Observation of Quantum Interferences via Light-Induced Conical Intersections in Diatomic Molecules

We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion ${\mathrm{H}}_2^{+}$. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed two-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state and the cone apex. These findings are supported by numerical solutions of the time-dependent Schrödinger equation for similar experimental conditions.

Figure 1

PESs of ${\mathrm{H}}_2^{+}$ and the LICI. (a) The dressed adiabatic surfaces versus the interatomic distance $R$ and angle $\theta$ between the laser polarization and the molecular axis exhibiting the LICI (field intensity: $4\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$). (b) The diabatic potential energy curves of the lower $1s{\sigma }_g$ (solid black line) and field dressed excited $2p{\sigma }_u$ states (dashed blue line) of ${\mathrm{H}}_2^{+}$ form a LICI at $R\simeq 4.8\mathrm{a}.\mathrm{u}.$ The red curves show a cut at $\theta =0$ where the adiabatic dynamics prevails.

Figure 2

Measured dissociation yield versus angle of ${\mathrm{H}}_2^{+}$ for different kinetic energy release values that correspond to the vibration levels (a) $v=7$ at 0.5 eV, (b) $v=8$ at 0.67 eV, and (c) $v=9$ at 0.83 eV. The angular distributions reveal modulations at different angles that increase from $v=7$ to $v=9$. The shaded area represents the standard error of the measurement. The solid traces are the angular distributions following symmetrization around $\theta =0$.

Figure 3

Snapshots of the total probability density as a function of the internuclear separation $R$ and angle $\theta$. The initial wave function was the $|v=9,J=0⟩$ rovibrational bound eigenstate of ${\mathrm{H}}_2^{+}$, which depends only on $R$. As the laser pulse interacts with the molecule, we see a transition from a smooth angular distribution to strong modulations. The position of the LICI is at $\theta =\pm \pi /2$ and $R\simeq 4.8$. The laser pulse was 30 fs (FWHM) around 795 nm and its peak intensity happens at $t=0\mathrm{fs}$.

Figure 4

Top: calculated dissociation probability as a function of time and angle for molecules that were initially in the ground rotational state of the (a) $v=7$, (b) $v=8$, and (c) $v=9$ vibrational states. We note that the closer the initial state is to resonance with the laser field, the more time it interacts with the LICI, resulting in more complex interferences in the angular distributions of the instantaneous dissociation probability. Bottom: calculated kinetic energy release curves for the same values and energy bin sizes that are presented in Fig. 2. The kinetic energy release distributions were calculated from the dissociating part of the wave packet of each initial vibration state, and were then normalized by their Franck-Condon coefficient. The interference peaks at $\pm 10°$ and $\pm 35°$ are accurately captured by the model. The differences in intensity, especially around $\theta =0$, are due to the volume averaging effect and the finite rotational temperature that are excluded from this calculation.