Timing Dissociative Ionization of ${\mathrm{H}}_2$ Using a Polarization-Skewed Femtosecond Laser Pulse

We experimentally observe the bond stretching time of one-photon and net-two-photon dissociation pathways of singly ionized ${\mathrm{H}}_2$ molecules driven by a polarization-skewed femtosecond laser pulse. By measuring the angular distributions of the ejected photoelectron and nuclear fragments in coincidence, the cycle-changing polarization of the laser field enables us to clock the photon-ionization starting time and photon-dissociation stopping time, analogous to a stopwatch. After the single ionization of ${\mathrm{H}}_2$, our results show that the produced ${\mathrm{H}}_2^{+}$ takes almost the same time in the one-photon and net-two-photon dissociation pathways to stretch to the internuclear distance of the one-photon coupled dipole-transition between the ground and excited electronic states. The spatiotemporal mapping character of the polarization-skewed laser field provides us a straightforward route to clock the ultrafast dynamics of molecules with sub-optical-cycle time resolution.

Figure 1

(a) The $1s{\sigma }_g^{+}$ and $2p{\sigma }_u^{+}$ potential energy curves of ${\mathrm{H}}_2^{+}$. The red and blue arrows illustrate the one-photon and net-two-photon dissociation pathways, respectively. The dashed horizontal lines indicate the vibrational states of $\nu =3$ and $\nu =9$ on the $1s{\sigma }_g^{+}$ potential energy curve. The inset (green curve) shows the measured KER spectrum of the ${\mathrm{H}}_2(1,0)$ channel, where the highlighted red and blue areas correspond to the one-photon and net-two-photon dissociation pathways, respectively. (b) The time-dependent internuclear distance of the stretching ${\mathrm{H}}_2^{+}$ simulated by our classical model for the one-photon (red curve) and net-two-photon (blue curve) dissociation pathways.

Figure 2

(a) The sketch of the stopwatch using a polarization-skewed laser pulse (red rotating curve). The yellow curve in the “electrons” inset illustrates the trajectory of the photoelectron emitted from ${\mathrm{H}}_2$ at ionization instant $t_i$. Driven by the remaining laser field after $t_i$, the ultimate momentum of the photoelectron is given by the vector potential $\mathit{A}(t_i)$ at the ionization instant, i.e., ${\varphi }_{\mathrm{ele}}={\varphi }_A+180°$. As illustrated in the “protons” inset, the stretched ${\mathrm{H}}_2^{+}$ transits to the excited state at instant $t_i+{\tau }_{\omega H}$, where the dipole-transition rate depends on the strength and orientation of the instantaneous laser field $\mathit{E}(t_i+{\tau }_{\omega H})$ with respect to the molecular orientation ${\varphi }_{\mathrm{mol}}$. The ${\varphi }_{\mathrm{mol}}$ is read from the measured emission direction of the ejected ${\mathrm{H}}^{+}$, i.e., ${\varphi }_{\mathrm{mol}}={\varphi }_{\mathrm{ion}}$. (b),(c) Measured momentum distributions of the photoelectrons and correlated nuclear fragments ${\mathrm{H}}^{+}$ produced from the ${\mathrm{H}}_2(1,0)$ channel. The events within the dashed red and blue rings in (c) are selected to observe the bond stretching time of the one-photon and net-two-photon dissociation pathways.

Figure 3

(a) The photoelectron momentum distribution of the one-photon dissociative ionization pathway of ${\mathrm{H}}_2$ correlated with molecules oriented along ${\varphi }_{\mathrm{mol}}=40°$. (b) The angular distributions of photoelectrons emitted from molecules oriented along ${\varphi }_{\mathrm{mol}}=40°$ (red curve) and 30° (blue curve). The pink arrow indicates the rotating direction of the polarization of the laser field. (c) The corresponding dissociative ionization probabilities $P_{\mathrm{id}}(t_i)$ deduced from the photoelectron angular distributions in (b) by relating ${\varphi }_{\mathrm{ele}}$ to the ionization instant $t_i$. (b) Shares the same vertical axis as (c), which represents the yield of photoelectrons as labeled in the right of (c). (d)–(f) The same as (a)–(c) but for the net-two-photon dissociative ionization pathway of ${\mathrm{H}}_2$.

Figure 4

Experimentally extracted bond stretching time of different dissociation pathways of ${\mathrm{H}}_2$ as a function of the molecular orientation ${\varphi }_{\mathrm{mol}}$. The curve with red circles shows ${\tau }_{\omega H}$ of the one-photon pathway of ${\mathrm{H}}_2$. The blue solid and open circle curves are the effective bond stretching times of ${\tau }_{\mathrm{eff}}$ and ${\tau }_{(3–1)\omega H}$ of the net-two-photon pathway of ${\mathrm{H}}_2$, respectively.