  We propose an experimental setup to observe coherent elastic neutrino-atom
scattering (CE$\nu$AS) using electron antineutrinos from tritium decay and a
liquid helium target. In this scattering process with the whole atom, that has
not beeen observed so far, the electrons tend to screen the weak charge of the
nucleus as seen by the electron antineutrino probe. The interference between
the nucleus and the electron cloud produces a sharp dip in the recoil spectrum
at atomic recoil energies of about 9 meV, reducing sizeably the number of
expected events with respect to the coherent elastic neutrino-nucleus
scattering case. We estimate that with a 60 g tritium source surrounded by 500
kg of liquid helium in a cylindrical tank, one could observe the existence of
CE$\nu$AS processes at 3$\sigma$ in 5 years of data taking. Keeping the same
amount of helium and the same data-taking period, we test the sensitivity to
the Weinberg angle and a possible neutrino magnetic moment for three different
scenarios: 60 g, 160 g, and 500 g of tritium. In the latter scenario, the
Standard Model (SM) value of the Weinberg angle can be measured with a
statistical uncertainty of
$\sin^2{\vartheta_W^{\mathrm{SM}}}^{+0.015}_{-0.016}$. This would represent the
lowest-energy measurement of $\sin^2{\vartheta_W}$, with the advantage of being
not affected by the uncertainties on the neutron form factor of the nucleus as
the current lowest-energy determination. Finally, we study the sensitivity of
this apparatus to a possible electron neutrino magnetic moment and we find that
using 60 g of tritium it is possible to set an upper limit of about
$7\times10^{-13}\,\mu_B$ at 90% C.L., that is more than one order of magnitude
smaller than the current experimental limit.
