Velocity map imaging as a tool for gaining mechanistic insight from closed-loop control studies of molecular fragmentation

Strong-field closed-loop control schemes using shaped ultrafast laser pulses have been used to selectively fragment a variety of molecules in recent years. The resulting pulses are often complex and resist an easy mechanistic interpretation. We report on the use of velocity map imaging to study the dissociative ionization of CO molecules by optimally-shaped ultrafast laser pulses. Using this technique, a mechanism is identified for the optimized CO${}^{+}$ $\to$ C $+$ ${\mathrm{O}}^{+}$ dissociation, and some of the observed control over the CO${}^{+}$ dissociation branching ratio is ascribed to an angular discrimination effect. Furthermore, we demonstrate that the acquisition of two-dimensional velocity map images is rapid enough to incorporate directly into the adaptive control loop.

Figure 1

Conceptual picture of the experimental setup. The laser pulses from the Ti:sapphire oscillator are shaped by the AOPDF and then amplified and focused in the VMI spectrometer. An effusive jet directs the target gas into the spectrometer perpendicular to the laser beam. The 2D images are collected by the data acquisition system (DAQ) and either used for later analysis (as in Sec. 3a) or, as depicted in the figure, used as feedback by the genetic algorithm (GA) as it searches for an optimal pulse. The latter variation of the experiment is described in Sec. 3b.

Figure 2

Polarization-gate frequency resolved optical gating (PG-FROG) representation, adapted from Ref. [17], of the shaped laser pulse that optimized [C $+$ ${\mathrm{O}}^{+}$]/[C${}^{+}$ $+$ O]. This pulse essentially doubled the [C $+$ ${\mathrm{O}}^{+}$]/[C${}^{+}$ $+$ O] yield compared to a baseline FTL pulse. Section 3a describes our examination of the underlying mechanisms.

Figure 3

Potential energy curves for various states of CO${}^{+}$ [48, 49]. The lowest state that goes to C $+$ ${\mathrm{O}}^{+}$ at the separate atom limit is the $I$$\hspace{0.5em}{}^2{\Sigma }^{+}$ state. The shaded region represents the range of internuclear distances populated by Franck-Condon transitions from the CO ground state.

Figure 4

Density plot of dissociation as a function of KER and cos($\theta$) for the C $+$ ${\mathrm{O}}^{+}$ (left) and ${\mathrm{C}}^{+}$ $+$ O (right) channels for pulses tailored to optimize [C $+$ ${\mathrm{O}}^{+}$]/[C${}^{+}$ $+$ O] (top) and [C${}^{+}$ $+$ O]/[C $+$ ${\mathrm{O}}^{+}$] (middle) feedback targets, where $\theta$ is the angle between the laser polarization and the CO internuclear axis. The results obtained with a FTL pulse are shown on the bottom for comparison.

Figure 5

Relative probability vs KER for ${\mathrm{O}}^{+}$ fragments produced by FTL pulses (dashed red line) and pulses that optimize [C $+$ ${\mathrm{O}}^{+}$]/[C${}^{+}$ $+$ O] (solid blue line). The inset magnifies the single-ionization region below 3 eV.

Figure 6

Field-dressed potential-energy curves of CO${}^{+}$ and suggested pathways leading to the observed KER distributions of ${\mathrm{O}}^{+}$ fragments for peaks $\alpha$ and $\beta$ in the inset of Fig. 5. (a) The $X$ ${}^2{\Sigma }^{+}$ $\to$ $B$$\hspace{0.5em}{}^2{\Sigma }^{+}-4\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-n\omega$ pathways, with the pathways indicated by the violet arrows. (b) The $B$$\hspace{0.5em}{}^2{\Sigma }^{+}$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-5\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-3\omega$ and the $B$$\hspace{0.5em}{}^2{\Sigma }^{+}$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-5\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-3\omega$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-4\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-4\omega$ paths, again denoted by the violet arrows. These paths should also lead to the intermediate path $B$$\hspace{0.5em}{}^2{\Sigma }^{+}$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-5\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-3\omega$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-3\omega$, with a ${\mathrm{C}}^{+}$ $+$ O final state and an expected KER of 1.2 eV. The dashed green arrow represents a $B$$\hspace{0.5em}{}^2{\Sigma }^{+}$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-6\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-3\omega$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-5\omega$ $\to$ $I$$\hspace{0.5em}{}^2{\Sigma }^{+}-4\omega$ $\to$ 3$\hspace{0.5em}{}^2{\Sigma }^{-}-4\omega$ path with an expected KER of 2.3 eV.

Figure 7

Relative probability vs KER for ${\mathrm{C}}^{+}$ $+$ O dissociative ionization produced by FTL pulses (dashed red line) and pulses that optimize [C $+$ ${\mathrm{O}}^{+}$]/[C${}^{+}$ $+$ O] (solid blue line).

Figure 8

Polar plots of the normalized angular distributions obtained for the C $+$ ${\mathrm{O}}^{+}$ channel with laser pulses tailored to optimize [C $+$ ${\mathrm{O}}^{+}$]/[C${}^{+}$ $+$ O] feedback targets (blue) and with FTL pulses (red). The left distribution is for peak $\alpha$ (0.53–1.48 eV) from the inset of Fig. 5, and the right distribution is for peak $\beta$ (1.86–2.60 eV). The laser polarization is along the 0${}^{°}$-180${}^{°}$ axis. Both FTL distributions are fit with a ${\text{cos}}^{32}(\theta )$ (red lines) function. The optimized data are fit with ${\text{cos}}^{12}(\theta )$ and ${\text{cos}}^6(\theta )$ (blue lines) for the left and right distributions, respectively.

Figure 9

(a)–(c) Raw, unsymmetrized, 2D VMI plots of ${\mathrm{O}}^{+}$ fragments with various feedback gate settings as used in the experiment and discussed in the text. The interior part of the plot, defined by the red circle in plot (a), contains the dissociation channels, while the outside contains higher-energy fragments from multiple ionization of CO. (d) Inverted image representing a slice at $p_z=$ 0 of the 3D momentum distribution of the same image after being symmetrized and inverted to remove the undesirable azimuthal contribution. The feedback gates derived from the raw VMI plots contain more noise, and therefore a gate on an inverted image is desirable.