Optimal control of multiphoton ionization of ${\mathrm{Rb}}_2$ molecules in a magneto-optical trap

We present optimal control, using femtosecond laser pulses in a closed-loop experiment, of the ionization process of ultracold rubidium molecules formed in a magneto-optical trap. The resulting spectrum of the optimally shaped pulse exhibits two frequency bands, which drive a resonantly enhanced three-photon ionization. The obtained data reveals the ionization process where only the electronic states corresponding to the $5s5d$-asymptote are utilized for the second excitation step.

Figure 1

(Color online) Evolution of the ion yield of the mean individual during the optimization experiment.

Figure 2

(Color online) Spectrum of the best individual of the optimization, exhibiting two frequency bands at 12 815 and $12883{\mathrm{cm}}^{-1}$ (780.4 and $776.2\mathrm{nm}$).

Figure 3

(Color online) (a) Ion signal depending on the position of a needle in the Fourier plane. (b) Corresponding fluorescence. The inset shows the associated spectrum at a needle position of $12903{\mathrm{cm}}^{-1}$ $\left(775\mathrm{nm}\right)$ and the absence of frequencies beneath $12599{\mathrm{cm}}^{-1}$ $\left(793.7\mathrm{nm}\right)$.

Figure 4

(Color online) Energy potential scheme of potentials belonging to the participating asymptotes from Park et al. [22], represented in Hund’s case (a) notation. The molecules are present in the ${}^1\Sigma _g$, ${}^3\Sigma _g$, and ${}^3\Sigma _u$ ground state in the vibrational energy levels just below the $5s5s$-asymptote. This population is transferred to the energy potentials related to the $5s5p_{3∕2}$-asymptote, namely ${}^3\Sigma _u^{+}$, ${}^1\Sigma _g^{+}$, ${}^1\Sigma _u^{+}$, ${}^1\Pi _g$, ${}^1\Pi _u$, ${}^3\Pi _g$, and ${}^1\Pi _u$. In the next excitation step the wave packet is driven by the frequency components of the second band at $12883{\mathrm{cm}}^{-1}$ $\left(776.2\mathrm{nm}\right)$ to the $5s5d_{3∕2,5∕2}$-asymptote which is the bottleneck in this process. The electronic states which are associated with this asymptote are ${}^1\Pi _g$, ${}^1\Delta _g$, ${}^3\Sigma _g^{+}$, ${}^3\Pi _g$, ${}^3\Delta _g$, ${}^1\Sigma _u^{+}$, ${}^1\Pi _u$, ${}^1\Delta _u$, ${}^3\Pi _u$, and ${}^3\Delta _u$. In the third step, the molecule is ionized by one of the two frequency bands to the ${}^2\Sigma _g$ ionic ground state.