  Triangular symmetric molecules with mirror symmetry perpendicular to the
3-fold axis are forbidden to have a fixed electrical dipole moment. However, if
the ground state is orbitally degenerate and lacks inversion symmetry, then a
``quantum'' dipole moment does exist. The system of 3 electrons in D_3h
symmetry is our example. This system is realized in triatomic molecules like
Na_3. Unlike the fixed dipole of a molecule like water, the quantum moment does
not point in a fixed direction, but lies in the plane of the molecule and takes
quantized values +/- mu_0 along any direction of measurement in the plane. An
electric field F in the plane leads to a linear Stark splitting +/- mu_0 F}. We
introduce a toy model to study the effect of Jahn-Teller distortions on the
quantum dipole moment. We find that the quantum dipole property survives when
the dynamic Jahn-Teller effect is included, if the distortion of the molecule
is small. Linear Stark splittings are suppressed in low fields by molecular
rotation, just as the linear Stark shift of water is suppressed, but will be
revealed in moderately large applied fields and low temperatures. Coulomb
correlations also give a partial suppression.
