We study radiative relaxation at terahertz frequencies in n-type Ge/SiGe quantum wells, optically pumped with a terahertz free electron laser. Two wells coupled through a tunneling barrier are designed to operate as a three-level laser system with non-equilibrium population generated by optical pumping around the 1→3 intersubband transition at 10 THz. The non-equilibrium subband population dynamics are studied by absorption-saturation measurements and compared to a numerical model. In the emission spectroscopy experiment, we observed a photoluminescence peak at 4 THz, which can be attributed to the 3→2 intersubband transition with possible contribution from the 2→1 intersubband transition. These results represent a step towards silicon-based integrated terahertz emitters.