Geometric phase and non-adiabatic resonance of the Rabi model
Geometric phase and non-adiabatic resonance of the Rabi model
复制标题
拉比模型的几何相位和非绝热共振
DOI：
10.1088/1751-8121/ac2a04
复制
发表时间：
2021-11-05
影响因子：
2.1
通讯作者：
Zheng, Hang
中科院分区：
文献类型：
--
作者：
Liu, Sijiang;Lu, Zhiguo;Zheng, Hang
我们研究了反向旋转项对几何相位的影响及其与Rabi模型共振的关系。我们将单参数幺正变换应用于Rabi模型，得到了包含多个调和项的变换后的哈密顿量。将反转杂化双折射波方法与含时微扰理论相结合，系统地求解了时间演化算符，得到了二能级系统的几何相位。我们的结果超越了绝热近似和行波近似。当驱动频率等于拉比频率的高次谐波时，发生高次谐波共振。与数值精确结果相比，我们的计算结果在很宽的参数空间范围内都是精确的，特别是在高次谐波共振区域。在这些制度中，我们证明几何相位变化显着，而那些RWA是光滑的。即使驱动力非常弱，RWA也完全无效。我们发现高次谐波项对循环态起着重要的作用，并揭示了高次谐波共振区几何相位的特征。我们还提出了几何相位和准能的变化率的解析形式，即使在强驱动的情况下，也与数值精确的一致。所开发的方法可用于探索强驱动量子比特的动力学和高阶谐波过程的物理性质。
We investigate the effects of counterrotating terms on geometric phase and its relation to the resonance of the Rabi model. We apply the unitary transformation with a single parameter to the Rabi model and obtain the transformed Hamiltonian involving multiple harmonic terms. By combining the counter-rotating-hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically time evolution operator and then obtain the geometric phase of the two-level system. Our results are beyond adiabatic approximation and rotating-wave approximation (RWA). Higher-order harmonic resonance happens when driving frequency is equal to higher-order subharmonic of the Rabi frequency. In comparison with numerically exact results, our calculated results are accurate over a wide range of parameters space, especially in higher-order harmonic resonance regimes. In these regimes we demonstrate geometric phases change dramatically while those of the RWA are smooth. The RWA is thoroughly invalid even if the driving strength is extremely weak. We find it is the higher-order harmonic terms that play an important role on the cyclic state and demonstrate the characters of geometric phase in higher-order harmonic resonance regime. We also present analytical formalism of the change rate of geometric phase and quasienergies, which agree well with numerically exact ones even in the strong driving case. The developed method can be applied to explore the dynamics of strongly driven qubits and physical properties of higher-order harmonic processes.