Understanding strong-field coherent control: Measuring single-atom versus collective dynamics

We compare the results of two strong field coherent control experiments: one which optimizes multi-photon population transfer in atomic sodium (from the 3s to the 4s state, measured by spontaneous emission from the 3p-3s transition) with one that optimizes stimulated emission on the 3p-3s transition in an ensemble of sodium atoms. Both experiments make use of intense, shaped ultrafast laser pulses discovered by a Genetic Algorithm inside a learning control loop. Optimization leads to improvements in the spontaneous and stimulated emission yields of about $4$ and ${10}^4$, respectively, over an unshaped pulse. We interpret these results by modeling both the single atom dynamics as well as the stimulated emission buildup through numerical integration of Schrödinger’s and Maxwell’s equations. Our interpretation leads to the conclusion that modest yields for controlling single quantum systems can lead to dramatic effects whenever an ensemble of such systems acts collectively following controlled impulsive excitation.

Figure 1

(Color online) (a) Experimental apparatus. (b) Sodium energy level diagram for the two-photon transition $3\mathrm{s}\to 4\mathrm{s}$ and yoked superflourescence.

Figure 2

(a) Population transfer (as measured by florescence yield on the 3p-3s transition) as a function of generation. The dashed line indicates the yield for an unshaped (transform limited) laser pulse. (b) Stimulated emission yield vs generation. The dashed line shows the value for an unshaped laser pulse.

Figure 3

(a) Experimental cross correlation measurement of the stimulated emission pulse profiles for atomic densities of $3.16\times {10}^{21}{\mathrm{m}}^{-3}$ (dashed), $1.55\times {10}^{21}{\mathrm{m}}^{-3}$ (dotted), and $9.56\times {10}^{20}{\mathrm{m}}^{-3}$ (full) with a propagation length $Z=10\mathrm{cm}$. (b) Calculated stimulated emission pulse profiles for the same densities as used in the measurements.

Figure 4

Stimulated emission yield vs 4s population $\left(Q_{22}\right)$. Parameters used for the calculation are $N=1.33\times {10}^{21}{\mathrm{m}}^{-3}$, $z=10\mathrm{cm}$, $Q_{32}(z=0,t=5\times {\tau }_L)={10}^{-6}$. Inset: Experimental stimulated emission yield (SF) vs drive pulse energy.