  Matter-wave interferometers with micro-particles will enable the next
generation of quantum sensors to probe minute quantum phase information.
Therefore, estimating the loss of coherence and the degree of entanglement
degradation for such interferometers is essential. In this paper, we will
provide a noise analysis in frequency-space focusing on electromagnetic sources
of dephasing. We will assume that our matter-wave interferometer has a residual
charge or dipole which can interact with a neighbouring particle in the
ambience. We will investigate the dephasing due to the Coulomb, charge-induced
dipole, charge-permanent dipole, and dipole-dipole interactions. All these
interactions constitute electromagnetically driven dephasing channels that can
affect single or multiple interferometers. As an example, we will apply the
obtained formulae to situations with two adjacent micro-particles, which can
provide insight for the noise analysis in the quantum gravity-induced
entanglement of masses (QGEM) protocol and the C-NOT gate: we will compute the
dephasing due to a gas of environmental particles interacting via dipole-dipole
and charge-charge couplings, respectively. To obtain simple analytical
dephasing formulae, we will employ uniform probability distributions for the
impact parameter and for the angles characterizing the relative orientation
with respect to the interferometer and a Gaussian distribution for the
velocities of the environmental particles. In both cases, we will show that the
dephasing rate grows with the number density of particles present in the vacuum
chamber, as expected.
