  Photonic synthesis of radiofrequency revived the quest for unrivalled
microwave purity by its seducing ability to convey the benefits of the optics
to the microwave world. In this work, we perform a high-fidelity transfer of
frequency stability between an optical reference and a microwave signal via a
low-noise fiber-based frequency comb and cutting-edge photo-detection
techniques. We demonstrate the generation of the purest microwave signal with a
fractional frequency stability below 6.5 x 10^-16 at 1 s and a timing noise
floor below 41 zs.Hz^-1/2 (phase noise below -173 dBc.Hz^-1 for a 12 GHz
carrier). This outclasses existing sources and promises a new era for
state-of-the-art microwave generation. The characterization is achieved by
building two auxiliary low noise optoelectronic microwave reference and using a
heterodyne cross-correlation scheme with lowermost detection noise. This
unprecedented level of purity can impact domains such as radar systems,
telecommunications and time-frequency metrology. Furthermore, the measurement
methods developed here can benefit the characterization of a broad range of
signals, beyond comb-based systems.
