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.

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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. London 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," Opt. 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 deamplification of 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 precision measurements," 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]

Other

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

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]

R. J. Glauber and M. Lewenstein, "Quantum optics of dielectic media," Phys Rev. A 43, 467-491 (1991).
[CrossRef] [PubMed]

H. Khosravi and R. Loudon, "Vacuum field fluctuations and spontaneous emission in a dielectric slab," Proc. R. Soc. London Ser. A 436, 373-389 (1992).
[CrossRef]

P. D. Drummond, "Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics," Phys. Rev. A 42, 6845-6857 (1990).
[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).

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]

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]

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]

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

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

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

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]

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 precision measurements," Phys. Rev. Lett. 68, 2859 (1992).
[CrossRef] [PubMed]

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]

D. H. Auston, "Picosecond optoelectronic switching and gating in silicon," Appl. Phys. Lett. 26, 101-103 (1975).
[CrossRef]

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

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

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]

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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)

Equations on this page are rendered with MathJax. Learn more.

[ 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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