We investigate the dynamics of a driven two-level system (semi-classical Rabi model) using the counter-rotating-hybridized rotating-wave method (CHRW), which is a simple method based on a unitary transformation . After comparing the results of different RWA schemes and those of the numerically exact method in a wide range of parameter regime, we show that the CHRW method gives the accurate driven dynamics which is in good agreement with the numerical method[1-2]. The CHRW method reveals the effects of the CR terms clearly by means of coherent destruction of tunneling, Bloch-Siegert (BS) shift，and fluorescence spectrum. In quantitative comparison with the numerically exact BS shift obtained by Floquet formalism as well as the previous BS results, we confirm that our calculated results are not only accurate in the weak-driving regime but also correct in the strong-driving limit. In the intermediate strong-driving regime, the calculated values of the BS shift are nearly the same as the exact ones. It turns out that our calculation for the BS shift is beyond perturbation. Meanwhile, we demonstrate the signatures caused by the BS shift by monitoring the excited-state population and the probe-pump spectrum under the experiment accessible conditions [3-4].
【1】 Zhiguo Lü, and Hang Zheng, Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift, Phys. Rev. A86, 023831(2012).
【2】Zhiguo Lü, Yiying Yan, Hsi-Sheng Goan and Hang Zheng, Bias-modulated dynamics of a strongly driven two-level system, Phys. Rev. A93, 033803(2016).
【3】Y. Yan, Zhiguo Lü, and H. Zheng, Bloch-Siegert shift of the Rabi model, Phys. Rev. A91, 053834(2015).
【4】Y. Yan, Zhiguo Lü, and H. Zheng, Effects of counter-rotating-wave terms of the driving field on the spectrum of resona