  We propose a new method to detect low-energy neutrinos and low-mass dark
matter at or below the MeV scale, through their coherent scatterings from
freely falling heavy atoms and the resulting kinematic shifts. We start with a
simple calculation for illustration: for $10^7$ heavy atoms of a mass number
around 100 with a small recoil energy of 1 meV, the corresponding velocities
can reach $0.01, {\rm m/s}$ and produce significant kinematic shifts that can
be detected. We then show that the proposed device should be able to probe vast
low-energy regions of neutrinos from meV to MeV and can surpass previous limits
on sub-MeV dark matter by several orders of magnitude. Such a proposal can be
useful to (1) detect sub-MeV-scale dark matter: with $10^2$ atom guns shooting
downwards, for example, CsI or lead clusters consisting of $10^{7}$ atoms with
a frequency around $10^3$ Hz, it can already be sensitive to scattering
cross-sections at the level of $10^{-33 (-34)}\rm{cm}^{2}$ for 1 (0.1) MeV dark
matter and surpass current limits. Technological challenges include
high-quality atom cluster production and injections. (2) Measure coherent
neutrino-nuclei scatterings at the 0.1-1 MeV region for the first time: with
$10^4$ atom guns shooting downwards CsI clusters consisting of $10^{11}$ atoms
and a frequency of $10^{6}$ Hz. One can expect 10 events from MeV solar
neutrinos to be observed per year. Furthermore, (3) this method can be extended
to probe very low-energy neutrinos down to the eV-KeV region and may be able to
detect the cosmic neutrino background, although it remains challenging.
