Transverse Confinement of Photon Position in Light-Atom Interaction

In light-pulsed atom interferometry, the phase accumulated by atoms depends on the effective wave vector of the absorbed photons. In this work, we proposed a theory model to analyses the effective wave vector of photons in structured light. As for monochromatic optical field, a transverse confinement could lead to diffraction. We put forward that in light-atom interaction, the atom wave function could also provide a transverse confinement thus affect the effective wave vector of the absorbed photons. We calculated the relative shift of the photon effective wave vector when an atom with a Gaussian wave function absorbs one photon at the waist in a Gaussian beam. This shift could lead to a systematic effect related to atom spatial distribution in high precision experiment based on light-pulsed atom interferometry.