Subfemtosecond Tracing of Molecular Dynamics during Strong-Field Interaction

We introduce and experimentally demonstrate a method where the two intrinsic timescales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photoelectron photoion coincidence experiment. In our experiment, elliptically polarized, 750 nm, 4.5 fs laser pulses were focused to an intensity of $9\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ onto ${\mathrm{H}}_2$. Using coincidence imaging, we directly observe the nuclear wave packet evolving on the $1s{\sigma }_g$ state of ${\mathrm{H}}_2^{+}$ during its first round-trip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.

Figure 1

(a) Schematics of the relevant potential energy surfaces of ${\mathrm{H}}_2$. Indicated by arrows are the two ionization steps (➊ and ➋) delayed to each other by $\mathrm{\Delta }t$. (b) Cartoon of the electron and ion momentum vectors after double ionization of ${\mathrm{H}}_2$ in an intense elliptically polarized few-cycle laser pulse. (c) Distribution of the proton momentum from intrapulse double ionization in the polarization plane. The histogram is filled with two detected protons which satisfy a center-of-mass momentum $<10\mathrm{a}.\mathrm{u}.$ The minimum around $p_{p1,z}=0$ a.u. is due to the dead time of the detector. (d) Kinetic energy release. The lines A–D label certain values of $\mathrm{\Delta }t$. (e) Photoelectron energy distribution. Upper axis: corresponding laser intensity. (f) Relative emission angle between the two photoelectrons. Upper axis: corresponding ionization delay on a subcycle scale.

Figure 2

(a) Double ionization yield as a function of kinetic energy release and the relative electron emission angle, integrated over the photoelectron energy. (b) Energy distribution of the two emitted photoelectrons (symmetrized about the diagonal). The marked areas $A1$, $A2$ correspond to regions of constant sum energy. Most of the photoelectrons are created with similar energies which indicates that the two-electron emission is symmetrically distributed around the laser pule peak. (c) Measured fragmentation yield as a function of $\alpha$ and KER obtained when the momenta of the two emitted electrons lie within range $A1$ indicated in (b). (d) Same as (c) but for electron momenta within range $A2$. The thin line in (c) and (d) shows the classical expectation value obtained for vibrational motion on the $1s{\sigma }_g$ potential energy curve (see text and Supplemental Material [39] for details).

Figure 3

Measured fragmentation yield (dots) over $R$ for ionization events separated by an odd (a) and even (b) number of half cycles. (a) The distributions result from the selection $\alpha =[160°,180°]$, corresponding to ionization events taking place within a range of $\pm 70$ as around $\mathrm{\Delta }t=(2n+1)(T/2)$, $n=0$, 1, 2. (b) Same as (a) but for $\alpha =[0°,20°]$, corresponding to $\pm 70$ as around $\mathrm{\Delta }t=2n(T/2)$, $n=0$, 1, 2. The colored lines labeled A–D are Gaussian fits to the data. The labels A–D correspond with those in Fig. 1. (c) Measured fragmentation yield (dots) from (a),(b) but with additional restrictions on the magnitude of the electron momentum (see Supplemental Material [39] for details), with statistical error bars, in comparison with the Gaussian fits from (a),(b). The areas of the distributions A–D were normalized to one.