Quantum Diagonalization Method in the Tavis-Cummings Model

Abstract

To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term $e^{-itg(S_{+}\otimes a+S_{-}\otimes a^{†})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{†}$ 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 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 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.

Latex files, 21 pages; minor changes. To appear in International Journal of Geometric Methods in Modern Physics

References in corpus (1)

• A New Symmetric Expression of Weyl Ordering

Cited by in corpus (1)

• Standard and Non-Standard Quantum Models : A Non-Commutative Version of the Classical System of SU(2) and SU(1,1) Arising from Quantum Optics