  Recently, the Hellings Downs correlation has been observed by different
pulsar timing array (PTA) collaborations, such as NANOGrav, European PTA,
Parkes PTA, and Chinese PTA. These PTA measurements of the most precise pulsars
within the Milky Way show the first evidence for the stochastic gravitational
wave background of our Universe. We study the ultralight axion interpretation
of the new discovery by investigating the gravitational wave from axion
transitions between different energy levels of the gravitational atoms, which
are composed of cosmic populated Kerr black holes and their surrounding axion
clouds formed from the superradiant process. We demonstrate that this new
observation naturally admits an ultralight axion interpretation around
$2\times10^{-21}$~eV, which is consistent with the typical fuzzy dark matter.
