## Quantum fluctuations in the time-dependent linearly driven degenerate parametric amplifier

JOSA B, Vol. 23, Issue 10, pp. 2174-2179 (2006)

http://dx.doi.org/10.1364/JOSAB.23.002174

Enhanced HTML Acrobat PDF (171 KB)

### Abstract

The time-dependent, linearly driven Fokker–Planck equation for the degenerate parametric amplifier is derived when the pump depletion is present both above and below threshold. A model that the driving force *ε* and quantum operator *τ*, the long-time behavior of our solution shows that the squeezing is always quite different from the linear theory. It is shown that the maximal squeezing can be obtained at large pump parameter

© 2006 Optical Society of America

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 20, 2005

Revised Manuscript: June 24, 2006

Manuscript Accepted: July 11, 2006

**Citation**

Chaoying Zhao and Weihan Tan, "Quantum fluctuations in the time-dependent linearly driven degenerate parametric amplifier," J. Opt. Soc. Am. B **23**, 2174-2179 (2006)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-10-2174

Sort: Year | Journal | Reset

### References

- B. Yurke, "Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors," Phys. Rev. A 32, 300-310 (1985). [CrossRef] [PubMed]
- C. W. Gardiner and M. J. Collett, "Input and output in damped quantum systems: quantum stochastic differential equations and the master equation," Phys. Rev. A 31, 3761-3774 (1985). [CrossRef] [PubMed]
- M. J. Collett and D. F. Walls, "Squeezing spectra for nonlinear optical systems," Phys. Rev. A 32, 2887-2892 (1985). [CrossRef] [PubMed]
- L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986). [CrossRef] [PubMed]
- P. Kinsler and P. D. Drummond, "Quantum dynamics of the parametric oscillator," Phys. Rev. A 43, 6194-6208 (1991). [CrossRef] [PubMed]
- P. Kinsler and P. D. Drummond, "Critical fluctuations in the quantum parametric oscillator," Phys. Rev. A 52, 783-790 (1995). [CrossRef] [PubMed]
- L. I. Plimak and D. F. Walls, "Dynamical restrictions to squeezing in a degenerate optical parametric oscillator," Phys. Rev. A 50, 2627-2641 (1994). [CrossRef] [PubMed]
- P. D. Drummond and C. W. Gardiner, "Generalised P-representations in quantum optics," J. Phys. A 13, 2353-2368 (1980). [CrossRef]
- D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994), p. 178.
- R. S. Bondurant, P. Kumar, J. H. Shapiro, and M. Maeda, "Degenerate four-wave mixing as a possible source of squeezed-state light," Phys. Rev. A 30, 343-353 (1984). [CrossRef]
- P. Kumar and J. H. Shapiro, "Squeezed-state generation via forward degenerate four-wave mixing," Phys. Rev. A 30, 1568-1571 (1984). [CrossRef]
- M. Wolinsky and H. J. Carmichael, "Squeezing in the degenerate parametric oscillator," Opt. Commun. 55, 138-142 (1985). [CrossRef]
- W. H. Tan, Y. F. Li, and W. P. Zhang, "The solution of the Fokker-Planck equation with zero or negative diffusion coefficients in quantum optics," Opt. Commun. 64, 195-199 (1987). [CrossRef]
- C. J. Mertens, T. A. B. Kennedy, and S. Swain, "Many-body theory of quantum noise," Phys. Rev. Lett. 71, 2014-2017 (1993). [CrossRef] [PubMed]
- C. J. Mertens, T. A. B. Kennedy, and S. Swain, "Many-body quantum theory of the optical parametric oscillator," Phys. Rev. A 48, 2374-2385 (1993). [CrossRef] [PubMed]
- O. Veits and M. Fleischhauer, "Quantum fluctuations in the optical parametric oscillator in the limit of a fast decaying subharmonic mode," Phys. Rev. A 52, R4344-R4347 (1995). [CrossRef] [PubMed]
- L. I. Plimak and D. F. Walls, "Dynamical restrictions to squeezing in a degenerate optical parametric oscillator," Phys. Rev. A 50, 2627-2641 (1994). [CrossRef] [PubMed]
- C. Y. Zhao, W. H. Tan, and Q. Z. Guo, "The solution of the Fokker-Planck equation of non-degenerate parametric amplification system for generation of squeezed light," Acta Phys. Sin. 52, 2694-2699 (2003) (in Chinese).
- S. Chaturvedi, K. Dechoum, and P. D. Drummond, "Limits to squeezing in the degenerate optical parametric oscillator," Phys. Rev. A 65, 033805 (2002). [CrossRef]
- P. D. Drummond, K. Dechoum, and S. Chaturvedi, "Critical quantum fluctuations in the degenerate parametric oscillator," Phys. Rev. A 65, 033806 (2002). [CrossRef]
- B. C. dos Santos, K. Dechoum, A. Z. Khoury, L.F. da Silva, and M. K. Olsen, "Quantum analysis of the non-degenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005). [CrossRef]
- G. E. Uhlenbeck and L. S. Ornstein, "On the theory of the Brownian motion," Phys. Rev. 36, 823-841 (1930). [CrossRef]
- C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, 1983).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.