  Quantum coherence is an essential resource to gain advantage over classical
physics and technology. Recently, it has been proposed that a low-temperature
environment can induce quantum coherence of a spin without an external coherent
pump. We address a critical question if such coherence is extractable by a weak
coupling to an output system dynamically affecting back the spin-environment
coupling. Describing the entire mechanism, we prove that such extraction is
generically possible for output spins (also oscillators or fields) and, as
well, in a fermionic analogue of such a process. We compare the internal spin
coherence and output coherence over temperature and characteristic frequencies.
The proposed optimal coherence extraction opens paths for the upcoming
experimental tests with atomic and solid-state systems.
