arXiv 1208.57362012-08-22quant-phcond-mat.mes-hallcond-mat.mtrl-sciphysics.atom-phphysics.optics

关于Bloch方程的非正统解

On unorthodox solutions of the Bloch equations

Alexander Moroz

备注：: 26 pages comprising 4 figures

摘要：

对时谐驱动经典光场中的布洛赫方程进行了系统、严格、全面的研究。我们的处理是独特的，因为它充分利用实数域上的部分分式分解，这使得有可能找到和分类的所有解析解。Torrey以指数阻尼谐波振荡形式的解析解[Phys. Rev. { \bf 76}，1059（1949）]被发现在参数空间中占主导地位，这证明了它在原子、分子和量子点的磁共振和量子光学中的许多场合的使用。布洛赫方程的非正统解不具有指数阻尼谐波振荡的形式，仅限于相当小的失谐$δ^2\lesssim (γ-γ_t)^2/27$和小的场强$Ω^2\lesssim 8 (γ-γ_t)^2/27$，其中$γ$和$γ_t$分别描述激发态的衰减速率（总布居弛豫速率）和相干性。非正统的解决方案是很容易获得实验的特点是相当无特征的时间依赖性。

英文摘要：

A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number field, which makes it possible to find and classify all analytic solutions. Torrey's analytic solution in the form of exponentially damped harmonic oscillations [Phys. Rev. {\bf 76}, 1059 (1949)] is found to dominate the parameter space, which justifies its use at numerous occasions in magnetic resonance and in quantum optics of atoms, molecules, and quantum dots. The unorthodox solutions of the Bloch equations, which do not have the form of exponentially damped harmonic oscillations, are confined to rather small detunings $δ^2\lesssim (γ-γ_t)^2/27$ and small field strengths $Ω^2\lesssim 8 (γ-γ_t)^2/27$, where $γ$ and $γ_t$ describe decay rates of the excited state (the total population relaxation rate) and of the coherence, respectively. The unorthodox solutions being readily accessible experimentally are characterized by rather featureless time dependence.

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