Controlling strong-field fragmentation of H${{}_2}^{+}$ by temporal effects with few-cycle laser pulses

In a joint experimental and theoretical endeavor, we explore the laser-induced dissociation and ionization dynamics of H${{}_2}^{+}$ beams using sub-10-fs, 800 nm laser pulses. Our theory predicts considerable control over the branching ratio of two-photon and three-photon above-threshold dissociation (ATD) by gating the dissociation pathway on a few-femtosecond timescale. We are able to experimentally demonstrate this control. Moreover, our theory also shows the importance of the highly excited H(2$l$) states of H${{}_2}^{+}$ that contribute to ATD structure in dissociation. As is the case for dissociation, we find that ionization is also sensitive to the effective laser interaction time.

Figure 1

Potential energy curves of H${{}_2}^{+}$ displaying the H(1$l$) states leading to ${\text{H}}^{+}+\text{H}\left(1s\right)$ and the H(2$l$) states leading to ${\text{H}}^{+}+\text{H}\left(2l\right)$. The ionization curve, 1/$R$, leading to ${\text{H}}^{+}+{\text{H}}^{+}$ is also displayed. The vertical arrows labeled $R_1$ and $R_3$ denote the one-photon and three-photon resonance positions, respectively.

Figure 2

Schematic of experimental setup. Pulses from a hollow-core fiber and chirped-mirror arrangement are focused onto the ion-beam target. Neutral and ion fragments are then separated in flight time using a static electric field from the spectrometer. They are subsequently measured in coincidence and their momentum imaged using a position- and time-sensitive detector.

Figure 3

(a) Dressed-states potential energy curves of H${{}_2}^{+}$, showing the diabatic and adiabatic curves at $1\times {10}^{13}$ W/cm${}^2$. The notation $|2p{\sigma }_g-1\omega \rangle$ indicates the $2p{\sigma }_u$ state dressed by one photon, for example. The labels 1$\omega$, 3$\omega$, and 5$\omega$ denote the curve crossings of $2p{\sigma }_u$ with the $1s{\sigma }_g$ ground state. Calculated unperturbed vibrational levels are shown by the horizontal lines. (b) Same as (a) but for diabatic curves only and including the dressed H(2$l$) states.

Figure 4

Experimental KER-cos$\theta$ density plots of dissociation of H${{}_2}^{+}$ [(a)–(d)], HD${}^{+}$ [(e)–(g)], and D${{}_2}^{+}$ [(h)–(k)] at intensities indicated (in W/cm${}^2$) for 7 fs, 800 nm laser pulses.

Figure 5

Theoretical KER-cos$\theta$ density plots of dissociation of H${{}_2}^{+}$ using 7 fs pulses at intensities indicated (in W/cm${}^2$). The false-color scale denotes the dissociation probability density. The data are plotted over the same dynamic range as the experiment in Fig. 4.

Figure 6

Theoretical KER-cos$\theta$ density plots of dissociation of H${{}_2}^{+}$ using 7 fs pulses at $1\times {10}^{13}$ W/cm${}^2$. The false-color scale denotes the dissociation probability density. (a) The 1$s{\sigma }_g$ dissociation probability which includes zero-photon (0$\omega$) and two-photon (2$\omega$) dissociation. (b) The 2$p{\sigma }_u$ dissociation probability, including one-photon (1$\omega$) and three-photon (3$\omega$) dissociation. Note that the dissociation probability density in this plot spans a range two orders of magnitude greater than that in Fig. 5d.

Figure 7

Theoretical KER distributions for dissociation of H${{}_2}^{+}$ using 7 fs pulses at intensities indicated (in W/cm${}^2$). The labels in panel (b) denote the final electronic states and are the same for all panels. The labels in panel (c) indicate to which photon process the peaks correspond.

Figure 8

(a)–(c) The solid bars show the calculated dissociation probabilities (left axis) of H${{}_2}^{+}$ vibrational states using 7 fs, $1\times {10}^{14}$ W/cm${}^2$ pulses leading to dissociation on the (a) 2$p{\sigma }_u$, (b) 1$s{\sigma }_g$, and (c) H(2$l$) electronic states. The dashed lines show the Franck-Condon weighted probabilities (right axis); that is, the product of the dissociation probability times the Franck-Condon population [see panel (d)]. (d) Franck-Condon population distribution of H${{}_2}^{+}$ vibrational states.

Figure 9

Theoretical KER distributions for select vibrational states of H${{}_2}^{+}$ using 7 fs, $1\times {10}^{14}$ W/cm${}^2$ pulses: (a) $v=1$, (b) $v=3$, and (c) $v=9$. (d) The individual contributions from the H(2$l$) states are shown for $v=9$. The labels denote the final electronic states.

Figure 10

Experimental angular distributions for H${{}_2}^{+}$ and D${{}_2}^{+}$ dissociation, integrated over all KER, using 7 fs pulses at the intensities indicated. The data (symbols) are fit with cos${}^n\theta$ distributions (solid lines) as marked. The H${{}_2}^{+}$ and D${{}_2}^{+}$ distributions are normalized to each other's peak.

Figure 11

Experimental KER distributions for (a) D${{}_2}^{+}$, (b) HD${}^{+}$, and (c) H${{}_2}^{+}$ using 7 fs pulses at $2\times {10}^{13}$and $7.5\times {10}^{15}$ W/cm${}^2$ corresponding to the plots in Fig. 4. The distributions are all normalized to their peak values. Error bars denote the statistical error in the data.

Figure 12

Theoretical KER-cos$\theta$ distributions for [(a)–(c)] H${{}_2}^{+}$ and [(d)–(f)] D${{}_2}^{+}$ at $1\times {10}^{14}$ W/cm${}^2$ and pulse durations of 5, 7, and 10 fs as indicated. The color bar denotes the probability density. Plots for H${{}_2}^{+}$ and D${{}_2}^{+}$ are over the same dynamic range.

Figure 13

Calculated KER distributions for [(a)–(c)] H${{}_2}^{+}$ and [(d)–(f)] D${{}_2}^{+}$ at $1\times {10}^{14}$ W/cm${}^2$ and pulse durations of 5, 7, and 10 fs as indicated. The labels in panel (a) denote the final electronic state and are the same used for all panels.

Figure 14

Comparison of the calculated KER distributions for dissociation on the 2$p{\sigma }_u$ state of H${{}_2}^{+}$ and D${{}_2}^{+}$ at $1\times {10}^{14}$ W/cm${}^2$ and pulse durations of 5, 7, and 10 fs as indicated. The distributions are all normalized to the peak of the H${{}_2}^{+}$, 10 fs total probability density.

Figure 15

Experimental KER distributions for dissociation of D${{}_2}^{+}$ using 7 and 10 fs pulses at $6\times {10}^{14}$ and $7.5\times {10}^{15}$ W/cm${}^2$ as indicated. The distributions are all normalized to their peak values. Error bars denote the statistical error in the data.

Figure 16

Experimental KER and KER-cos$\theta$ distributions for ionization of H${{}_2}^{+}$ and D${{}_2}^{+}$ (as labeled) using 7 fs pulses at intensities indicated (in W/cm${}^2$). The H${{}_2}^{+}$ and D${{}_2}^{+}$ distributions are normalized to the peak of each other. Error bars denote the statistical error in the data.

Figure 17

Experimental KER distributions for ionization of D${{}_2}^{+}$ using 7 and 10 fs pulses (as labeled) at $7.5\times {10}^{15}$ W/cm${}^2$. The distributions are normalized to the peak of each other. Error bars denote the statistical error in the data.