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We report on an original and simple formulation of the phase shift inN-light-pulse atom interferometers. We consider atomic interferometers based ontwo-photon transitions (Raman transitions or Bragg pulses). Starting from theexact analytical phase shift formula obtained from the atom optics ABCDformalism, we use a power series expansion in time of the position of theatomic wave packet with respect to the initial condition. The result of thisexpansion leads to a formulation of the interferometer phase shift where theleading coefficient in the phase terms up to T^k dependences (k >= 0) in thetime separation T between pulses, can be simply expressed in terms of a productbetween a Vandermonde matrix, and a vector characterizing the two-photon pulsesequence of the interferometer. This simple coefficient dependence of the phaseshift reflects very well the atom interferometer's sensitivity to a specificinertial field in the presence of multiple gravito-inertial effects.Consequently,we show that this formulation is well suited when looking forselective atomic sensors of accelerations, rotations, or photon recoil only,which can be obtained by simply zeroing some specific coefficients. We give atheoritical application of our formulation to the photon recoil measurement.

A phase shift formulation for N-light-pulse atom interferometers: application to inertial sensing