Effects of counter-rotating couplings of the Rabi model with frequency modulation
Effects of counter-rotating couplings of the Rabi model with frequency modulation
复制标题
调频拉比模型反向旋转耦合的影响
DOI：
10.1103/physreva.96.033802
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发表时间：
2017-09
影响因子：
2.9
通讯作者：
Zheng Hang
中科院分区：
文献类型：
--
作者：
Yan Yiying;Lü Zhiguo;Luo JunYan;Zheng Hang
我们从理论上研究了具有频率调制的Rabi模型的动力学和共振位移，即，采用反向旋转-杂化双折射波（CHRW）方法，研究了外加慢纵场驱动的Rabi模型，旨在说明横向场的反向旋转（CR）项的影响. CHRW方法是基于一个酉变换，并减少了非周期性的哈密尔顿到一个有效的周期哈密尔顿，可以有效地处理Floquet理论。有效的哈密顿量和广泛使用的行波近似（RWA）哈密顿量的有效性进行了仔细检查相比，在很宽的参数范围内的数值精确的结果。结果表明，有效哈密顿量给出了正确的描述，而RWA在强驱动区发生了故障。有趣的是，我们表明，在某些条件下的纵向场可以用来修改共振宽度，使共振宽度可以与布洛赫Siegert（BS）移位的幅度，这反过来又使CR引起的BS移位显着，并导致完全击穿的RWA，即使在一个中等强度的驱动制度（其中RWA持有的拉比模型没有频率调制）。此外，通过使用有效哈密顿量，我们可以有效地访问双色驱动量子比特的共振位置，并研究由于CR项和频率调制的组合效应，共振如何移位。对于一个弱的纵向场，我们表明，共振位置可以解析计算的有效拉比频率的有效哈密顿量，这是非常符合数值精确的结果。
We theoretically study the dynamics and resonance shift of the Rabi model with frequency modulation, i.e., the Rabi model driven additionally by a slow longitudinal field, by using the counterrotating-hybridized rotating-wave (CHRW) method, aiming to illustrate the effects of the counterrotating (CR) terms of the transverse field. The CHRW method is based on a unitary transformation and reduces the aperiodic Hamiltonian to an effective periodic Hamiltonian that can be efficiently treated by Floquet theory. The validity of the effective Hamiltonian and widely used rotating-wave approximation (RWA) Hamiltonian is carefully examined compared to the numerically exact results over a wide parameter range. It is found that the effective Hamiltonian gives a correct description, while the RWA breaks down in the strong driving regime. Interestingly, we show that under certain conditions the longitudinal field can be used to modify resonance widths such that resonance widths can be comparable to the magnitude of the Bloch-Siegert (BS) shift, which in turn makes the CR-induced BS shift significant and leads to the complete breakdown of the RWA even in a moderately strong driving regime (in which the RWA holds for the Rabi model without frequency modulation). In addition, by using the effective Hamiltonian, we can efficiently access resonance positions for the bichromatically driven qubit and study how the resonance shifts due to the combined effects of the CR terms and frequency modulation. For a weak longitudinal field, we show that resonance positions can be analytically calculated from the effective Rabi frequency for the effective Hamiltonian, which are in excellent agreement with the numerically exact results.