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Invariants and Schrödinger Uncertainty Relation for Nonclassical Light

  • V. I. Man’ko
Chapter

Abstract

The aim of this work is to discuss integrals of the motion and uncertainty relations and to obtain the distribution function of photons in squeezed and correlated light for the multimode case. The distribution function of photons in squeezed light for one mode field was discussed by Schleich and Wheeler,1 by Agarwal and Adam,2 and by Chaturvedi and Srinivasan.3 The photon distribution function for squeezed and correlated light4,5 was discussed by Dodonov, Klimov and Man’ko.6 This distribution function depends not only on squeezing parameters, but also on correlation parameters connected with the Schrödinger uncertainty relation7
$$\delta q\delta p \ge \frac{\hbar }{2}\frac{1}{{\sqrt {1 - {r^2}} }},$$
, where the parameter r is the correlation coefficient of the position and momentum
$$r = {(\delta q\delta p)^{ - 1}}\left\{ {\frac{1}{2}\langle \hat q\hat p + \hat p\hat q\rangle - \langle \hat q\rangle \langle \hat p\rangle } \right\}.$$
.

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References

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Copyright information

© Plenum Press, New York 1993

Authors and Affiliations

  • V. I. Man’ko
    • 1
  1. 1.Levedev Physics InstituteMoscowRussia

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