  Post-starburst (PSB) galaxies may be in rapid transition from star-forming to
quiescence and are excellent candidates to constrain active galactic nuclei
(AGN) feedback models. We study galactic winds in the stacked spectrum of 560
AGN PSBs and that of a control sample of star-forming galaxies in the Sloan
Digital Sky Survey (SDSS). Using a two component (inter-stellar +wind)
absorption-line model of the \ion{Na}{i} doublet, and after accounting for the
stellar photospheric absorption, we find that the AGN PSBs have a centroid wind
velocity shift of $-252^{+64}_{-57}$ km s$^{-1}$ and a maximum blueshift
velocity of $-678^{+54}_{-53}$ km s$^{-1}$. In comparison, the control sample,
which is matched with the AGN PSBs in redshift, stellar mass, axis-ratio, the
4000 {\AA} break index, Balmer decrement, and WISE 12 $\mu$m to 4.6 $\mu$m flux
ratio, has a centroid wind velocity shift of $-119^{+33}_{-41}$ km s$^{-1}$ and
a maximum velocity of $-406^{+51}_{-61}$ km s$^{-1}$. The equivalent widths due
to the winds in both samples are similar: $0.36^{+0.10}_{-0.07}$ {\AA} for the
AGN PSBs and $0.24^{+0.07}_{-0.06} $ {\AA} for the control sample. Despite
having a higher velocity, the observed winds in the AGN PSBs are still not
powerful enough to sweep significant amounts of gas out of the halos of the
host galaxies. We also detect winds of similar velocities in the stacked
spectra of shocked and quenched PSBs.
