We analyze the recoil shift for atoms in Gaussian laser beams and microwave cavities. The frequency shifts from the transverse photon recoils must be understood for the most accurate atom interferometers and atomic fountain clocks.
When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.
We report on the observation of collapse and revival of the fringe pattern in a multiple-beam atom interferometer, when the drift time between the beam splitting processes is varied. The atomic beam splitters are realized with laser pulses pumping the atoms into velocity selective dark states. For small drift times, the interference signal shows the sharply peaked Airy function-like pattern characteristic for multiple-beam interference. The fringe pattern collapses for larger drift times due to a recoil phase shift increasing quadratically with the transverse atomic momentum. When the total interaction time reaches an integer multiple of the inverse two-photon recoil energy in frequency units, the original fringe pattern is revived.
In an atom interferometry experiment, the output phase shift depends on the wave vector of photons and the recoil momentum in optical transitions. This Letter puts forward a hypothesis that in light-atom interaction, the atom wave function could provide a transverse confinement to photons and thus could affect the mean recoil momentum. We propose a model to analyze the photon effective wave vector in a monochromatic optical field and calculate the relative shift of |k[over →]_{eff}| to k when an atom with a 3D Gaussian wave function absorbs one photon in a Gaussian beam. This shift could lead to a systematic effect related to the spatial distribution of atoms and the transverse beam profile in high-precision experiments based on atom interferometry.