Acceleration Noise Induced Decoherence in Stern-Gerlach Interferometers for Gravity Experiments

TL;DR

This paper theoretically analyzes how acceleration noise causes decoherence in Stern-Gerlach interferometers used for gravity experiments, focusing on dephasing, contrast loss, and position localisation effects.

Contribution

It provides a rigorous proof of dephasing as a linear response to noise and distinguishes the effects of stochastic acceleration noise from higher-order noise.

Findings

Stochastic acceleration noise induces dephasing but not contrast loss or localisation decoherence.

Higher-order noise can cause contrast loss and localisation decoherence, resonant with the test mass.

Analysis of magnetic field noise and quadratic noise as typical sources.

Abstract

Stern-Gerlach interferometer (SGI) is a kind of matter-wave interferometer driven by magnetic field and has been proposed for various gravity experiments. Stochastic noises can lead to decoherence problems of SGI via various mechanisms. In this paper, I will theoretically study several mechanisms including dephasing, contrast loss and position localisation decoherence. I will firstly present a rigorous proof that the dephasing behaves as a linear response to the noise, with a transfer function given by the Fourier transform of the unperturbed classical trajectories. Then I will demonstrate that stochastic acceleration noise only induces dephasing to the witness operator constructed in spin space, while it does not lead to contrast loss or position localisation decoherence due to common mode cancellation. In contrast, higher-order noise can induce both contrast loss and position localisation decoherence, contributing a decay factor proportional to the noise power spectrum density at the intrinsic frequency, which can be physically interpreted as the resonance between the noise and test mass. Based on the result, I apply the framework to analyse two typical noise sources, magnetic field noise and quadratic noise.