  We present here a method for the extraction of the differential phase of an
atom gradiometer that exploits the correlation of the vibration signal measured
by an auxiliary classical sensor, such as a seismometer or an accelerometer. We
show that sensitivities close to the quantum projection noise limit can be
reached, even when the vibration noise induces phase fluctuations larger than
2$\pi$. This method doesn't require the correlation between the atomic and
classical signals to be perfect and allows for an exact determination of the
differential phase, with no bias. It can also be applied to other
configurations of differential interferometers, such as for instance
gyrometers, conjugate interferometers for the measurement of the fine structure
constant, or differential accelerometers for tests of the equivalence principle
or detection of gravitational waves.
