Modelling Gravitational Noise from Background Particles in Atom Interferometry

As atom interferometers increase their extent in space and time, the increased sensitivity demands analysis of new noise sources, for example noise from uncontrolled gravitating background particles. Modelling this noise with the standard collisional decoherence theory presents two challenges: first, the standard collisional decoherence formula diverges for 1/r interactions, and second, collisional decoherence fails to incorporate the equivalence principle, thus overestimating the effect of far away bath particles. Here we analyze a model of atom interferometry in the presence of a gravitating bath that explicitly includes the effect of the bath on the control apparatus, not just the atoms, doing all calculations in a finite-time framework to avoid unphysical divergences. We find the bath phase space can be usefully separated into two sectors: far away particles, which give rise to a stochastic spacetime curvature background, and a collision cone which causes decoherence "events" localized in time. We comment on prospects for observing gravitational noise from each bath phase space sector.