Figure 1

(Color online) (a) Time dependence of population in level $C$ for the Gaussian $\Omega \left(t\right)={\Omega }_0{e}^{-{\left(\alpha t\right)}^2}$ pulse. Curve (1) corresponds to the linear solution of Eq. (4); (2) and (3) are the solutions of Eqs. (2, 3) for RWA and exact for $\nu /{\omega }_{cd}=1/3$. (b) Population left in the upper level $|c⟩$ after applying Gaussian pulse as a function of the pulse frequency $\nu$ obtained for linear solution given by Eq. (4)—curve (1), RWA—curve (2), and exact—curve (3). In calculations we take $\alpha =0.08{\omega }_c$ and ${\Omega }_0=0.02{\omega }_c$ (for RWA), and ${\Omega }_0=0.04{\omega }_c$ (for exact solution).Reuse & Permissions

Figure 2

(Color online) Population left in the upper level $|c⟩$ after applying $\Omega \left(t\right)={\Omega }_0\left[\text{sech}\left(\alpha t\right)+\text{sech}\left(\alpha t-3\right)\right]$ pulse as a function of the frequency $\nu$ obtained by numerical solution of Eq. (2) (dots) and using our approximate analytical result (15) (solid line). In calculations we take ${\Omega }_0=0.05{\omega }_c$ and $\alpha =0.05{\omega }_c$.Reuse & Permissions

Figure 3

(Color online) (a) The level structure of a spin-1/2 system. Three-photon excitation for linearly polarized magnetic field is shown to demonstrate the role of a counter-rotating term in Eq. (21). (b) Level structure of Rb atomic system. All population optically pump in $|F=1,m=+1⟩$. (c) Calculated amplitude $\left|a_{F=2,m=+1}\right|$ [shown by solid line (1)] are the results for the linearly polarized magnetic field. Calculated amplitude $\left|a_{F=2,m=+2}\right|$ for circularly polarized magnetic field are shown by the dashed line (2) (the results of numerical simulations that take into account all levels) and by dotted line (3) (the results of simulations that take into account only levels $|F=1,m=+1⟩$ and $|F=2,m=+2⟩$).Reuse & Permissions

Figure 4

(a) Level structure of Rb atomic system. All population optically pump in $|F=1,m=+1⟩$. (b) Experimentally observed excited population vs the ratio $\frac{\nu }{{\omega }_{cd}}$ for the Gaussian pulse.Reuse & Permissions