Probing Cosmic Neutrino Background through Parametric Fluorescence

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., $\nu^{}_{i} + M \to \nu^{}_{j} + \gamma^{}_{\rm S} + M$, 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 $T^{}_{\rm c} = 10~{\rm \mu s}$). This event rate appears to be very promising in consideration of an even longer coherence time that is achievable in solid systems.