
[Crossref]

Kumar, P.

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Op. Lett. 12, 161 (1987).
[Crossref]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

Lewenstein, M.

R. J. Glauber and M. Lewenstein, “Quantum optics of dielectic media,” Phys Rev. A 43, 467–491 (1991).
[Crossref] [PubMed]

Loudon, R.

H. Khosravi and R. Loudon, “Vacuum field fluctuations and spontaneous emission in a dielectric slab,” Proc. R. Soc. Lon don Ser. A 436, 373–389 (1992).
[Crossref]

Maeda, M. W.

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Op. Lett. 12, 161 (1987).
[Crossref]

Matthews, P. J.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[Crossref]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Milonni, P. W.

P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42, 1991 (1995).

Mullen, J. A.

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407 (1962).
[Crossref]

Natarajan, V.

F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
[Crossref] [PubMed]

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

Potasek, M. J.

M. J. Potasek and B. Yurke, “Dissipative effects on squeezed light generated in systems governed by the nonlinear Schrödinger equation,” Phys. Rev. A 38, 1335–1348 (1988).
[Crossref] [PubMed]

Pritchard, D. E.

F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
[Crossref] [PubMed]

Rugar, D.

D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699 (1991).
[Crossref] [PubMed]

Shapiro, J. H.

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Op. Lett. 12, 161 (1987).
[Crossref]

Shelby, R. M.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

Shirasaki, M.

Siegman, A. E.

A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulse widths and pulse shapes in CW mode-locked lasers,” IEEE J. Quantum Electron. 6, 212–215 (1970).
[Crossref]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Taylor, H. F.

H. F. Taylor, “An electrooptic analog-to-digital converter-design and analysis,” IEEE J. Quantum. Electron. 15, 210–216 (1979).
[Crossref]

Twichell, J. C.

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” Phot. Tech. Lett. 12, 1237–1239 (2000).
[Crossref]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

VanderLinde, J.

F. Hong-Yi and J. VanderLinde, “Squeezed-state wave functions and their relation to classical phase-space maps,” Phys. Rev. A 40, 4785 (1989).
[Crossref]

Vogel, W.

L. Knöll, W. Vogel, and D.-G. Welsch, “Action of passive, lossless optical systems in quantum optics,” Phys. Rev. A 36, 3803–3818 (1987).
[Crossref] [PubMed]

Walls, D. F.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

Welsch, D.-G.

L. Knöll, W. Vogel, and D.-G. Welsch, “Action of passive, lossless optical systems in quantum optics,” Phys. Rev. A 36, 3803–3818 (1987).
[Crossref] [PubMed]

Wu, H.

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[Crossref] [PubMed]

Wu, L.

M. Xiao, L. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 53, 278 (1987).
[Crossref]

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[Crossref] [PubMed]

Xiao, M.

M. Xiao, L. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 53, 278 (1987).
[Crossref]

Yurke, B.

M. J. Potasek and B. Yurke, “Dissipative effects on squeezed light generated in systems governed by the nonlinear Schrödinger equation,” Phys. Rev. A 38, 1335–1348 (1988).
[Crossref] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26, 101–103 (1975).
[Crossref]

Electron. Lett. (1)

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[Crossref]

Europhys. Lett. (1)

B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett. 16, 177 (1991).
[Crossref]

IEEE J. Quantum Electron. (1)

A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulse widths and pulse shapes in CW mode-locked lasers,” IEEE J. Quantum Electron. 6, 212–215 (1970).
[Crossref]

IEEE J. Quantum. Electron. (1)

H. F. Taylor, “An electrooptic analog-to-digital converter-design and analysis,” IEEE J. Quantum. Electron. 15, 210–216 (1979).
[Crossref]

J. Mod. Opt. (1)

P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42, 1991 (1995).

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

Op. Lett. (1)

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Op. Lett. 12, 161 (1987).
[Crossref]

Phot. Tech. Lett. (1)

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” Phot. Tech. Lett. 12, 1237–1239 (2000).
[Crossref]

Phys Rev. A (1)

R. J. Glauber and M. Lewenstein, “Quantum optics of dielectic media,” Phys Rev. A 43, 467–491 (1991).
[Crossref] [PubMed]

Phys. Rev. (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407 (1962).
[Crossref]

Phys. Rev. A (4)

L. Knöll, W. Vogel, and D.-G. Welsch, “Action of passive, lossless optical systems in quantum optics,” Phys. Rev. A 36, 3803–3818 (1987).
[Crossref] [PubMed]

