  Quantum sensors based on the superposition of neutral atoms are promising for
sensing the nature of dark matter (DM). In this study, we utilize the
Stern-Gerlach (SG) interferometer configuration to seek a novel method for the
detection of detect axion-like particles (ALPs). Using an SG interferometer, we
create a spatial quantum superposition of neutral atoms such as $^{3}$He and
$^{87}$Rb. It is shown that the interaction of ALPs with this superposition
induces a relative phase between superposed quantum components. We use the
quantum Boltzmann equation (QBE) to introduce a first-principles analysis that
describes the temporal evolution of the sensing system. The QBE approach
employs quantum field theory (QFT) to highlight the role of the quantum nature
of the interactions with the quantum systems. The resulting exclusion area
demonstrates that our scheme allows for the exclusion of a range of ALP mass in
the range of $10^{-10}\leq m_{a}\leq 10^{2}\,\mathrm{eV}$ and ALP-atom coupling
constant in the range $10^{-13}\leq g_{ae}\leq 10^{0}$.
