  The motion of doped electrons or holes in an antiferromagnetic lattice with
strong on-site Coulomb interactions touches one of the most fundamental open
problems in contemporary condensed matter physics. The doped charge may
strongly couple to elementary spin excitations resulting in a dressed
quasiparticle which is subject to confinement. This 'spin-polaron' possesses
internal degrees of freedom with a characteristic 'ladder' excitation spectrum.
Despite its fundamental importance for understanding high-temperature
superconductivity, clear experimental spectroscopic signatures of these
internal degrees of freedom are scarce. Here we present scanning tunneling
spectroscopy results of the spin-orbit-induced Mott insulator Sr$_2$IrO$_{4}$.
Our spectroscopy data reveal distinct shoulder-like features for occupied and
unoccupied states beyond a measured Mott gap of $\Delta\approx620$~meV. Using
the self-consistent Born approximation we assign the anomalies in the
unoccupied states to the spin-polaronic ladder spectrum with excellent
quantitative agreement and estimate the Coulomb repulsion $U$ = 2.05 ...2.28 eV
in this material. These results confirm the strongly correlated electronic
structure of this compound and underpin the previously conjectured paradigm of
emergent unconventional superconductivity in doped Sr$_2$IrO$_{4}$.
