Quantum gases in optical lattices offer a well-controlled and defect free environment to simulate and study phenomena from condensed matter physics. In particular, questions related to conductivity and charge carrier mobility lie at the heart of the properties of many fascinating materials like superconductors, graphene and semiconductors. The latter become conductive if irradiated with photons. This effect is called photoconductivity and results from photon-induced interband transitions of electrons, leading to the creation of electron and hole excitations, which subsequently serve as free charge carriers. Photoconductivity is widely used in technological applications such as semiconductor photodiodes and photoresistors and as a powerful probe for novel materials.