  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.
