  We present the first characterization of the circumgalactic medium of
Ly$\alpha$ emitters (LAEs), using a sample of 96 $z\approx3.3$ LAEs detected
with the VLT/MUSE in fields centered on 8 bright background quasars. The LAEs
have low Ly$\alpha$ luminosities ($\sim 10^{42}\,\text{erg}\,\text{s}^{-1}$)
and star formation rates (SFRs) $\sim 1~\text{M}_\odot\,\text{yr}^{-1}$, which
for main sequence galaxies corresponds to stellar masses of only $\sim
10^{8.6}\,\text{M}_\odot$. The median transverse distance between the LAEs and
the quasar sightlines is 165 proper kpc (pkpc). We stacked the high-resolution
quasar spectra and measured significant excess HI and CIV absorption near the
LAEs out to 500 $\text{km}\,\text{s}^{-1}$ and at least $\approx 250$ pkpc
(corresponding to $\approx 7$ virial radii). At $\lesssim
30~\text{km}\,\text{s}^{-1}$ from the galaxies the median HI and CIV optical
depths are enhanced by an order of magnitude. The absorption is significantly
stronger around the $\approx 1/3$ of our LAEs that are part of `groups', which
we attribute to the large-scale structures in which they are embedded. We do
not detect any strong dependence of either the HI or CIV absorption on
transverse distance (over the range $\approx 50-250$ pkpc), redshift, or the
properties of the Ly$\alpha$ emission line (luminosity, full width at half
maximum, or equivalent width). However, for HI, but not CIV, the absorption at
$\lesssim 100\,\text{km}\,\text{s}^{-1}$ from the LAE does increase with the
SFR. This suggests that LAEs surrounded by more HI tend to have higher SFRs.
