## Comment on: Quantum optics with particles of light

Optics Express, Vol. 10, Issue 3, pp. 155-156 (2002)

http://dx.doi.org/10.1364/OE.10.000155

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### Abstract

Errors in the recent article, “Quantum optics with particles of light,” are discussed. “Dispersed states” resulting from linear optics are simply coherent states, and have no interesting quantum statistics.

© Optical Society of America

1. V. V. Kozlov. Quantum optics with particles of light.Opt. Express , **8**,688 (2001). http://www.opticsexpress.org/oearchive/source/34146.htm [CrossRef] [PubMed]

1. V. V. Kozlov. Quantum optics with particles of light.Opt. Express , **8**,688 (2001). http://www.opticsexpress.org/oearchive/source/34146.htm [CrossRef] [PubMed]

*X̂*and

*P̂*operators evolve as free-particle coordinates, as discussed extensively for the soliton case [2

2. H. A. Haus and Y. Lai. Quantum theory of soliton squeezing: a linearized approach.J. Opt. Soc. Am. B , **7**,386 (1990). [CrossRef]

3. P. L. Hagelstein. Application of a photon configuration-space model to soliton propagation in a fiber Phys.Rev. A. , **54**, 2426 (1996). [CrossRef]

3. P. L. Hagelstein. Application of a photon configuration-space model to soliton propagation in a fiber Phys.Rev. A. , **54**, 2426 (1996). [CrossRef]

4. J. M. Fini, P. L. Hagelstein, and H. A. Haus. Configuration-space quantum-soliton model including loss and gain.Phys. Rev. A , **57**,4842 (1998). [CrossRef]

*linear*system seems counter-intuitive. This is for good reason. We have shown that the fluctuations of the relevant operator

*q̂*=

*t*

_{c}

*P̂*cos(

*ψ*) +

*X̂*sin(

*ψ*) are equal to (not below) the standard quantum limit. Further, the dispersed state is simply a coherent state.

*z*. That is, if

*ψ*(

*z*)〉 is an exact coherent-state solution of the Schrödinger equation, as confirmed with a few steps of algebra. This is unlike the evolution of squeezing systems, whose states cannot satisfy Eq. (2) for all

*z*. Since it is a coherent state, the dispersed state has no special quantum properties—for important physical reasons (see [5, pp. 192,217] and [6, Sec. 9.2]) the coherent-state is considered the most “ordinary” field state.

1. V. V. Kozlov. Quantum optics with particles of light.Opt. Express , **8**,688 (2001). http://www.opticsexpress.org/oearchive/source/34146.htm [CrossRef] [PubMed]

*is*a coherent state this is clearly not so.

*ϕ̂*(

*τ*)

*ψ*(

*z*)〉 =

*ϕ*

_{0}(

*τ*,

*z*)

*ψ*(

*z*)〉. Naturally, we must include the correlations (perhaps neglected by Kozlov), which are essential to the reduction of fluctuations. For example,

*q̂*

^{2}

*z*≫

*Z*

_{D}and

*z*/2

*Z*

_{d}) specified by Kozlov, 〈

*q̂*

^{2}

**8**,688 (2001). http://www.opticsexpress.org/oearchive/source/34146.htm [CrossRef] [PubMed]

*z*increases, but the standard quantum limit also reduces, and so the fluctuations are always at, not below, this limit. Since the dispersed state is a coherent state, the equality (6) of their fluctuations is obvious. We have calculated it explicitly to show the consistency of our interpretation.

*q̂*as a variable with observable quantum field fluctuations. As he points out, the uncertainty of this projection decreases with

*z*, but this is a property of the classical projection function. For any projection of the field,

*r̂*= ∫

*dτf*

^{*}(

*τ*)

*ϕ̂*(

*τ*) + h.a., the coherent-state fluctuation is

## References and links

1. | V. V. Kozlov. Quantum optics with particles of light.Opt. Express , |

2. | H. A. Haus and Y. Lai. Quantum theory of soliton squeezing: a linearized approach.J. Opt. Soc. Am. B , |

3. | P. L. Hagelstein. Application of a photon configuration-space model to soliton propagation in a fiber Phys.Rev. A. , |

4. | J. M. Fini, P. L. Hagelstein, and H. A. Haus. Configuration-space quantum-soliton model including loss and gain.Phys. Rev. A , |

5. | Claude Cohen-Tannoudji. |

6. | H. A. Haus. |

7. | J. M. Fini and P. L. Hagelstein. Momentum squeezing of quantum optical pulses. Submitted to Phys.Rev. A. |

8. | V. V. Kozlov. private communication, dated September 17, 2001. |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 19, 2001

Revised Manuscript: January 16, 2002

Published: February 11, 2002

**Citation**

John Fini, "Comment on: Quantum optics with particles of light," Opt. Express **10**, 155-156 (2002)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-3-155

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### References

- V. V. Kozlov. "Quantum optics with particles of light," Opt. Express 8, 688 (2001), <a href="http://www.opticsexpress.org/oearchive/source/34146.htm">http://www.opticsexpress.org/oearchive/source/34146.htm</a> [CrossRef] [PubMed]
- H. A. Haus and Y. Lai, ?Quantum theory of soliton squeezing: a linearized approach,? J. Opt. Soc. Am. B 7, 386 (1990). [CrossRef]
- P. L. Hagelstein. ?Application of a photon configuration-space model to soliton propagation in a fiber,? Phys. Rev. A 54, 2426 (1996). [CrossRef]
- J. M. Fini, P. L. Hagelstein, and H. A. Haus, ?Configuration-space quantum-soliton model including loss and gain,? Phys. Rev. A 57, 4842 (1998). [CrossRef]
- Claude Cohen-Tannoudji. Atom-Photon Interactions, (New York, Wiley, 1992).
- H. A. Haus, Electromagnetic noise and quantum optical measurements, (New York, Springer, 2000).
- J. M. Fini and P. L. Hagelstein. ?Momentum squeezing of quantum optical pulses,? Submitted to Phys. Rev. A.
- V. V. Kozlov, Private communication, dated September 17, 2001.

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