Dephasing due to electromagnetic interactions in spatial qubits

Matter-wave interferometers with micro-particles are excellent quantum sensors as they can be sensitive to a minute quantum phase information, which a classical detector cannot. Two such adjacent micro-particles in the interferometers can be entangled solely via the quantum nature of gravity known as the quantum gravity-induced entanglement of masses (QGEM) protocol. The micro-particles can also be entangled via EM interactions. Therefore, it is essential to estimate the decoherence, noise/dephasing rate for such interferometers. In this paper, we will focus on a particular source of an electromagnetic interaction. We will treat this interaction as a noise which will lead to dephasing. We assume that our matter-wave interferometer has a residual charge which can interact with a neighbouring ion in the ambience, e.g., inside the experimental capsule. This will provide dephasing of the matter-wave interferometer due to the Coulomb interaction with external charges and the charge-dipole interaction with external dielectrics or dipoles. Similarly, we will consider neutral micro-particles, which can interact with charged and/or neutral particles in the ambience via induced dipole-charge, permanent dipole-charge, and dipole-dipole interactions. All these interactions constitute electromagnetically driven dephasing to a single and a twin interferometer. We will discuss their relevance for the QGEM experiment and provide insight into the noise of an entangled state for charged micro-particles kept adjacently with an implication for the C-NOT gate.