M. J. Potasek and B. Yurke, “Dissipative effects on squeezed light generated in systems governed by the nonlinear Schrödinger equation,” Phys. Rev. A 38, 1335–1348 (1988).
[Crossref] [PubMed]

P. D. Drummond, “Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics,” Phys. Rev. A 42, 6845–6857 (1990).
[Crossref] [PubMed]

F. Hong-Yi and J. VanderLinde, “Squeezed-state wave functions and their relation to classical phase-space maps,” Phys. Rev. A 40, 4785 (1989).
[Crossref]

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplificationof quantum noise in an optical fiber,” Phys. Rev. B 57, 691 (1986).
[Crossref]

Phys. Rev. Lett. (5)

D. Rugar and P. Grutter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699 (1991).
[Crossref] [PubMed]

F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Classical amplitude squeezing for precisionm easurements,” Phys. Rev. Lett. 68, 2859 (1992).
[Crossref] [PubMed]

L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[Crossref] [PubMed]

M. Xiao, L. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 53, 278 (1987).
[Crossref]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by 4-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Proc. of the IEEE (1)

H. A. Haus, “Steady-state quantum analysis of linear systems,” Proc. of the IEEE 58, 1599–1611 (1970).
[Crossref]

Proc. R. Soc. Lon don Ser. A (1)

H. Khosravi and R. Loudon, “Vacuum field fluctuations and spontaneous emission in a dielectric slab,” Proc. R. Soc. Lon don Ser. A 436, 373–389 (1992).
[Crossref]

Other (1)

L. S. Brown, Quantum Field Theory (Cambridge University Press, 1992).

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Figures (2)

Fig. 1.
Fig. 1.

Schematic of system analyzed for Fig. 2 where ω is the group-velocity dispersion, and T the propagation delay.

Fig. 2.
Fig. 2.

R=(MΩM2 /υg2 )2〈|Δ|〉2/〈|Δ|〉2 for the cases (a) Rin =2 an d (b) Rin =1 where SRout /Rin , X≡(MΩM2 /υg2 )ω T 1, and Y≡(MΩM2 /υg2 )ω2 T 2. The pulse position fluctuations are reduced in the regions where S<1. Regions for S>1 are not shown.

Equations (19)

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[ a ̂ ( T , x ) , a ̂ ( T , x ) ] = δ ( x x )
a ̂ = a 0 + Δ a ̂
[ Δ a ̂ ( T , x ) , Δ a ̂ ( T , x ) ] = δ ( x x )
a 0 = A 0 ψ 0 ( x ξ )
ψ n ( x ξ ) = 1 2 n n ! ξ π H n ( x ξ ) e i x 2 2 ω ( T i b ) e i ( n + 1 ) ϕ
ξ 2 = ξ 0 2 [ 1 + ( T b ) 2 ]
Δ a ̂ = Σ n Δ A ̂ n ψ n ( x ξ )
Δ A ̂ n = Δ A ̂ n ( 1 ) + i Δ A ̂ n ( 2 )
A 0 ψ 0 ( x , T , Δ X , Δ ω ) = A 0 ξ π exp [ i ( x Δ X + ω Δ ω T ν g ) 2 2 ω ( T i b ) ] exp [ i Δ ω x ν g ] exp [ i ϕ ]
Δ A ̂ 1 = 1 2 ( Δ X ̂ ξ 0 i Δ ω ̂ ν g ξ 0 ) = 1 2 ( Δ X ̂ ξ 0 + i Δ P ̂ ξ 0 )
Δ ω ̂ ν g = Δ P ̂
Δ X ̂ = 2 A 0 ξ 0 Δ A ̂ 1 ( 1 ) and Δ P ̂ = 2 A 0 1 ξ 0 Δ A ̂ 1 ( 2 )
[ Δ A ̂ 1 ( 1 ) , Δ A ̂ 1 ( 2 ) ] = i 2
[ Δ X ̂ , Δ P ̂ ] = i n
Δ X ̂ ( T ) = Δ X ̂ ( 0 ) + ω T Δ P ̂ ( 0 )
Δ P ̂ out = Δ P ̂ in M Ω M 2 v g 2 Δ X ̂
[ Δ X ̂ out Δ P ̂ out ] = [ A B C D ] [ Δ X ̂ in Δ P ̂ in ]
[ A B C D ] = [ 1 ω T 0 1 ]
[ A B C D ] = [ 1 0 M Ω M 2 v g 2 1 ]

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