OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 4, Iss. 10 — Oct. 1, 1987
  • pp: 1621–1626

Space–time description of squeezing

Zofia Bialynicka-Birula and Iwo Bialynicki-Birula  »View Author Affiliations

JOSA B, Vol. 4, Issue 10, pp. 1621-1626 (1987)

View Full Text Article

Enhanced HTML    Acrobat PDF (744 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a field-theoretical description of the squeezed states of the electromagnetic field. A definition of the squeezed state is introduced that is a natural generalization of the definition for one or two modes. We show that the squeezing produced by the medium with space- and time-dependent material coefficients and μ is directly related to the photon-pair production. In Appendix A we describe the time evolution of the Gaussian squeezed states in terms of the field variables.

© 1987 Optical Society of America

Original Manuscript: February 5, 1987
Manuscript Accepted: June 16, 1987
Published: October 1, 1987

Zofia Bialynicka-Birula and Iwo Bialynicki-Birula, "Space–time description of squeezing," J. Opt. Soc. Am. B 4, 1621-1626 (1987)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. I. Bialynicki-Birula, “Beyond the coherent states: Gaussons of the electromagnetic field,” in Coherence, Cooperation and Fluctuations, F. Haake, L. M. Narducci, D. Walls, eds. (Cambridge U. Press, Cambridge, 1986), pp. 159–170.
  2. B. L. Schumaker, “Quantum mechanical pure states with Gaussian wave functions,” Phys. Rep. 135, 317–408 (1986). [CrossRef]
  3. D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983). [CrossRef]
  4. The fact that the D field and not the E field is the canonically conjugate momentum was previously recognized by M. Born and L. Infeld in their study of nonlinear electrodynamics [M. Born, L. Infeld, “On the quantization of the new field equations I,” Proc. R. Soc. London Ser. A 147, 522–546 (1934); “On the quantization of the new field equations II,” Proc. R. Soc. London Ser. A 150, 141–166 (1935)]. Cf. also I. Bialynicki-Birula, Z. Bialynicka-Birula, Quantum Electrodynamics (Pergamon, Oxford, 1975). [CrossRef]
  5. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), pp. 158–161.
  6. H. A. Kramers, Quantum Mechanics (North-Holland, Amsterdam, 1957), pp. 418–441.
  7. There is a systematic error in Ref. 1 where these equations were derived; viz., the imaginary unit i should be replaced by −i everywhere.

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