Quantum cascade driving: Dissipatively mediated coherences

Quantum cascaded systems offer the possibility to manipulate a target system with the quantum state of a source system. Here, we study in detail the differences between a direct quantum cascade and coherent/incoherent driving for the case of two coupled cavity-QED systems. We discuss qualitative differences between these excitations scenarios, which are particular strong for higher-order photon-photon correlations: $g^{(n)}(0)$ with $ n>2 $. Quantum cascaded systems show a behavior differing from the idealized cases of individual coherent/incoherent driving and allow to produce qualitatively different quantum statistics. Furthermore, the quantum cascaded driving exhibits an interesting mixture of quantum coherent and incoherent excitation dynamics. We develop a measure, where the two regimes intermix and quantify these differences via experimentally accessible higher-order photon correlations.