Abstract

The concept of particles of light is introduced by ascribing a mechanical degree of freedom to a radiational wave packet. Evolution of the position and momentum observables of such particle in a dispersive dielectric is studied. It is shown that an initial coherent state evolves into a dispersed state which is characterized by a reduction of quantum fluctuations below Standard Quantum Limit when a certain combination of the position and momentum observables is measured.

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References

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  1. L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).
  2. T. D. Newton and E. P. Wigner, "Localized states for elementary systems,' Rev. Mod. Phys. 21, 400 (1949).
    [CrossRef]
  3. A. B. Matsko and V. V. Kozlov, "Second-quantized models for optical solitons in nonlinear fibers: Equal-time versus equal-space commutation relations," Phys. Rev. A 62, 033811 (2000).
    [CrossRef]
  4. B. Huttner and S. M. Barnett, "Quantization of the electromagnetic field in dielectrics," Phys. Rev. A 46, 4306-4322 (1992).
    [CrossRef] [PubMed]
  5. G. P. Agrawal, Chapter 3, Nonlinear fiber optics (Academic Press, 2001).
  6. C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  7. H. A. Haus, Electromagnetic noise and quantum optical measurements (Springer-Verlag, 2000).
  8. I. A. Walmsley, "Spectral quantum fluctuations in a stimulated Raman generator: a description in terms of temporally coherent modes," Opt. Lett. 17, 435-437 (1992).
    [CrossRef] [PubMed]
  9. S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
    [CrossRef]

Other (9)

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

T. D. Newton and E. P. Wigner, "Localized states for elementary systems,' Rev. Mod. Phys. 21, 400 (1949).
[CrossRef]

A. B. Matsko and V. V. Kozlov, "Second-quantized models for optical solitons in nonlinear fibers: Equal-time versus equal-space commutation relations," Phys. Rev. A 62, 033811 (2000).
[CrossRef]

B. Huttner and S. M. Barnett, "Quantization of the electromagnetic field in dielectrics," Phys. Rev. A 46, 4306-4322 (1992).
[CrossRef] [PubMed]

G. P. Agrawal, Chapter 3, Nonlinear fiber optics (Academic Press, 2001).

C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693 (1981).
[CrossRef]

H. A. Haus, Electromagnetic noise and quantum optical measurements (Springer-Verlag, 2000).

I. A. Walmsley, "Spectral quantum fluctuations in a stimulated Raman generator: a description in terms of temporally coherent modes," Opt. Lett. 17, 435-437 (1992).
[CrossRef] [PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

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Figures (1)

Fig. 1.
Fig. 1.

Sketch of the balanced homodyne detection for measuring position-momentum quadrature Eq. (20). A Gaussian pulse is splitted (BS1) into signal and local oscillator (LO). Both propagate through the same fiber (and thereby broaden similarly). Phase shift introduced by PS and shape transformation produced by “transformer” (e.g. by means of Fourier optics) shape the LO as Lq (τ)∝fq (τ), Eq. (20). Delay lines serve for spatial separating the signal and the LO.

Equations (20)

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[ E ̂ ( z , t ) , E ̂ ( z , t ) ] = c 4 π 0 S k e i [ k ( z z ) ω ( t t ) ] dk ,
E ̂ ( z , t ) = ( k 0 4 π 0 S ) 1 2 ϕ ̂ ( z , t ) e i ( k 0 z ω 0 t ) ,
[ ϕ ̂ ( z , t ) , ϕ ̂ ( z , t ) ] = δ ( t t ) .
X ̂ lim ε 0 t ϕ ̂ ( z , t ) ϕ ̂ ( z , t ) dt ( ε + N ̂ ) 1 ,
[ X ̂ , P ̂ ] = i ,
P ̂ i 2 ( ϕ ̂ t ϕ ̂ ϕ ̂ ϕ ̂ t ) dt ,
c ̂ ± ( z , ω ) z = ± ik ( ω ) c ̂ ± ( z , ω ) ± 2 Im [ k ( ω ) ] f ̂ ( z , ω ) ,
[ c ̂ ± ( z , ω ) , c ̂ ± ( z , ω ) ] = δ ( ω ω )
k ( ω ) = k 0 + k ( ω ω 0 ) + ( 1 2 ) k ( ω ω 0 ) 2 ,
E ̂ + ( z , t ) = i 4 π 0 S d ω [ k ( ω ) ] 1 2 c ̂ + ( z , ω ) e i ω t .
i z ϕ ̂ ( z , τ ) = k 2 2 τ 2 ϕ ̂ ( z , τ ) ,
X ̂ 1 n 0 ( τ ϕ * υ ̂ + τ ϕ υ ̂ ) d τ , P ̂ i ( ϕ * τ υ ̂ ϕ τ υ ̂ ) d τ ,
P ̂ ( z ) = P ̂ 0 , X ̂ ( z ) = X ̂ 0 + ( k z n 0 ) P ̂ 0 ,
[ X ̂ ( z ) , P ̂ ( z ) ] = i .
ϕ ( z , τ ) = n 0 π T p ( z ) exp [ τ 2 2 T p 2 ( z ) ] exp [ i τ 2 2 T p 2 ( z ) z Z D i 2 arctg z Z D ] ,
Δ P ̂ 2 coh ( in ) = ϕ ( 0 , τ ) τ 2 d τ = n 0 2 τ p 2 , Δ X ̂ 2 coh ( in ) = τ 2 ϕ ( 0 , τ ) 2 d τ n 0 2 = τ p 2 2 n 0 .
q ̂ = t c P ̂ cos ψ + t c 1 X ̂ sin ψ and q ̂ = t c P ̂ sin ψ + t c 1 X ̂ cos ψ ,
Δ q ̂ 2 min = 1 2 [ 1 + ( z 2 Z D ) 2 z 2 Z D ] 2 ,
Δ P ̂ 2 coh ( out ) = ϕ ( z , τ ) τ 2 d τ = n 0 2 τ p 2 , Δ X ̂ 2 coh ( out ) = τ 2 ϕ ( z , τ ) 2 d τ n 0 2 = T p 2 ( z ) 2 n 0 ,
q ̂ = [ f q * υ ̂ ( z , τ ) + H . c . ] d τ , f q it c ϕ ( z , τ ) τ cos ψ + τ ϕ ( z , τ ) t c n 0 sin ψ ,

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