  We revisit the confinement-induced p-wave resonance in quasi-one-dimensional
(quasi-1D) atomic gases and study the induced molecules near resonance. We
derive the reduced 1D interaction parameters and show that they can well
predict the binding energy of shallow molecules in quasi-1D system.
Importantly, these shallow molecules are found to be much more spatially
extended compared to those in three dimensions (3D) without transverse
confinement. Our results strongly indicate that a p-wave interacting atomic gas
can be much more stable in quasi-1D near the induced p-wave resonance, where
most weight of the molecule lies outside the short-range regime and thus the
atom loss could be suppressed.
