## 2 Interaction of Light and Medium  
In consideration of the result of [PERSON] et al. [31], the laser-induced Rashba effect is treated as an effective magnetic field. As shown in Figure 1, the sub-bands \(\mid\)1\(>\) and \(\mid\)3\(>\) split by the effective field and the virtual state \(\mid\)2\(>\) constitute the \(\Lambda\) three-level system. For the femtosecond laser, the monochromaticity is relatively poor. \(\omega_{\text{e}}\) and \(\omega_{\text{r}}\) correspond to different wavelengths included in the femtosecond laser. \(\Delta_{\text{e}}\) (\(\Delta_{\text{r}}\)) is the mismatch of the energy of the incident photos, \(\omega_{\text{e}}\) (\(\omega_{\text{r}}\)), and the energy gap between \(\mid\)1\(>\) and \(\mid\)2\(>\), \(\omega_{12}\) (\(\mid\)3\(>\) and \(\mid\)2\(>\), \(\omega_{23}\)). The dynamics of electrons shown in Figure 1 describe the process of SRS [36,37]. Electrons are originally steady at state \(\mid\)1\(>\) with spin-up. After the incidence of laser, electrons are stimulated to virtual state \(\mid\)2\(>\). Meanwhile, the incident laser, including the frequency \(\omega_{\rm r}\) that is approximate to \(\omega_{\rm 23}\), stimulates electrons radiating to state \(\mid\)3\(>\). Therefore, SRS transfers electrons between different energy bands; the Rashba effect-induced effective field gives states \(\mid\)1\(>\) and \(\mid\)13\(>\) with specific spin states. More importantly, the effective field does not only maintain the quasi-stationary state, but also break the transition forbidden for spin-flip. We are going to use the Rabi model to describe the process of SRS instead of the form of nonlinear polarization, because the distribution of laser in the spatial domain is neglected. However, in the framework of the Rabi model without decay, electrons will remain on the virtual state, because of the sudden stop of the laser. Therefore, we investigate the transition in a three-level system by the Lindblad equation, which is easy to describe how a density operator evolves in an open system with decay. Diagonal elements of the density matrix represent the probability of electrons occupying the state:  
\[\dot{\rho}=-{\rm i}[H,\rho]+{\rm L}_{(\rho)} \tag{1}\]  
\[{\rm L}_{(\rho)}=C\rho C^{*}-\frac{1}{2}(C^{*}C\rho+\rho C^{*}C) \tag{2}\]  
where the first term of the right-hand side of Equation (1) is the Liouville-von Neumann equation [33], describing the unitary evolution of the density operator; \(\rho\) is the density matrix of the three-level system and \(\dot{\rho}\) represents the elements of density matrix take a derivative of time; H is a 3 \(\times\) 3 matrix expression of Hamiltonian and the elements of the matrix are written as \(\omega_{\rm nm}\); C describes the decay of electrons to ground state; C\({}^{*}\) is the transpose of C. We choose specific time-dependent phases to simplify the diagonal elements of H, and define the elements as:  
\[ \begin{array}{c}W_{11}=0,\ W_{22}=\hbar\Delta_{1}=\hbar\Delta_{e},\\ W_{33}=\hbar\Delta_{2}=\hbar(\Delta_{e}-\Delta_{r})\end{array}  \tag{3}\]  
\[\Delta_{e}=\omega_{12}-\omega_{\rm e},\ \Delta_{r}=\omega_{23}-\omega_{\rm r} \tag{4}\]  
where \(\omega_{12}\) and \(\omega_{23}\) are the angular frequencies corresponding to the difference of energy of states \(\mid\)2\(>\), 1\(>\) and \(\mid\)2\(>\), 1\(>\)3\(>\), respectively; \(\omega_{\rm e}\) and \(\omega_{\rm r}\) are the angular frequencies of incident femtosecond laser. The off-diagonal elements of interaction Hamiltonian is considered as electric dipole transitions, \({\rm d}_{\rm nm}\), for which an atomic dipole moment is affected by a classical electric field, \({\rm E}_{\rm nm}\)(t). \({\rm E}_{\rm nm}\)(t) is the  
Figure 1: The schematic diagram of a \(\Lambda\) three-level system. The ground state is split into two fine energy bands, caused by the Rashba effect, in the ming blue background. 1\(>\) and 1\(>\) are spin-up or -down, respectively. 1\(>\) is a virtual state in the stimulated Raman scattering process, \(\Gamma_{1}\) and \(\Gamma_{2}\) are the decay rates.