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Squeezed States of Light

  • Pierre Meystre
  • Murray SargentIII

Abstract

The Heisenberg uncertainty principle ΔAΔB\(\frac{1}{2}\)> |<[A,B]>| 1 between the standard deviations of two arbitrary observables, ΔA = <(A- <A>)2>1/2 and similarly for ΔB, has a built-in degree of freedom: one can squeeze the standard deviation of one observable provided one “stretches” that for the conjugate observable. For example the position and momentum standard deviations obey the uncertainty relation
$$\Delta x\Delta p \geqslant \hbar /2$$
(1)
and we can squeeze Δx to an arbitrarily small value at the expense of accordingly increasing the standard deviation Δp. All quantum mechanics requires is that the product be bounded from below. As discussed in Sec. 12-1, the electric and magnetic fields from a pair of observables analogous to the position and momentum of a simple harmonic oscillator. Accordingly they obey a similar uncertainty relation
$$\Delta E\Delta B \geqslant (cons\tan t)\hbar /2$$
(2)

Keywords

Coherent State Master Equation Phase Conjugation Vacuum Mode Minimum Uncertainty 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. An, S. and M. Sargent III (1989), Phys. Rev. A40, 7039.Google Scholar
  2. Cohen-Tannoudji, C., J. Dupont-Roc, and G. Grynberg (1988), Processus d’interaction entre photons et atomes, InterEditions et Editions du CNRS, Paris give a clear tutorial discussion of squeezing. English edition to be published by John Wiley, New York.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Pierre Meystre
    • 1
  • Murray SargentIII
    • 1
  1. 1.Optical Sciences CenterUniversity of ArizonaTucsonUSA

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