λ型和V型三能级系统场模量子化的动力学对称破缺
Dynamical symmetry breaking of lambda and vee-type three-level systems on quantization of the field modes
摘要：
本文发展了一种利用SU（3）群生成元构造λ型、vee型和级联型三能级组态哈密顿量的方法。事实证明，这种方法提供了一个定义良好的选择规则，为每个配置提供不同的哈密顿。分别采用双模经典场和量子化场，在不同的初始条件下精确求解了λ型和V型组态。对于经典场，λ模型的Rabi振荡与Vee模型的Rabi振荡相似，Vee模型的动力学特性可以通过简单的反演从λ模型中恢复，反之亦然。然后，我们着手解决这两个模型的量化版本，引入一种新的欧拉矩阵形式主义。结果表明，这种动力学对称性表现在拉比振荡的两个配置的半经典模型是完全破坏的量子化的场模式。当两个场模都处于平均光子数较大的相干态时，量子化模型中的对称性可以通过拉比振荡的坍缩和恢复得到恢复。
英文摘要：
We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give different Hamitonians for each configurations. The lambda and vee type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields . For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when the field modes are both in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.
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