  Laser-induced molecular alignment is well understood within the framework of
the Born-Oppenheimer (BO) approximation Without the BO approximation, however,
the concept of molecular structure is lost, making alignment hard to define
precisely. In this work, we demonstrate the emergence of alignment from the
first-ever non-BO quantum dynamics simulations, using the HD molecule exposed
to ultrashort laser pulses as a few-body test case We extract the degree of
alignment from the non-BO wave function by means of an operator expressed in
terms of pseudo-proton coordinates that mimics the BO-based definition of
alignment The only essential approximation, in addition to the semiclassical
electric-dipole approximation for the matter-field interaction, is the choice
of time-independent explicitly correlated Gaussian basis functions. We use a
variational, electric-field-dependent basis-set construction procedure, which
allows us to keep the basis-set dimension low whilst capturing the main effects
of electric polarization on the nuclear and electronic degrees of freedom. The
basis-set construction procedure is validated by comparing with virtually exact
grid-based simulations for two one-dimensional model systems: laser-driven
electron dynamics in a soft attractive Coulomb potential and nuclear
rovibrational dynamics in a Morse potential.
