  Atomic interferometers measure forces and acceleration with exceptional
precision. The conventional approach to atomic interferometry is to launch an
atomic cloud into a ballistic trajectory and perform the wave-packet splitting
in momentum space by Raman transitions. This places severe constraints on the
possible atomic trajectory, positioning accuracy and probing duration. Here, we
propose and analyze a novel atomic interferometer that uses micro-optical traps
(optical tweezers) to manipulate and control the motion of atoms. The new
interferometer allows long probing time, sub micrometer positioning accuracy,
and utmost flexibility in shaping of the atomic trajectory. The cornerstone of
the tweezer interferometer are the coherent atomic splitting and combining
schemes. We present two adiabatic schemes with two or three tweezers that are
robust to experimental imperfections and work simultaneously with many
vibrational states. The latter property allows for multi-atom interferometry in
a single run. We also highlight the advantage of using fermionic atoms to
obtain single-atom occupation of vibrational states and to eliminate mean-field
shifts. We examine the impact of tweezer intensity noise and demonstrate that,
when constrained by shot noise, the interferometer can achieve a relative
accuracy better than $10^{-11}$ in measuring Earth's gravitational
acceleration. The sub-micrometer resolution and extended measurement duration
offer promising opportunities for exploring fundamental physical laws in new
regimes. We discuss two applications well-suited for the unique capabilities of
the tweezer interferometer: the measurement of gravitational forces and the
study of Casimir-Polder forces between atoms and surfaces. Crucially, our
proposed tweezer interferometer is within the reach of current technological
capabilities.
