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Atomic Coherent States in Quantum Optics

  • F. T. Arecchi
  • E. Courtens
  • R. Gilmore
  • H. Thomas
Conference paper

Abstract

The central problem of Quantum Optics (laser theory, super-radiance, resonant propagation, etc.) is the description of the interaction between N atoms and an electromagnetic field confined in a cavity of finite volume. A suitable model Hamiltonian for this problem is the following one (ℏ = 1)
$$\begin{array}{*{20}{l}} {{\rm{H = }}\sum\limits_{\rm{k}} {{{\rm{\omega }}_{\rm{k}}}} {\rm{a}}_{\rm{k}}^{\rm{ + }}{{\rm{a}}_{\rm{k}}}{\rm{ + }}\frac{{{{\rm{\omega }}_{\rm{o}}}}}{{\rm{2}}}\sum\limits_{{\rm{i = 1}}}^{\rm{N}} {{{\rm{S}}_{{\rm{3}}\left( {\rm{i}} \right)}}} }\\ {{\rm{ + }}\sum\limits_{{\rm{k,i}}} {{{\rm{g}}_{\rm{k}}}\left( {{{\rm{a}}_{\rm{k}}}{\rm{S}}_{\rm{i}}^{\rm{ + }}{{\rm{e}}^{{\rm{i \bullet }}{{{\rm{}}}_{\rm{i}}}}}{\rm{ + a}}_{\rm{k}}^{\rm{ + }}{\rm{S}}_{\rm{i}}^{\rm{ - }}{{\rm{e}}^{{\rm{ - i \bullet }}{{{\rm{}}}_{\rm{i}}}}}} \right)} {\rm{,}}} \end{array}$$
where ak, a k + are Bose operators describing the k-th field mode and S i ± ,S3i are Pauli operators describing the atom located at position x i as a two-level system.

Keywords

Irreducible Representation Coherent State Commutation Relation Invariant Subspace Coset Representative 
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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Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • F. T. Arecchi
    • 1
  • E. Courtens
    • 2
  • R. Gilmore
    • 3
  • H. Thomas
    • 4
  1. 1.Università di Pavia & Laboratori C.I.S.E.MilanoItaly
  2. 2.IBM Research LaboratoryZürichSwitzerland
  3. 3.Massachusetts Institute of TechnologyCambridgeUSA
  4. 4.J. W. Goethe UniversitätFrankfurtGermany

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