Quantum diagonalization method in the Tavis-Commings model

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato, Tatsuo Suzuki, Yukako Wada

Research output: Contribution to journalArticle

3 Citations (Scopus)

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†) explicitly which is very hard. In this paper we try to make the quantum matrix A ≡ S+⊗a+S-⊗a diagonal to calculate 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 the first nontrivial examples as far as we know, and reproduce the calculations of e-itgA given in quant-ph/0404034. We also give a hint to an application to non-commutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the non-commutativity of operators in quantum physics. Our method may open a new point of view in mathematical or quantum physics.

Original languageEnglish
Pages (from-to)425-440
Number of pages16
JournalInternational Journal of Geometric Methods in Modern Physics
Volume2
Issue number3
DOIs
Publication statusPublished - 2005 Jun 1

Keywords

  • Evolution operator
  • Non-commutativity
  • Quantum diagonalization
  • Tavis-Cummings model

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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