Steady-state coherences by composite system-bath interactions

We identify sufficient conditions on the structure of the interaction Hamiltonian between a two-level quantum system and a thermal bath which, without any external drive or coherent measurement, guarantee the generation of steady-state coherences (SSC). The SSC this way obtained remarkably turn out to be independent on the initial state of the system, which therefore could be even taken initially incoherent. We characterize in detail this phenomenon first analytically in the weak coupling regime for two paradigmatic models, and then numerically in more complex systems without any assumption on the coupling strength. In all these cases we find that SSC become increasingly significant as the bath is cooled down. These results can be therefore directly verified in many experimental platforms.