Femtosecond Rotational Dynamics of ${\mathrm{D}}_2$ Molecules in Superfluid Helium Nanodroplets

Rotational dynamics of ${\mathrm{D}}_2$ molecules inside helium nanodroplets is induced by a moderately intense femtosecond pump pulse and measured as a function of time by recording the yield of ${\mathrm{HeD}}^{+}$ ions, created through strong-field dissociative ionization with a delayed femtosecond probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant $B_{\mathrm{He}}$ of the in-droplet ${\mathrm{D}}_2$ molecule, determined by Fourier analysis, is the same as $B_{\mathrm{gas}}$ for an isolated ${\mathrm{D}}_2$ molecule. Our observations show that the ${\mathrm{D}}_2$ molecules inside helium nanodroplets essentially rotate as free ${\mathrm{D}}_2$ molecules.

Figure 1

(a) Schematic diagram of the experimental setup. (b) Relevant potential energy curves of ${\mathrm{D}}_2$, ${\mathrm{D}}_2^{+}$, and ${\mathrm{D}}_2^{2+}$ ($1/R$ Coulomb potential), adapted from Ref. [26]. The blue vertical arrows illustrate the ${\mathrm{D}}_2(1,0)$ and ${\mathrm{D}}_2(1,1)$ dissociative ionization channels; see text. (c) Measured position $y$-TOF spectrum of the ions produced when the probe pulse interacts with the doped He nanodroplets. The signal originating from the residual gas in the interaction chamber (e.g., ${\mathrm{H}}_2$, ${\mathrm{H}}_2\mathrm{O}$, and ${\mathrm{N}}_2$) was subtracted from the spectrum for clarity.

Figure 2

(a) Yield of the ionic fragments with $m/q=6$ as a function of the kinetic energy and the time delay. (b) Time-dependent yield obtained by integrating the yield over the low-$E_{\mathrm{kin}}$ and the high-$E_{\mathrm{kin}}$ ranges. (c),(d) Time-dependent yields of ${\mathrm{HeD}}^{+}$ (from ${\mathrm{D}}_2$ in He droplets) and ${\mathrm{D}}^{+}$ [from the ${\mathrm{D}}_2(1,0)$ channel of the isolated gas-phase ${\mathrm{D}}_2$ molecules] in two selected time intervals. The shaded area represents the error bars. The time step sizes for the intervals of 19.42–20.02 and 100.1–100.7 ps are 6.7 and 10 fs, respectively.

Figure 3

(a),(b) Time-dependent yields of ${\mathrm{HeD}}^{+}$ (from ${\mathrm{D}}_2$ in He droplets) and ${\mathrm{D}}^{+}$ [from the ${\mathrm{D}}_2(1,0)$ channel of the gas-phase ${\mathrm{D}}_2$ molecules] in the 1–7 ps time interval. (c) Power spectra of the yield traces in (a) and (b). (d),(e) Central frequencies of ($J-J+2$) peaks in the power spectra versus $J$. The full lines represent the best fits using the least square method; see text. The B and D constants from the fits are given with 95% confidence bounds.