arXiv subjects
Publications and source records attributed to Kyoko Higashida.
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 Schr{\" o}dinger 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 five level systems.
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 Schr{\" o}dinger equation of the model in the weak coupling regime to construct the controlled NOT gate in the case of n=2, and to construct the controlled-controlled NOT gate in the case of n=3 by making use of several resonance conditions and rotating wave approximation associated to them. We also present an idea to construct general quantum circuits. The approach is more sophisticated than that of the paper [K. Fujii, Higashida, Kato and Wada, Cavity QED and Quantum Computation in the Weak Coupling Regime, J. Opt. B : Quantum Semiclass. Opt. {\bf 6} (2004), 502]. Our method is not heuristic but completely mathematical, and the significant feature is based on a consistent use of Rabi oscillations.
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger}$ 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.
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 Schr{\" o}dinger equation of the model in the case of n=2 and construct the controlled NOT gate by making use of a resonance condition and rotating wave approximation associated to it. Our method is not heuristic but completely mathematical, and the significant feature is a consistent use of Rabi oscillations. We also present an idea of the construction of three controlled NOT gates in the case of n=3 which gives the controlled-controlled NOT gate.
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.
In this letter the explicit form of evolution operator for the four atoms Tavis-Cummings model is given.
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.
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 NOT operation (gate) in quantum computation.
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 case and examine it in detail in the case of three level system.