Optical conductivity due to orbital polarons in systems with orbital degeneracy

We consider the impact of orbital polarons in doped orbitally ordered systems on optical conductivity using the simplest generic model capturing the directional nature of either $t_{2g}$ (or $e_g$) orbital states in certain transition metal oxides, or $p$ orbital states of cold atoms in optical lattices. The origin of the optical transitions is analyzed in detail and we demonstrate that the optical spectra: (i) are determined by the string picture, i.e., flipped orbitals along the hole hopping path, and (ii) consist of three narrow peaks which stem from distinct excitations. They occur within the Mott-Hubbard gap similar to the superconducting cuprates but indicate hole confinement, in contrast to the spin t-J model. Finally, we point out how to use the point group symmetry to classify the optical transitions.