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
Externally publishedYes

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differential geometry
operators
physics
ambiguity
matrices
atoms

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Quantum diagonalization method in the Tavis-Commings model. / Fujii, Kazuyuki; Higashida, Kyoko; Kato, Ryosuke; Suzuki, Tatsuo; Wada, Yukako.

In: International Journal of Geometric Methods in Modern Physics, Vol. 2, No. 3, 06.2005, p. 425-440.

Research output: Contribution to journalArticle

Fujii, Kazuyuki ; Higashida, Kyoko ; Kato, Ryosuke ; Suzuki, Tatsuo ; Wada, Yukako. / Quantum diagonalization method in the Tavis-Commings model. In: International Journal of Geometric Methods in Modern Physics. 2005 ; Vol. 2, No. 3. pp. 425-440.
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