OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 10, Iss. 11 — Nov. 1, 1993
  • pp: 2100–2106

Analytical solution to the master equation for a quantized cavity mode

A. Mufti, H. A. Schmitt, A. B. Balantekin, and M. Sargent, III  »View Author Affiliations


JOSA B, Vol. 10, Issue 11, pp. 2100-2106 (1993)
http://dx.doi.org/10.1364/JOSAB.10.002100


View Full Text Article

Enhanced HTML    Acrobat PDF (698 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We solve analytically the master equation for a quantized cavity mode, finding the time-dependent reduced density operator. The formalism applies to both amplifiers and attenuator, permitting the results to be converted between them by introducing a temperature that can be negative. We obtain a quasi-probability distribution function similar to that obtained by Glauber [ GlauberR. J., ed., Quantum Optics ( Academic, New York, 1969)] from our reduced density matrix and equate his parameters with the coefficients appearing in the master equation. We illustrate the formalism by calculating variances, expectation values, and photon statistics for the damped simple harmonic oscillator and the linear amplifier.

© 1993 Optical Society of America

History
Original Manuscript: December 30, 1992
Revised Manuscript: May 28, 1993
Published: November 1, 1993

Citation
A. Mufti, H. A. Schmitt, A. B. Balantekin, and M. Sargent, "Analytical solution to the master equation for a quantized cavity mode," J. Opt. Soc. Am. B 10, 2100-2106 (1993)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-10-11-2100


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. N. S. Goel, N. Richter-Dyn, Stochastic Models in Biology (Academic, New York, 1974).
  2. A. Ben-Shaul, Y. Haas, K. L. Kompa, R. D. Levine, Lasers and Chemical Change (Springer-Verlag, Berlin, 1981). [CrossRef]
  3. M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1977).
  4. V. Weisskopf, E. Wigner, Z. Phys. 63, 54 (1930). [CrossRef]
  5. P. Meystre, M. Sargent, Elements of Quantum Optics (Springer-Verlag, Berlin, 1990). [CrossRef]
  6. R. J. Glauber, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Adam Hilger, Bristol, Mass., 1986).
  7. R. J. Glauber, in Quantum Optics, Proceedings of the International School of Physics, “Enrico Fermi,” Course XLII, R. J. Glauber, ed. (Academic, New York, 1969).
  8. M. Sargent, D. A. Holm, M. S. Zubairy, Phys. Rev. A 31, 3112 (1985); D. A. Holm, M. Sargent, S. Stenholm, J. Opt. Soc. Am. B 2, 1456 (1985). [CrossRef]
  9. B. R. Mollow, R. J. Glauber, Phys. Rev. 160, 1076 (1967). [CrossRef]
  10. A. B. Balantekin, N. Takigawa, Ann. Phys. (N.Y.) 160, 441 (1985). [CrossRef]
  11. R. Gilmore, J. M. Yuan, J. Chem. Phys. 86, 130 (1987). [CrossRef]
  12. F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, Phys. Rev. A 6, 2211 (1972), use matrix representations to discuss Baker–Campbell–Hausdorf relations for the group SU(5). [CrossRef]
  13. R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications (Wiley, New York, 1974); K. T. Hecht, The Vector Coherent State Method and Its Application to Problems of Higher Symmetry (Springer-Verlag, Berlin, 1987).
  14. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, San Diego, 1980).
  15. D. R. Truax, Phys. Rev. D 31, 1988 (1985). [CrossRef]
  16. K. E. Cahill, R. J. Glauber, Phys. Rev. 177, 1857 (1969); Phys. Rev. 177, 1882 (1969). [CrossRef]
  17. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973). See especially Section 6.5.
  18. J. E. Campbell, Proc. London Math. Soc. 28, 381 (1897); H. F. Baker, Proc. London Math. Soc. 34, 347 (1902); F. Hausdorff, Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. K1. 58, 19 (1906).
  19. T. Schoendorff, H. Risken, Phys. Rev. A 41, 5147 (1990). [CrossRef] [PubMed]

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.

CrossCheck Deposited