Experiment

In our experiments, the molecular ions are produced in an ion source  by a DC electric discharge. They are accelerated to kinetic energies of 11 keV, mass selected and then formed into a well collimated ion beam (Figure 1).

Figure 1. The ion beam apparatus.

A commercial femtosecond laser system produces up to 1000 laser pulses per second, that are centered at a wavelength of 790 nm and have a pulse duration below 100 fs. The laser beam is focused by a lens onto the ion beam achieving very high intensities of up to 10¹⁵ W/cm². This corresponds to electric field of about 10⁹ V/cm. The fragments from the photodissociation and the Coulomb explosion channel are detected on a multichannel plate detector. In this way, we obtain a two-dimensional projection of the fragments' velocity distribution (Figure 2).

Figure 2. Velocity distribution of H₂⁺ fragments as projected onto the two-dimensional detector (laser intensity was I=1·10¹⁵ W/cm² and pulse duration τ=90 fs). The direction of the laser polarization is shown with the arrow. The inserted scale marks kinetic energies per one fragment in the polarization direction. Only one side of the image was really experimentally recoreded, the other side (obtained by mirroring) is shown for completeness.

The fragments from the dissociation (at lower kinetic energies) and the Coulomb explosion (higher kinetic energies) are clearly separated. The Coulomb explosion channel shows a much narrower angular distribution. Also the fragments with low energies in the dissociation channel have a narrow angular distribution due to the nonlinear bond-softening effects. The narrowing of the angular distribution with increasing intensity is shown in Figure 3.

Figure 3. The two-dimensional projection on the detector of H atoms from the photodissociation of H₂⁺ at two different intrensities. The left image was made at an intensity of I=3.5·10¹³ W/cm² (τ=135  fs) and the right one at an intensity of 1.5·10¹⁴ W/cm² (τ=575  fs).

The velocity distributions of fragments originating from different vibrational levels of H₂⁺ were distinguished here for the first time. When intensity is increased, the fragments from lower vibrational levels (v<9) can dissociate via the bond-softening mechanism. They appear at lower kinetic energies in Figure 3 (right) and particular in Figure 4, where the data along the laser polarization direction are shown.

Figure 4. The projected velocity distribution of fragments along the laser polarization axis. The pulse energy was 0.3 mJ and the pulse durations were τ=130 fs (red) and τ=690 fs (green). The comb marks the expected kinetic energy releases for the fragments from different vibrational levels  in one-photon dissociation process. The trapping process for v=11 has been demonstrated for the first time.

The red curve measured at a higher intensity shows the appearance of bond-softening fragments from vibrational level v=7 and v=8. We have found that the energies of these fragments are shifted to lower values with respect to what is expected for an unperturbated molecule. This level-shifting effect can also be understood as a classical effect.