Probing the Structure and Dynamics of Molecular Clusters Using Rotational Wave Packets

Rotational wave packets of the weakly bound ${\mathrm{C}}_2{\mathrm{H}}_2\text{−}\mathrm{He}$ complex have been created using impulsive alignment. The coherent rotational dynamics were monitored for 600 ps enabling extraction of a frequency spectrum showing multiple rotational energy levels up to $J=4$. spectrum has been combined with ab initio calculations to show that the complex has a highly delocalized structure and is bound only by ca. $7{\mathrm{cm}}^{-1}$. The experiments demonstrate how highly featured rotational spectra can be obtained from an extremely cold environment where only the lowest rotational energy states are initially populated.

Figure 1

Schematic of experimental setup. Helium-${\mathrm{C}}_2{\mathrm{H}}_2$ complexes produced by expansion of 0.01% ${\mathrm{C}}_2{\mathrm{H}}_2$ in 9 MPa He through a cooled Even-Lavie valve were irradiated by femtosecond pulses originating from a 30 fs, 1 kHz Ti:sapphire laser operating at 800 nm (KM Labs Red Dragon). Both pump and probe laser beams, comprised of separate grating compressors (not shown), were colinearly focused through a $f=500\mathrm{mm}$ lens into the molecular beam 50 mm downstream from the nozzle exit.

Figure 2

Velocity map images of the Coulomb explosion process. These particular images focus on the ${\mathrm{C}}^{+}$ fragment and were recorded with different nozzle temperatures $T_0$, namely, (a) 293 K ($P_0=7\mathrm{MPa}$) and (b) 203 K ($P_0=6.4\mathrm{MPa}$), but under otherwise identical conditions. Corresponding angularly integrated and normalized kinetic energy distributions are shown in (c): pure ${\mathrm{C}}_2{\mathrm{H}}_2$ (black line with squares) and ${\mathrm{C}}_2{\mathrm{H}}_2$ with ${\mathrm{C}}_2{\mathrm{H}}_2\text{−}{\mathrm{He}}_n$ complexes present (red line with circles). Production of complexes between helium and acetylene is enhanced in (b), supported by increased kinetic energy compared to (a). The yellow double-headed arrow indicates the direction of the pump and probe laser polarizations, which are parallel to the $y$ axis in Fig. 1. In (a) and (b) the dashed circles are guides to the eye and the axes $p_x$ and $p_y$ are given in atomic units of momentum.

Figure 3

Time-resolved alignment. (a) Rotational revivals obtained under conditions where the helium stagnation pressure and temperature were 6.4 MPa and 217 K, respectively. Note that the average geometric alignment $⟨{\cos }^2\theta {⟩}_{\text{geom}}=0.78$ has been subtracted. The data have been smoothed by a five-step-wide moving average filter. The rotational period of acetylene is indicated by a double-headed arrow. (b) For time delays up to the maximum of 600 ps, no damping in the amplitude was observed. The coherence time of the wave packet for free ${\mathrm{C}}_2{\mathrm{H}}_2$ molecules is therefore at least 600 ps.

Figure 4

Overview spectra. (a) Fourier amplitude spectrum of the time-resolved molecular alignment recorded at a pump laser intensity of $5\times {10}^{12}\mathrm{W}{\mathrm{cm}}^{-2}$ ($P_0=6.4\mathrm{MPa}$ and $T_0=217\mathrm{K}$). (b) Spectrum recorded under similar conditions, but at a lower pump laser intensity of $2.5\times {10}^{11}\mathrm{W}{\mathrm{cm}}^{-2}$ ($P_0=4\mathrm{MPa}$ and $T_0=212\mathrm{K}$). The amplitude spectra are dominated by strong peaks arising from beats between rotational levels of free ${\mathrm{C}}_2{\mathrm{H}}_2$ connected by $\mathrm{\Delta }J=\pm 2$. The labels of the transitions correspond to the $J$ quantum number of the final states, e.g., “2” labels the final state of the $J^{\prime }=2\leftarrow J^{\prime \prime }=0$ excitation. (c) The rotational levels in the wave packet are excited via virtual states through sequential Raman excitations with an 800 nm ($12500{\mathrm{cm}}^{-1}$) laser pulse.

Figure 5

Expanded view of the frequency region below $5{\mathrm{cm}}^{-1}$. An average of five spectra recorded for similar expansion conditions is shown in panel (a). Two spectra acquired at pump laser intensities of $5\times {10}^{12}$ and $2.5\times {10}^{11}\mathrm{W}{\mathrm{cm}}^{-2}$ are shown in panels (b) and (c), respectively. Prominent features assigned to ${\mathrm{C}}_2{\mathrm{H}}_2\text{−}\mathrm{He}$ are also annotated by numbers 1–5. The transitions which were not safely established in (a) are marked by dashed-dot arrows. See text and the energy level diagram in Fig. 6 for further information. Amongst other unassigned features, the peak at $0.25{\mathrm{cm}}^{-1}$ is particularly prominent. We note that larger complexes may contribute lines and that this low frequency region is particularly susceptible to artifacts, hence we treat this region with caution.

Figure 6

Rotational energy level diagram of ${\mathrm{C}}_2{\mathrm{H}}_2\text{−}\mathrm{He}$. The arrows designate the transitions observed, whereas the dashed-dotted, gray arrows indicate transitions which were not safely established in the experimental data.