We propose a tractor atom interferometer (TAI) based on three-dimensional (3D) confinement and transport of split atomic wavefunction components in potential wells that follow programmed paths. The paths are programmed to split and recombine atomic wavefunctions at well-defined space-time points, guaranteeing closure of the interferometer. Uninterrupted 3D confinement of the interfering wavefunction components in the tractor wells eliminates coherence loss due to wavepacket dispersion. Using Crank-Nicolson simulation of the time-dependent Schrodinger equation, we compute the quantum evolution of scalar and spinor wavefunctions in several TAI sample scenarios. The interferometric phases extracted from the wavefunctions allow us to quantify gravimeter sensitivity, for the TAI scenarios studied. We show that spinor-TAI supports matter-wave beam splitters that are more robust against non-adiabatic effects than their scalar-TAI counterparts. We confirm the validity of semiclassical path-integral phases taken along the programmed paths of the TAI. Aspects for future experimental realizations of TAI are discussed.
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