Acceleration Noise Induced Decoherence in Stern-Gerlach Interferometers for Gravity Experiments (2406.10832v3)

Abstract: Stern-Gerlach interferometer (SGI) is a kind of matter-wave interferometer driven by magnetic field and has been proposed for many gravity experiments. Acceleration noises such as vibration and inertial forces, together with higher-order noises like the fluctuation of the gravity gradient or the magnetic field, can cause decoherence problems of SGI, including dephasing, loss of contrast and position localization decoherence. In this paper, I will theoretically study these mechanisms of decoherence based on the analytical time-evolution operator of an SGI modelled as a harmonic oscillator under acceleration noises described by Gaussian stochastic processes. As will be proved, for a single arm of an SGI, the shape of the Wigner function keeps invariant under an acceleration noise, although the phase and the coordinate in the classical phase space fluctuate as linear responses to the noise, and the spatial quantum state of a single path experiences a fidelity loss and position localization decoherence. For the witness constructed in the spin space, the degrees of freedom in the classical phase space have to be traced out, then acceleration noises can lead to dephasing effects on the witness, while the fidelity loss or position localization decoherence don't affect the density matrix in spin space as long as the noise is uniform to both arms of the interferometer. By contrast, path-dependent noises can lead to a loss of Loschmidt echo, resulting in a decoherence in the spin space, known as the Humpty-Dumpty problem. A final remark is that the randomness of the noise is essential for dephasing and position-localization decoherence, and these two mechanisms don't cause purity loss or entropy increase if the noise is determinstic rather than stochastic.