Spin contrast, finite temperature, and noise in matter-wave interferometer

In this paper, we will show how finite-temperature corrections and spin-dependent/independent noise will affect the contrast in a matter-wave interferometer, especially with massive objects and large spatial superposition sizes. Typically, spin is embedded in a nanoparticle as a defect, which can be manipulated by the external magnetic field to create a macroscopic quantum superposition. These massive matter-wave interferometers are the cornerstone for many new fundamental advancements in physics; particularly, macroscopic quantum superposition can use entanglement features to, e.g., test physics beyond the Standard Model, test the equivalence principle, improve quantum sensors, and test the quantum nature of spacetime in a lab. We will consider a Stern-Gerlach type apparatus to create macroscopic quantum superposition in a harmonic oscillator trap, and figure out the spin contrast loss due to linear spin-independent and spin-dependent noise in a single interferometer. We will show that spin contrast loss due to spin-independent noise does not depend on the initial thermal state of the matter wave function. However, spin contrast loss due to spin-dependent fluctuations do depend on the initial thermal occupation of the quantum state. We will keep our discussion general as far as the noise parameters are concerned.