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In this paper we consider a model of quantum computation based on n atoms of laser–cooled and trapped linearly in a cavity and realize it as the n atoms Tavis– Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schrödinger equation of the model in the case of n=2 and construct the controlled NOT gate by making use of a resonance… (More)

In this paper we treat a cavity QED quantum computation. Namely, we consider a model of quantum computation based on n atoms of laser–cooled and trapped linearly in a cavity and realize it as the n atoms Tavis–Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schrödinger equation of the model in the weak coupling regime to… (More)

In this paper we consider a model of an atom with n energy levels interacting with n(n-1)/2 external (laser) fields which is a natural extension of two level system, and assume the rotating wave approximation (RWA) from the beginning. We revisit some construction of analytical solutions (which correspond to Rabi oscillations) of the model in the general… (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… (More)

In this paper we consider a general model of an atom with n energy levels interacting with n–1 external (laser) fields which is a natural extension in the two and three level systems. We exactly solve the Schrödinger equation to obtain a Rabi oscillation when n = 4 and 5, which will constitute a quantum logic gate of Quantum Computation based on four and… (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… (More)

In this paper we consider the two atoms Tavis–Cummings model and give an explicit form to the solution of this model which will play a central role in quantum computation based on atoms of laser–cooled and trapped linearly in a cavity. We also present a problem of three atoms Tavis–Cummings model which is related to the construction of controlled–controlled… (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. The purpose of this letter 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… (More)

In this letter the explicit form of evolution operator for the four atoms Tavis– Cummings model is given. This paper is a sequel to the papers [1] and the purpose is to give an explicit form to the evolution operator of Tavis–Cummings model ([2]) with four atoms. This model is a very important one in Quantum Optics and has been studied widely, see [3] as… (More)

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