  We experimentally demonstrate two multidimensional atom interferometers
capable of measuring both the magnitude and direction of applied inertial
forces. These interferometers do not rely on the ubiquitous light-pulses of
traditional atom sensors, but are instead built from an innovative design that
operates entirely within the Bloch bands of an optical lattice formed by
interfering laser beams. Through time-dependent control of the position of the
lattice in three-dimensional space, we realize simultaneous Bloch oscillations
in two dimensions, and a vector atomic Michelson interferometer. Fits to the
observed Bloch oscillations demonstrate the measurement of an applied
acceleration of $2g$ along two axes, where $g$ is the average gravitational
acceleration at the Earth's surface. For the Michelson interferometer, we
perform Bayesian inferencing from a 49-channel output by repeating experiments
for selected examples of two-axis accelerations. We demonstrate the resulting
accuracy and sensitivity for vector parameter estimation. Our acceleration can
be measured from a single experimental run and does not require repeated shots
to construct a fringe. We find the performance of our device to be near the
quantum limit for the interferometer size and quantum detection efficiency of
the atoms. We discuss the reconfigurability of the vector accelerometer and the
pathway toward further sensitivity.
