Isotope Selective Ionization by Optimal Control Using Shaped Femtosecond Laser Pulses

We report on selective optimization of different isotopes in an ionization process by means of spectrally broad shaped fs-laser pulses. This is demonstrated for ${}^{39,39}K_2$ and ${}^{39,41}K_2$ by applying evolution strategies in a feedback loop, whereby a surprisingly high enhancement of one isotope versus the other and vice versa is achieved (total factor $\approx 140$). Information about the dynamics on the involved vibrational states is extracted from the optimal pulse shapes, which provides a new spectroscopical approach of yielding distinct frequency pattern on fs-time scales. The method should, in principle, be feasible for all molecules.

Figure 1

(a) Ionization path of $K_2$ proposed in Refs. 23, 24. On the right are the potential energy curves and vibrational levels of the $2^1{\Pi }_g$ (b) and $A^1{\Sigma }_u^{+}$ state (c). The solid lines indicate the vibrational levels of the ${}^{39,39}K_2$ isotope and the dotted lines the levels of the ${}^{39,41}K_2$ isotope. The states $v^{\prime }{}_A=12$, 13 of the lighter isotope are disturbed by spin-orbit coupling with the $b^3{\Pi }_u$ state and therefore shifted by $+1.2{\mathrm{c}\mathrm{m}}^{-1}$ and $+2.1{\mathrm{c}\mathrm{m}}^{-1}$, respectively [5, 25]. (c) also shows the spectrum of the unshaped laser light at 833 nm central wavelength.

Figure 2

Progressions of the mean ${}^{39,39}K_2{/}^{39,41}{K}_2$ ion ratio during single pulse optimization for maximization (a) and minimization (b). The considerable alteration of the isotope ratio by a factor of about 140 is illustrated as well in the corresponding mass spectra on the right.

Figure 3

Laser pulse spectra for maximization (a) and minimization (b) of the isotope ratio ${}^{39,39}K_2{/}^{39,41}{K}_2$. The gray bars denote the corresponding transmission pixel pattern of the optimized pulses. The highest peaks are assigned to transitions between particular vibrational energy levels of the different electronic states $X^1{\Sigma }_g^{+}$, $A^1{\Sigma }_u^{+}$, and $2^1{\Pi }_g$ of the ${}^{39,39}K_2$ isotope in (a) and the ${}^{39,41}K_2$ isotope in (b). Even indications of the mentioned distortion of the $v^{\prime }=13$ vibrational level in the $A^1{\Sigma }_u^{+}$ state might be observed as a small peak shift, yet we do not claim this since it is at the limit of our shaper resolution.

Figure 4

XFROG traces for maximization (a) and minimization (b) of the isotope ratio ${}^{39,39}K_2{/}^{39,41}{K}_2$. The often observed subpulse distance of 250 fs ($\frac{1}{2}{T}_{\mathrm{o}\mathrm{s}\mathrm{c}}$ of the $A^1{\Sigma }_u^{+}$ state) and the wavelength shift of up to 1 nm between two adjacent subpulses indicate a successive excitation of the electronic states on the optimal ionization path. Particularly for minimization the higher frequency subpulses assigned to the $A^1{\Sigma }_u^{+}\leftarrow X^1{\Sigma }_g^{+}$ transition are followed by the lower frequency ones assigned to the $2^1{\Pi }_g^{+}\leftarrow A^1{\Sigma }_u^{+}$ transition [see Fig. 3b].