  Resonant inelastic x-ray scattering (RIXS) at the oxygen $K$-edge has
recently accessed multi-spinon excitations in the one-dimensional
antiferromagnet (1D-AFM) \sco, where four-spinon excitations are resolved
separately from the two-spinon continuum. This technique, therefore, provides
new opportunities to study fractionalized quasiparticle excitations in doped
1D-AFMs. To this end, we carried out exact diagonalization studies of the doped
$t$-$J$ model and provided predictions for oxygen $K$-edge RIXS experiments on
doped 1D-AFMs. We show that the RIXS spectra are rich, containing distinct two-
and four-spinon excitations, dispersive (anti)holon excitations, and
combinations thereof. Our results highlight how RIXS complements inelastic
neutron scattering experiments by accessing additional charge and spin
components of fractionalized quasiparticles.
