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

Abstract

High-precision atom interferometry allows application to dark-matter and gravitational-wave detection. This work investigates the wave-packet evolution for an atom's center of mass during a laser pulse driving a single photon or Raman transition of arbitrary duration as well as a Bragg transition in the deep Bragg regime. 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, with square and gaussian pulse shapes. The investigation further includes the most general case involving non-vanishing detuning. 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.