Control of populations of two-level systems by a single resonant laser pulse

We present a simple approach allowing one to obtain analytical expressions for laser pulses that can drive a two-level system in an arbitrarily chosen way. The proposed scheme relates every desired population-evolution path to a single resonant laser pulse. It allows one to drive the system from any initial superposition of the two states to a final state having the desired distribution of the populations. We exemplify the scheme with a concrete example, where the system is driven from a nonstationary superposition of states to one of its eigenstates. We argue that the proposed approach may have interesting applications for designing pulses that can control ultrafast charge-migration processes in molecules. Although focused on laser-driven population control, the results obtained are general and could be applied for designing other types of control fields.

Figure 1

(Upper panel) Laser pulse obtained through Eq. (14) using the following parameters: $\mu =6$ a.u., ${\omega }_0=0.02$ a.u., $a_i=0.4$, $a_f=1$, $\alpha =0.01$, and $\varphi =0$. (Lower panel) Evolution of the populations of the states $|1\rangle$ (red dotted) and $|2\rangle$ (green dash-dotted) of a two-level system driven by such a laser pulse. The control function $f\left(t\right)$ used to obtain the driving field is depicted in blue solid. We see that the system is driven from a coherent superposition of states $|1\rangle$ (40%) and $|2\rangle$ (60%) to a system being only in state $|1\rangle$.

Figure 2

(Upper panel) Laser pulse obtained through Eq. (14) using the same parameters as in Fig. 1 except $\alpha =0.05$. (Lower panel) Evolution of the populations of the states $|1\rangle$ (red dotted) and $|2\rangle$ (green dash-dotted) of a two-level system driven by such a laser pulse. The control function $f\left(t\right)$ used to obtain the driving field is depicted in blue solid. We see that the full solution start to deviate from the RWA and the pulse is not able to bring the system 100% to state $|1\rangle$.