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Explicit Form of the Evolution Operator of Tavis-Cummings Model: Three and Four Atoms Cases

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +2 more

In this letter the explicit form of 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. The purpose of this paper is to give an explicit form to the evolution operator of Tavis–Cummings model ([1]) with some atoms. This model is a very important one in Quantum Optics and has been studied widely, see [2] as general textbooks in quantum optics. We are studying a quantum computation and therefore want to study the model from this point of view, namely a quantum computation based on atoms of laser–cooled and trapped linearly in a cavity. We must in this model construct the controlled NOT gate or other controlled unitary gates to perform a quantum computation, see [3] as a general introduction to this subject. For that aim we need the explicit form of evolution operator of the models with one, two, three and four atoms (at least). As to the model of one atom or two atoms it is more or less known (see [4]), while as to the case of three and four atoms it has not been given as far as we know. Since we succeeded in finding the explicit form for three and four atoms cases we report it ([5]).In this letter the explicit form of 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. The purpose of this paper is to give an explicit form to the evolution operator of Tavis–Cummings model ([1]) with some atoms. This model is a very important one in Quantum Optics and has been studied widely, see [2] as general textbooks in quantum optics. We are studying a quantum computation and therefore want to study the model from this point of view, namely a quantum computation based on atoms of laser–cooled and trapped linearly in a cavity. We must in this model construct the controlled NOT gate or other controlled unitary gates to perform a quantum computation, see [3] as a general introduction to this subject. For that aim we need the explicit form of evolution operator of the models with one, two, three and four atoms (at least). As to the model of one atom or two atoms it is more or less known (see [4]), while as to the case of three and four atoms it has not been given as far as we know. Since we succeeded in finding the explicit form for three and four atoms cases we report it ([5]).

Jan 1, 20043 citations

Explicit Form of the Evolution Operator for the Four Atoms Tavis-Cummings Model

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +2 more

In this letter the explicit form of evolution operator for the four atoms Tavis-Cummings model is given.

arXiv:quant-ph/0406184Jun 25, 20041 citation

Explicit Form of Evolution Operator of Three Atoms Tavis-Cummings Model

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +2 more

In this letter the explicit form of evolution operator of three atoms Tavis-Cummings model is given, which is a generalization of the paper quant-ph/0403008.

arXiv:quant-ph/0404034Apr 6, 20044 citations

The Evolution Operator of The Three Atoms Tavis-Cummings Model

Cai Jin-Fang

The explicit form of evolution operator of the three atoms Tavis-Cummings Model is given.

arXiv:quant-ph/0405176May 28, 20040 citations

QUANTUM DIAGONALIZATION METHOD IN THE TAVIS–CUMMINGS MODEL

KAZUYUKI FUJII, KYOKO HIGASHIDA, RYOSUKE KATO +2 more

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.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.

arXiv:quant-ph/0410003International Journal of Geometric Methods in Modern PhysicsJun 1, 20053 citations

Explicit form of the evolution operator for the Tavis-Cummings model and quantum diagonalization method (力学系と微分幾何学研究集会報告集)

達夫鈴木

数理解析研究所講究録Dec 1, 20040 citations

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

Abstract

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

Abstract

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