Each atom in a
population of atoms can be characterized by a probability
density distribution (PDD). Using a shaken-lattice technique, each PDD is split into a pair of sub-PDDs. The sub-PDDs of a pair are propagated along different paths to a common endpoint of the paths, resulting in a matter-wave interference pattern that encodes a net phase between the paths, e.g., due to
differential effects associated with a
gravity gradient. The matter-wave interference pattern can be measured to yield a respective measurement for each atom. The measurements can be aggregated to yield a result distribution that can serve as a classical domain estimate of the
quantum-domain matter-wave interference pattern, and thus of the
gravity gradient. Other embodiments can determine gradients for other types of fields.