  Fractionalization of an electronic quasiparticle into spin, charge and
orbital parts is a fundamental and characteristic property of interacting
electrons in one dimension. However, real materials are never strictly
one-dimensional and the fractionalization phenomena are hard to observe. Here
we studied the spin and orbital excitations of the anisotropic ladder material
CaCu2O3, whose electronic structure is not one-dimensional. Combining
high-resolution resonant inelastic x-ray scattering experiments with
theoretical model calculations we show that: (i) spin-orbital fractionalization
occurs in CaCu2O3 along the leg direction x through the xz orbital channel as
in a 1D system; and (ii) no fractionalization is observed for the xy orbital,
which extends in both leg and rung direction, contrary to a 1D system. We
conclude that the directional character of the orbital hopping can select
different degrees of dimensionality. Using additional model calculations, we
show that spin-orbital separation is generally far more robust than the
spin-charge separation. This is not only due to the already mentioned selection
realized by the orbital hopping, but also due to the fact that spinons are
faster than the orbitons.
