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arXiv quant-ph/0203135quant-phhep-thmath-phmath.MP
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强耦合区域Rabi振荡的数学结构

Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime

Kazuyuki Fujii

摘要:

本文利用基于李代数su(1,1)和su(2)的算子推广了Jaynes-Cummings哈密顿量,并研究了强耦合下这些模型Rabi flopping的数学结构.我们表明,拉比频率的广义相干算子(quant-ph/0202081)的旋转波近似下的矩阵元素。前半部分我们对基于李代数su(1,1)和su(2)的凝聚算子和广义凝聚算子作了一个综述。在后半部分,我们进行了详细的检查Frasca(quant-ph/0111134)和推广他的方法,并提出了一些相关的问题。我们也将我们的结果应用于量子计算中的受控酉门的构造。最后对完整量子计算的应用作了简要的评述。

英文摘要:

In this paper we generalize the Jaynes--Cummings Hamiltonian by making use of some operators based on Lie algebras su(1,1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (quant--ph/0202081) under the rotating--wave approximation. In the first half we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1,1) and su(2). In the latter half we carry out a detailed examination of Frasca (quant--ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in Quantum Computation. Lastly we make a brief comment on application to Holonomic Quantum Computation.

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