Probing Cosmic Neutrino Background through Parametric Fluorescence

TL;DR

The paper proposes detecting the cosmic neutrino background via a novel parametric fluorescence mechanism in dense atomic/molecular media, where relic neutrinos coherently scatter off a dipole ensemble and induce a photon-emitting transition. By deriving the effective weak-interaction Hamiltonian and identifying a dominant magnetic dipole (M1) channel, the authors show resonance enhancements when the neutrino energy transfer matches a molecular transition, with the rate scaling as $\Gamma \sim G_F^2 n_d^2 |\bm{d}_{vg}|^2 |\bm{k}|^3 T_c^2$ on resonance, and potentially sizable rates given long coherence times. They further discuss slow-light phenomena near resonance (via two-level dispersion or EIT) to reduce momentum-spread limitations and improve phase matching, as well as backgrounds and practical pathways for experimental realization. The study provides optimistic scenarios where rates of order unity per year are achievable for realistic volumes and coherence times, highlighting a promising route to relic-neutrino detection and deeper insights into neutrino masses and Majorana nature.

Abstract

We point out that relic neutrinos from the Big Bang may induce the parametric fluorescence in atomic or molecular systems, which offers a novel way to discover cosmic neutrino background. By coherently scattering with molecular energy levels, a massive neutrino can spontaneously ``decay" into a lighter neutrino and an infrared signal photon, i.e., $ν^{}_{i} + M \to ν^{}_{j} + γ^{}_{\rm S} + M$, where the molecular state $M$ remains unchanged after the scattering. Because the amplitudes of different radiants are matched in phase, the rate is coherently enhanced and proportional to the squared density of ambient dipoles. When the energy transfer from neutrinos coincides with the energy-level difference, the fluorescence will be on resonance. Near the resonance, the rate is proportional to the square of the coherence time $T^{}_{\rm c}$ of the ensemble. For a nominal target volume of $5~{\rm m^3}$ (or $5~{\rm cm^3}$), the signal rate can reach $1~{\rm yr}^{-1}$ for $T^{}_{\rm c} = 10~{\rm ns}$ (or $T^{}_{\rm c} = 10~{\rm μs}$). This event rate appears to be very promising in consideration of an even longer coherence time that is achievable in solid systems.

Figures (7)

• Figure 1: Schematic diagrams for the parametric fluorescence induced by massive neutrinos, which collectively interact with molecular (or atomic) dipoles in the medium.
• Figure 2: The dependence curves of the photon energy $\omega$ (colorful curves) and the energy difference of neutrinos $E^{}_{3} - E^{\prime}_{1}$ (gray band) on the photon momentum $k$, where $m^{}_{3}=0.05~{\rm eV}$ and $m^{}_{1}=0~{\rm eV}$ are inputs. The shaded gray region denotes a momentum spread of order $10^{-3}~{\rm eV}$ for illustration. The intersection points marked by white triangles represent the resultant momentum and energy satisfying the conservation law. For photon's dispersion relation, the following parameters have been used for demonstration: $E^{}_{\rm vg} = 10~{\rm meV}$, $d^{}_{\rm vg} = e/(4 m^{}_{e})$, $n^{}_{d} = 6.02 \times 10^{23}~{\mathrm{cm}}^{-3}$ and $T^{}_{\rm c} = 10~{\rm \mu s}$. Similar dispersion curves can be found in Ref. Khurgin2010.
• Figure 3: A schematic plot of the experimental setup for detecting parameter fluorescence. The target is a solid film with dimensions $20~{\rm cm} \times 20~{\rm cm} \times 1~{\rm mm}$. Its surface is covered with superconducting photon and phonon sensors featuring $\mathcal{O}(10~{\rm meV})$ sensitivities. Two types of signals can arise, depending on whether the initial photon is absorbed by the medium before reaching the sensors. Similar geometry may be found in experiments searching for light dark matters Temples:2024ntvTemples:2025xew.
• Figure 4: The fundamental diagrams for the generation of additional electromagnetic couplings by coherently scattering with atomic/molecular energy levels: (a) the coupling $\gamma\gamma$ corresponding to the linear electric susceptibility which changes the refractive index of lights; (b) the coupling $\gamma\gamma\gamma$ corresponding to the nonlinear electric susceptibility that induces the down conversion of pumping photons. The ground and virtual states are denoted by $\left|\rm g \right>$ and $\left|\rm v \right>$ (or $\left|\rm v^\prime \right>$), respectively. Those scatterings are coherent because the transition returns back to the ground state via the short-lived intermediate state.
• Figure 5: A two-level system consisting of $\left|\mathrm{g}\right\rangle$ and $\left|\mathrm{v}\right\rangle$, or a three-level system where $\left|\mathrm{v}\right\rangle$ and $\left|\mathrm{v}^\prime\right\rangle$ represent hyperfine-split sublevels. The probe photon couples to the transition dipole $d_{\mathrm{vg}}$ with a small detuning $\Delta_{\mathrm{p}} = \omega - E_{\mathrm{vg}}$. In the three-level configuration, a control microwave field with Rabi frequency $\Omega_{\mathrm{c}} = d_{\mathrm{v}^\prime \mathrm{v}} \mathcal{E}^{}_{\mathrm{c}}$ is applied to realize electromagnetically induced transparency (EIT). The control field may also be detuned from resonance by $\Delta^{}_{\rm c} = \omega^{}_{\rm c} - E^{}_{\rm v v^\prime}$. In both the two- and three-level systems, the probe photon exhibits a reduced group velocity near the resonance.