  Understanding the crystal field splitting and orbital polarization in
non-centrosymmetric systems such as ferroelectric materials is fundamentally
important. In this study, taking BaTiO$_3$ (BTO) as a representative material
we investigate titanium crystal field splitting and orbital polarization in
non-centrosymmetric TiO$_6$ octahedra with resonant X-ray linear dichroism at
Ti $L_{2,3}$-edge. The high-quality BaTiO$_3$ thin films were deposited on
DyScO$_3$ (110) single crystal substrates in a layer-by-layer way by pulsed
laser deposition. The reflection high-energy electron diffraction (RHEED) and
element specific X-ray absorption spectroscopy (XAS) were performed to
characterize the structural and electronic properties of the films. In sharp
contrast to conventional crystal field splitting and orbital configuration
($d_{xz}$/$d_{yz}$ $<$ $d_{xy}$ $<$ $d_{3z^2-r^2}$ $<$ $d_{x^2-y^2}$ or
$d_{xy}$ $<$ $d_{xz}$/$d_{yz}$ $<$ $d_{x^2-y^2}$ $<$ $d_{3z^2-r^2}$) according
to Jahn-Teller effect, it is revealed that $d_{xz}$, $d_{yz}$, and $d_{xy}$
orbitals are nearly degenerate, whereas $d_{3z^2-r^2}$ and $d_{x^2-y^2}$
orbitals are split with an energy gap $\sim$ 100 meV in the epitaxial BTO
films. The unexpected degenerate states $d_{xz}$/$d_{yz}$/$d_{xy}$ are coupled
to Ti-O displacements resulting from competition between polar and Jahn-Teller
distortions in non-centrosymmetric TiO$_6$ octhedra of BTO films. Our results
provide a route to manipulate orbital degree of freedom by switching electric
polarization in ferroelectric materials.
