Squeezed States of Light

  • Pierre Meystre
  • Murray SargentIII


The Heisenberg uncertainty principle \( \Delta A\Delta B \geqslant \frac{1} {2}\left| {\left\langle {\left[ {A,B} \right]} \right\rangle } \right| \) between the standard deviations of two arbitrary observables, ΔA = 〈(A - (A))21/2 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
$$ \Delta x\Delta p \geqslant \hbar /2 $$
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 than the product be bounded from below. As discussed in Sect. 13.1, the electric and magnetic fields form a pair of observables analogous to the position and momentum of a simple harmonic oscillator. Accordingly, they obey a similar uncertainty relation
$$ \Delta E\Delta B \geqslant \left( {{\text{constant}}} \right)\hbar /2 $$


Coherent State Master Equation Bloch Equation Phase Conjugation Minimum Uncertainty 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Pierre Meystre
    • 1
  • Murray SargentIII
    • 2
  1. 1.Optical Science CenterUniversity of ArizonaTucsonUSA
  2. 2.Microsoft CorporationRedmontUSA

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