Abstract

Linear optical amplifiers are described quantum mechanically by a linear differential equation with Langevin operator noise sources. Even if the gain medium is composed of fermions, in the limit when the amplifier is a linear amplifier, the noise sources must have bosonlike commutation relations. I show in detail how the Tomonaga approximation produces the bosonic commutators of the noise sources.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 802–851 (1995).
  2. H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2415 (1962).
    [CrossRef]
  3. S. Tomonaga, Prog. Theor. Phys. 5, 544–552 (1950).
    [CrossRef]
  4. G. D. Mahan, Many-Particle Physics, 2nd ed. (Plenum, New York 1990), Sec. 4–4, pp. 324–331.
  5. K. D. Schotte and U. Schotte, “Tomonaga’s model and the threshold singularity of x-ray spectra of metals,” Phys. Rev. 132, 479–482 (1969).
    [CrossRef]
  6. H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, New York, 2000), pp. 150–154.
  7. H. A. Haus and Y. Yamamoto, “Theory of feedback-generated states,” Phys. Rev. A 34, 270–292 (1986).
    [CrossRef] [PubMed]

1995 (1)

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 802–851 (1995).

1986 (1)

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated states,” Phys. Rev. A 34, 270–292 (1986).
[CrossRef] [PubMed]

1969 (1)

K. D. Schotte and U. Schotte, “Tomonaga’s model and the threshold singularity of x-ray spectra of metals,” Phys. Rev. 132, 479–482 (1969).
[CrossRef]

1962 (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2415 (1962).
[CrossRef]

1950 (1)

S. Tomonaga, Prog. Theor. Phys. 5, 544–552 (1950).
[CrossRef]

Haus, H. A.

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated states,” Phys. Rev. A 34, 270–292 (1986).
[CrossRef] [PubMed]

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2415 (1962).
[CrossRef]

Henry, C. H.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 802–851 (1995).

Kazarinov, R. F.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 802–851 (1995).

Mullen, J. A.

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2415 (1962).
[CrossRef]

Schotte, K. D.

K. D. Schotte and U. Schotte, “Tomonaga’s model and the threshold singularity of x-ray spectra of metals,” Phys. Rev. 132, 479–482 (1969).
[CrossRef]

Schotte, U.

K. D. Schotte and U. Schotte, “Tomonaga’s model and the threshold singularity of x-ray spectra of metals,” Phys. Rev. 132, 479–482 (1969).
[CrossRef]

Tomonaga, S.

S. Tomonaga, Prog. Theor. Phys. 5, 544–552 (1950).
[CrossRef]

Yamamoto, Y.

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated states,” Phys. Rev. A 34, 270–292 (1986).
[CrossRef] [PubMed]

Phys. Rev. (2)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2415 (1962).
[CrossRef]

K. D. Schotte and U. Schotte, “Tomonaga’s model and the threshold singularity of x-ray spectra of metals,” Phys. Rev. 132, 479–482 (1969).
[CrossRef]

Phys. Rev. A (1)

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated states,” Phys. Rev. A 34, 270–292 (1986).
[CrossRef] [PubMed]

Prog. Theor. Phys. (1)

S. Tomonaga, Prog. Theor. Phys. 5, 544–552 (1950).
[CrossRef]

Rev. Mod. Phys. (1)

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 802–851 (1995).

Other (2)

G. D. Mahan, Many-Particle Physics, 2nd ed. (Plenum, New York 1990), Sec. 4–4, pp. 324–331.

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, New York, 2000), pp. 150–154.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (24)

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

powerflow=20μ01/2dωdωET(ω)·ET(ω)dS,
Eˆ(ω)=Nnaˆn(ω)en(r),
ndωdωaˆn(ω)aˆn(ω)=photonflow.
N=ω2 μoo1/21/2,
[aˆm(ω), aˆn(ω)]=12πδ(ω-ω)δmn.
aˆm(ω)z=-nγmnaˆn(ω)+nˆm(ω),
z[aˆm(ω), aˆp(ω)]=0=-nγmn[aˆn(ω), aˆp(ω)]-nγpn*[aˆm(ω), aˆn(ω)]+[nˆm(ω), aˆp(ω)]+[aˆm(ω), nˆp(ω)].
Δz(γmp+γpm*)=(1/2)Δz2{[nˆm(ω), nˆp(ω)]+[nˆm(ω), nˆp(ω)]}.
[nˆm(ω)nˆp(ω)]=(γmp+γpm*) 12π×δ(ω-ω)δ(z-z)δmp.
2em+pm2em=0,
eTm·eTn*dS=δnm.
hTm=iz×eTm.
hTm·hTn*dS=δnm.
Eˆ(ω)=Nmaˆm(ω)em(r),
Hˆ(ω)=Noμo1/2maˆm(ω)em(r).
Δ(iz×HˆT)=12 JˆTΔz=-Noμo1/2nΔaˆneTn.
zaˆm=-12N JˆT·eTm*dS.
Jˆ=Jˆind+Jˆ0.
Jˆind(ω, r)=χ¯¯(ω, r)·Aˆ(ω, r)=χ¯¯(ω, r)·Eˆ(ω, r)iω,
aˆm(ω)z=-12 μoo1/2Jˆind·eTm*dS-12 μoo1/2J0·eTm*dS.
γmn=-12 μoo1/2 1iω dSeTm*·χ¯¯(ω, r)eTn.
nˆm(ω)=-12N μoo1/2Jˆ0·eTm*dS.
[nˆm(ω), nˆp(ω)]=14N2 μoo eTm*(r)·[Jˆ0(ω, r), Jˆ0(ω, r)]·eTp(r)dSdS.
[Jˆo(ω, r), Jˆ(ω, r)]=(c/i){χ¯¯(ω)-χ¯¯(ω)}×δ(r-r)δ(ω-ω).

Metrics