Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

Xue-Ying Liu,Xue-Zao Ren,Chen Wang,Xian-Long Gao,Ke-Lin Wang

Figure 2. Evolution of (a) mean photon number $\langle \hat{n}\rangle $ and (b) atomic inversion $\langle {\hat{\sigma }}_{z}\rangle $ in the RWA-void BS model. The initial state is a vacuum $| t=0\rangle =| 0,e\rangle $ corresponding to $\alpha =0$ and θ = π/2 in equation (17) (meaning that no photons are excited at t = 0). Other parameters are ωf = 1 , ω0 = 3/4ωf and ${g}_{-}={g}_{+}=0.4{\omega }_{f}$. The results of equations (11)–(15) (black line) and the TEEE method (blue points) are plotted for comparison.