Wave-packet evolution during a laser pulse for single- and two-photon atomic diffraction

Abstract

Light-pulse atom interferometry is a valuable tool for high-precision inertial sensing and also offers promising prospects for dark-matter and gravitational-wave detection. This work investigates the wave-packet evolution for an atom's center of mass during a laser pulse of arbitrary duration driving either a single-photon transition or Raman diffraction, and the results are also valid for Bragg diffraction in the deep Bragg regime. In particular, we consider the effects of finite pulse duration on the central trajectory of the atomic wave packets for beam-splitter and mirror pulses as well as pulses with arbitrary pulse areas. Our analysis encompasses a wide range of the cases including square and Gaussian pulse shapes as well as an arbitrary detuning of the central momentum.

While the resulting deviations of the central trajectories are typically quite small, they can have a significant impact on the interferometric phase shift in high-precision measurements and a detailed analysis is therefore important. Our approach relies on a description of the matter-wave propagation in terms of central trajectories and centered wave packets.