Strong-Field Atomic Phase Matching

We interpret a learning-control experiment with the goal of optimizing multiphoton population transfer in atomic sodium in the strong-field limit. Despite multiple experimental constraints, a learning algorithm discovers optimal pulses that can be understood in terms of a simple dynamic picture of the atom-field interaction. We show that the shaped pulses counteract the dynamic Stark-induced stimulated emission that would otherwise impede the efficient use of a $\pi$ pulse to invert a multiphoton transition.

Figure 1

(a) Experimental setup. (b) Sodium energy level diagram.

Figure 2

Optimal pulses found by the GA for transferring population at (a) ${\lambda }_0=784\mathrm{nm}$, (b) ${\lambda }_0=772\mathrm{nm}$, and (c) ${\lambda }_0=777\mathrm{nm}$.

Figure 3

(a) Final $4s$ population after interacting with a pair of laser pulses as a function of pulse delay and detuning. (b) Final $4s$ population after interacting with three pulses as function of pulse delay for pulses with a $\pi /2$ phase jump between pulses.

Figure 4

Panels (a), (b), and (c) show the $4s$ population for shaped (solid line) and unshaped pulses (dash-dotted line) vs time for central wavelengths of ${\lambda }_0=784\mathrm{nm}$, ${\lambda }_0=772\mathrm{nm}$, ${\lambda }_0=777\mathrm{nm}$, respectively. Panels (a) and (b) are for parametrized pulse shapes, and panel (c) is for a measured pulse. Panel (d) shows the atom-field phase $\alpha (t)$ for an unshaped pulse (dash-dotted line) and the optimal pulse shown in panel (a) (solid line). All panels also show the shaped pulse intensity profiles (dotted line).