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.

We present a general framework for understanding carrier-envelope phase (CEP) effects in a quantum system interacting with an intense, short laser pulse. We establish a simple connection between the CEP and the wave function that can be exploited to obtain the full CEP dependence of an observable given the wave function at a single CEP. Within this framework, all CEP effects are interpreted as interference between different photon amplitudes which, in turn, can be used to put limits on the pulse lengths and intensities required to see significant CEP effects.

The elastic scattering amplitudes of indistinguishable, bosonic, strongly polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semiclassical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these universal characteristics are predicted.