  Engineering quantum particle systems, such as quantum simulators and quantum
cellular automata, relies on full coherent control of quantum paths at the
single particle level. Here we present an atom interferometer operating with
single trapped atoms, where single particle wave packets are controlled through
spin-dependent potentials. The interferometer is constructed from a sequence of
discrete operations based on a set of elementary building blocks, which permit
composing arbitrary interferometer geometries in a digital manner. We use this
modularity to devise a spacetime analogue of the well-known spin echo
technique, yielding insight into decoherence mechanisms. We also demonstrate
mesoscopic delocalization of single atoms with a "separation-to-localization"
ratio exceeding 500; this suggests their utilization beyond quantum logic
applications as nano-resolution quantum probes in precision measurements, being
able to measure potential gradients with precision $5\times 10^{-4}$ in units
of gravitational acceleration $g$.
