Decoherence of a matter-wave interferometer due to dipole-dipole interactions

Matter-wave interferometry with nanoparticles will enable the development of quantum sensors capable of probing ultraweak fields with unprecedented applications for fundamental physics. The high sensitivity of such devices however makes them susceptible to a number of noise and decoherence sources and as such can only operate when sufficient isolation from the environment is achieved. It is thus imperative to model and characterize the interaction of nanoparticles with the environment and to estimate its deleterious effects. The aim of this paper will be to study the decoherence of the matter-wave interferometer due to dipole-dipole interactions which is one of the unavoidable channels for decoherence even for a neutral micro-crystal. We will start the analysis from QED and show that it reduces to the scattering model characterized by the differential cross-section. We will then obtain simple expressions for the decoherence rate in the short and long wavelength limits that can be readily applied to estimate the available coherence time. We will conclude by applying the obtained formulae to estimate the dipole-dipole decoherence rate for the Quantum Gravity-induced Entanglement of Masses (QGEM) protocol and discuss if the effects should be mitigated.