Controlling ${\mathrm{H}\mathrm{D}}^{+}$ and ${\mathrm{H}}_2^{+}$ Dissociation with the Carrier-Envelope Phase Difference of an Intense Ultrashort Laser Pulse

Carrier-envelope phase difference effects in the dissociation of the ${\mathrm{H}\mathrm{D}}^{+}$ molecular ion in the field of an intense, linearly polarized, ultrashort laser pulse are studied in the framework of the time-dependent Schrödinger equation. We consider a reduced-dimensionality model in which the nuclei are free to vibrate along the field polarization and the electrons move in two dimensions. The laser has a central wavelength of 790 nm and a pulse length of 10 fs with intensities in the range $6\times {10}^{14}$ to $9\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. We find that the angular distribution of dissociation to $p+\mathrm{D}$ and $\mathrm{H}+d$ can be controlled by varying the phase difference, generating differences between the dissociation channels of more than a factor of 2. Moreover, the asymmetry is nearly as large for ${\mathrm{H}}_2^{+}$ dissociation.

Figure 1

Schematic of the domains in configuration space defining different final states. The difference between ${\Omega }_H$ and ${\Omega }_D$ is due to mass [see Eq. (2)].

Figure 2

Phase dependence of the ${\mathrm{H}\mathrm{D}}^{+}$ dissociation probabilities to $\mathrm{H}+d$ (solid lines) and to $p+\mathrm{D}$ (dashed lines) for different intensities: (a) $I=6.0$, (b) $I=7.0$, (c) $I=8.0$, and (d) $I=9.0$ in units of ${10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. The error bars indicate our estimated numerical error and are the same for each point in each plot.

Figure 3

Phase dependence of the ${\mathrm{H}}_2^{+}$ dissociation probabilities to H at 0° (solid lines) and to H at 180° (dashed lines) for $I=9\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$.