  We investigate the formation of dense stellar clumps in a suite of
high-resolution cosmological zoom-in simulations of a massive, star forming
galaxy at $z \sim 2$ under the presence of strong quasar winds. Our simulations
include multi-phase ISM physics from the Feedback In Realistic Environments
(FIRE) project and a novel implementation of hyper-refined accretion disk
winds. We show that powerful quasar winds can have a global negative impact on
galaxy growth while in the strongest cases triggering the formation of an
off-center clump with stellar mass ${\rm M}_{\star}\sim 10^{7}\,{\rm
M}_{\odot}$, effective radius ${\rm R}_{\rm 1/2\,\rm Clump}\sim 20\,{\rm pc}$,
and surface density $\Sigma_{\star} \sim 10^{4}\,{\rm M}_{\odot}\,{\rm
pc}^{-2}$. The clump progenitor gas cloud is originally not star-forming, but
strong ram pressure gradients driven by the quasar winds (orders of magnitude
stronger than experienced in the absence of winds) lead to rapid compression
and subsequent conversion of gas into stars at densities much higher than the
average density of star-forming gas. The AGN-triggered star-forming clump
reaches ${\rm SFR} \sim 50\,{\rm M}_{\odot}\,{\rm yr}^{-1}$ and $\Sigma_{\rm
SFR} \sim 10^{4}\,{\rm M}_{\odot}\,{\rm yr}^{-1}\,{\rm kpc}^{-2}$, converting
most of the progenitor gas cloud into stars in $\sim$2\,Myr, significantly
faster than its initial free-fall time and with stellar feedback unable to stop
star formation. In contrast, the same gas cloud in the absence of quasar winds
forms stars over a much longer period of time ($\sim$35\,Myr), at lower
densities, and losing spatial coherency. The presence of young, ultra-dense,
gravitationally bound stellar clumps in recently quenched galaxies could thus
indicate local positive feedback acting alongside the strong negative impact of
powerful quasar winds, providing a plausible formation scenario for globular
clusters.
