  Low-frequency classical $1/f$-noise and quantum noise from low-temperature
phonon modes are ubiquitous across various experimental platforms, and are
usually considered a hindrance for quantum technological applications. Here we
show that the simultaneous action of classical $1/f$ noise and a
low-temperature phonon bath on a nonlinear oscillator can result in the
generation of nonclassical antibunched radiation without the need for any
additional drive. The $1/f$ noise itself provides the source of energy for
generation of photons, while the phonon bath prevents heating up to infinite
temperature and takes the nonlinear oscillator to a noise-averaged
non-equilibrium steady state. The photon current in this non-equilibrium steady
state may be detected by a standard wide-band detector. For sufficient
nonlinearity and frequency dependence of the effective noise spectrum, the
detected radiation can be antibunched. This opens the possibility to turn two
of the most ubiquitous intrinsic noises in experimental platforms from a
hindrance to a resource. It shows that wasteful heat from unavoidable noises
can be converted into useful radiation. These results are based on the Redfield
equation, which provides a rigorously derived general approach to treat any
type of weak noise in a quantum system, specified only via the noise spectral
function, as we discuss in detail.
