  Obtaining full control over the internal and external quantum states of
molecules is the central goal of ultracold chemistry and allows for the study
of coherent molecular dynamics, collisions and tests of fundamental laws of
physics. When the molecules additionally have a permanent electric dipole
moment, the study of dipolar quantum gases and spin-systems with long-range
interactions as well as applications in quantum information processing are
possible. Rydberg molecules constitute a class of exotic molecules, which are
bound by the interaction between the Rydberg electron and the ground state
atom. They exhibit extreme bond lengths of hundreds of Bohr radii and giant
permanent dipole moments in the kilo-Debye range. A special type with
exceptional properties are the so-called butterfly molecules, whose electron
density resembles the shape of a butterfly. Here, we report on the
photoassociation of butterfly Rydberg molecules and their orientation in a weak
electric field. Starting from a Bose-Einstein condensate of rubidium atoms, we
fully control the external degrees of freedom and spectroscopically resolve the
rotational structure and the emerging pendular states in an external electric
field. This not only allows us to extract the bond length, the dipole moment
and the angular momentum of the molecule but also to deterministically create
molecules with a tunable bond length and orientation. We anticipate direct
applications in quantum chemistry, many-body quantum physics and quantum
information processing.
