Title: Phonon Induced Contrast in Matter Wave Interferometer

Abstract: Utilizing the Stern-Gerlach apparatus to create matter-wave superposition states is a long-sought-after goal, not only due to its potential applications in the quantum realm but also because of its fundamental implications for studying the quantum properties of gravity. The main challenge in creating a macroscopic quantum interferometer arises from the loss of coherence, primarily through two channels. One channel involves strong coupling with the environment for macroscopic matter, leading to decoherence. The other channel relates to the precision of wave packet overlap, which can occur due to external and internal fluctuations of various sources. The latter introduces a unique challenge for larger-scale masses by perturbing the centre of mass motion of the macroscopic object. Here, we study a particular challenge, namely, the issue of internal degrees of freedom, specifically phonon fluctuations and contrast reduction. This work will investigate the contrast reduction caused by spin-magnetic field and diamagnetic interactions at the phonon occupation level in the quantum gravity-induced entanglement of masses (QGEM) protocol configuration.