  Atom interferometers are powerful tools for both measurements in fundamental
physics and inertial sensing applications. Their performance, however, has been
limited by the available interrogation time of freely falling atoms in a
gravitational field. We realize an unprecedented interrogation time of 20
seconds by suspending the spatially-separated atomic wavepackets in a lattice
formed by the mode of an optical cavity. Unlike traditional atom
interferometers, this approach allows potentials to be measured by holding,
rather than dropping, atoms. After seconds of hold time, gravitational
potential energy differences from as little as microns of vertical separation
generate megaradians of interferometer phase. This trapped geometry suppresses
the phase sensitivity to vibrations by 3-4 orders of magnitude, overcoming the
dominant noise source in atom-interferometric gravimeters. Finally, we study
the wavefunction dynamics driven by gravitational potential gradients across
neighboring lattice sites.
