  We present a method utilizing atomic diffraction patterns and statistical
analysis tools to infer the Casimir-Polder interaction between Argon atoms and
a silicon nitride nanograting. The quantum model that supports the data is
investigated in detail, as are the roles of nanograting geometry, finite size
effects, slit width opening angles, and Lennard-Jones potentials. Our findings
indicate that the atom-surface potential strength parameter is C3 = 6.87 $\pm$
1.18 meV.nm3. This value is primarily constrained by the knowledge of the
nanograting geometry. The high sensitivity of our method paves the way for
precise determination of the Casimir-Polder potential and exploration of new
short-distance forces.
