Kyoko Higashida

Quantum Diagonalization Method in the Tavis-Cummings Model

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.

EXPLICIT FORM OF THE EVOLUTION OPERATOR OF TAVIS-CUMMINGS MODEL: THREE AND FOUR ATOMS CASES

In this letter the explicit form of the evolution operator of the Tavis–Cummings model with three and four atoms is given. This is an important progress in quantum optics or mathematical physics.