Atom interferometers have been used to measure acceleration with at best a
T2 scaling in sensitivity as the interferometer time
T is increased. This limits the sensitivity to acceleration which is theoretically achievable by these configurations for a given frequency of acceleration. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will scale as
T3. This enhanced scaling will allow an increase in achievable sensitivity for any given frequency of an oscillatory acceleration signal, which will be of particular use for inertial and navigational sensors, and proposed gravitational wave detectors. A straight forward extension should allow a
T4 scaling in acceleration sensitivity.