Diffractive Imaging of Coherent Nuclear Motion in Isolated Molecules

Observing the motion of the nuclear wave packets during a molecular reaction, in both space and time, is crucial for understanding and controlling the outcome of photoinduced chemical reactions. We have imaged the motion of a vibrational wave packet in isolated iodine molecules using ultrafast electron diffraction with relativistic electrons. The time-varying interatomic distance was measured with a precision 0.07 Å and temporal resolution of 230 fs full width at half maximum. The method is not only sensitive to the position but also the shape of the nuclear wave packet.

Figure 1

(a) Diagram of the experimental setup showing the laser beam (green), electron beam (blue), and gas jet (gray). (b) Potential energy surfaces of ground state (dashed blue line) and the $B$ excited state (dashed red line), along with the ground and excited state wave packets (solid lines). The blue and red colors represent ground and the excited states, respectively. (c) Simulated dynamics of the nuclear wave packet of ${\mathrm{I}}_2$ in the $B$ state, after excitation by a 530 nm laser pulse. The figure displays the amplitude of the wave function as a function of time, in arbitrary units.

Figure 2

(a) Experimental difference diffraction pattern $⟨\mathrm{\Delta }{I}_{\exp }(t,s,\varphi )⟩$ averaged over $t=50\mathrm{fs}$ to 550 fs. (b) Simulated difference diffraction pattern $⟨\mathrm{\Delta }{I}_{\mathrm{sim}}(t,s,\varphi )⟩$ averaged over $t=50\mathrm{fs}$ to 550 fs. The color scales are in arbitrary units. (c) through (f): experimental difference diffraction patterns $\mathrm{\Delta }{I}_{\exp }(ts,\varphi )$ at $t=-184\mathrm{fs}$, $t=17\mathrm{fs}$, $t=217\mathrm{fs}$, and $t=417\mathrm{fs}$, respectively.

Figure 3

(a),(b) The experimental (a) and simulated (b) time-resolved modified scattering intensity difference $\mathrm{\Delta }sM(t,s)$. (c), (d) The experimental (c) and simulated (d) time-resolved modified scattering intensity of the excited state $s{M}_{\text{Excited}}(t,s)$. The pattern in (c) was generated by adding the known contribution from ground state to the experimental pattern in (a). The pattern in (d) was generated by adding the known contribution from ground state to the simulated pattern in (b). The experiment misses $s$ values between 0 and $1.6{\AA }^{-1}$ (area underneath the white dashed line in each pattern) due to a hole in the detector that serves to transmit the main electron beam.

Figure 4

(a) Time-resolved experimental (blue circles with error bars) and simulated (red dashed line) bond lengths from a single sine fit of $sM$. (b) The experimental (left panel) and simulated (right panel) time-resolved probability density function of the wave packet, $P(t,r)$, calculated using Eq. (5). The dashed red line is the results of the theoretical calculation with the same spatial resolution as the experiment, and the solid green line includes also averaging due to the temporal resolution (230 fs). The black dotted line indicates the baseline for each curve.