Detection prospects for the Cosmic Neutrino Background using matter interferometers

TL;DR

This work investigates the feasibility of detecting the Cosmic Neutrino Background (CNB) with matter interferometers by linking CNB-induced weak-interaction potentials to observable phase shifts. It decomposes the CNB-induced interaction into a neutrino-matter MSW-type scalar potential and a spin-dependent Stodolsky term, expressing these effects via scalar potentials, pseudo magnetic fields, and spin-spin couplings, and it extends the analysis to fermionic Dark Matter analogs. The authors provide relativistic and non-relativistic limit expressions, estimate phase shifts for various interferometer types, and conclude that, under current and near-future capabilities, CNB signals are below detectable levels, though the Stodolsky effect remains comparatively more promising. The results establish quantitative benchmarks for CNB searches with matter interferometers and highlight dark-sector counterparts as potentially more accessible directions for experimental exploration and model-building in the future.

Abstract

In this paper we discuss how the Cosmic Neutrino Background can affect the measured phase difference in a matter interferometer. This phase is proportional to a difference in potential energies along the two interferometer paths. The relevant potentials here are the well-known neutrino matter potential and a potential related to the Stodolsky effect. We show how they can be rewritten in terms of scalar potentials, pseudo magnetic fields and spin-spin interactions. Unfortunately, current technology is unlikely to detect this effect and we discuss prospects for the future. We also briefly comment on fermionic Dark Matter which can give rise to very similar effects which can easily be larger than the neutrino case.

Figures (4)

• Figure 1: Simplified sketch of a matter interferometer. At the points $A$ and $C$, that is at $t=0$ and $t = 2 \, T$ a $\pi/2$ pulse is applied which acts as a beam splitter or merger. At $B_1$ and $B_2$ a $\pi$ pulse is applied which leads to an inversion of the ground and excited state.
• Figure 2: Dependence of $|\Delta \Phi|$ in an electron, neutron $^{87}$St and $^{87}$Rb interferometer with $T = 1$ s for the four cases we discuss. Here we plot the effect of the neutrino-matter potential depending on the combined parameter $r_\nu \, \Delta_\nu$ in $10^{-8}/$cm$^3$. The electron and neutron, and the $^{87}$St and $^{87}$Rb lines almost overlap. The current sensitivity taken here is 0.01 rad inspired from results on measuring the gravitational Aharonov-Bohm effect Overstreet:2021hea. In the future $^{87}$Rb based atom interferometers might be able to resolve phase shifts down to about $10^{-6}$ rad Aveline:2020klaFrye:2021jgcElliott:2018calDu:2022ceh (which we show as future prospects) and there are proposals aiming for $10^{-10}$ rad Du:2022ceh. For more details, see main text.
• Figure 3: Dependence of $|\Delta \Phi|$ in an electron, neutron $^{87}$St and $^{87}$Rb interferometer with $T = 1$ s for the four cases we discuss. Here we plot the effect of the Stodolsky potential depending on the parameter $\Delta_\nu$ in $1/$cm$^3$. The $^{87}$St and $^{87}$Rb lines almost overlap. The current sensitivity taken here is 0.01 rad inspired from current results from the spin-echo neutron interferometry result Parnell:2020wwb. For the future prospects we take the same number as in Fig. \ref{['fig:MSW']}. For more details, see main text.
• Figure 4: Dependence of $|\Delta \Phi|$ for the DM case with $T = 1$ s and $G_\text{DM} = 10 \, G_F$. Here we plot the effect of the DM-matter potential and the Dark Stodolsky potential depending on the DM mass. For more details, see main text.