  We present a novel method for probing the alignment of the molecular axis of
an ultracold, nonpolar dimer. These results are obtained using diatomic
$^{87}\textrm{Rb}_2$ molecules in the vibrational ground state of the lowest
triplet potential $a^3\Sigma_u^+$ trapped in a 3D optical lattice. We measure
the molecular polarizabilities, which are directly linked to the alignment,
along each of the $x$, $y$, and $z$ directions of the lab coordinate system. By
preparing the molecules in various, precisely defined rotational quantum states
we can control the degree of alignment of the molecular axis with high
precision over a large range. Furthermore, we derive the dynamical
polarizabilities for a laser wavelength of $1064.5\:\textrm{nm}$ parallel and
orthogonal to the molecular axis of the dimer, $\alpha_\parallel=(8.9 \pm
0.9)\times10^3\:\textrm{a.u.}$ and $\alpha_\perp=(0.9 \pm
0.4)\times10^3\:\textrm{a.u.}$, respectively. Our findings highlight that the
depth of an optical lattice strongly depends on the rotational state of the
molecule which has to be considered in collision experiments. The present work
paves the way for reaction studies between aligned molecules in the ultracold
temperature regime.
