Coherent control of strong field multiphoton absorption in the presence of dynamic Stark shifts

We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\mid 3s⟩$ ground state to the $\mid 4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.

Figure 1

Level distribution for multiphoton population transfer. Shown is also a single-photon resonant level.

Figure 2

Sodium $\mid 4s⟩$ population, ${\mid a_e\left(t\right)\mid }^2$, for different values of the phase compensation parameter $S$ for a $100\text{‐}\mathrm{fs}$ Gaussian pulse with peak intensity $I_0=1.44\times {10}^{15}\mathrm{W}∕{\mathrm{m}}^2$ $(1.44\times {10}^{11}\mathrm{W}∕{\mathrm{cm}}^2)$ tuned to the bare resonance, ${\lambda }_0=777\mathrm{nm}$. The inset shows the final $\mid 4s⟩$ and $\mid 7p⟩$ populations as a function of pulse duration (FWHM).

Figure 3

Final $\mid 4s⟩$ population, ${\mid a_e(t\to \infty )\mid }^2$, for a Gaussian pulse of $100\mathrm{fs}$ duration as a function of phase correction parameter $S$ and ${\lambda }_0$. Population is proportional to the darkness of the shading as indicated by the scale on the right-hand side, where 1 corresponds to 100% population transfer.