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Quantum diagonalization method in the Tavis-Cfilengs model

Oct, 2004
21 pages
Published in:
  • Int.J.Geom.Meth.Mod.Phys. 2 (2005) 425-440
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Abstract:
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term e−itg(S+⊗a+S−⊗a†){e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})} explicitly which is very hard. In this paper we try to make the quantum matrix A≡S+⊗a+S−⊗a†A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger} diagonal to calculate e−itgA{e}^{-itgA} and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of e−itgA{e}^{-itgA} given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.
Note:
  • Latex files, 21 pages; minor changes. To appear in International Journal of Geometric Methods in Modern Physics
  • Quantum diagonalization
  • Tavis-Cummings model
  • evolution operator
  • non-commutativity