Abstract We consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

中文翻译：

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椭圆极化的拉比问题

摘要 我们考虑经典/量子自旋在单色椭圆极化外场下的运动方程的解。经典的 Rabi 问题可以简化为具有多项式系数的三阶微分方程，因此可以根据幂级数进行求解，这与线性极化发生的合流 Heun 方程非常相似。Floquet 理论的应用产生了一些有趣的物理量，例如作为问题参数和共振频率的 Bloch-Siegert 位移表达式的函数的准能量。对各种极限情况进行了彻底调查。