Abstract
Despite their high relative abundance in our Universe, neutrinos are the least understood fundamental particles of nature. They also provide a unique system to study quantum coherence and the wavelike nature of particles in fundamental systems due to their extremely weak interaction probabilities. In fact, the quantum properties of neutrinos emitted in experimentally relevant sources are virtually unknown and the spatial extent of the neutrino wavepacket is only loosely constrained by reactor neutrino oscillation data with a spread of 13 orders of magnitude. Here, we present the first direct limits of this quantity through a new experimental concept to extract the energy width, σ_N,E, of the recoil daughter nucleus emitted in the nuclear electron capture (EC) decay of ⁷Be. The final state in the EC decay process contains a recoiling ⁷Li nucleus and an electron neutrino (ν_e) which are entangled at their creation. The ⁷Li energy spectrum is measured to high precision by directly embedding ⁷Be radioisotopes into a high resolution superconducting tunnel junction that is operated as a cryogenic sensor. The lower limit on the spatial uncertainty of the recoil daughter was found to be σ_N, x ≥ 6.2\,pm, which implies the final-state system is localized at a scale more than a thousand times larger than the nucleus itself. From this measurement, the first direct lower limits on the spatial extent of the neutrino wavepacket were extracted using two different theoretical methods. These results have wide-reaching implications in several areas including the nature of spatial localization at sub-atomic scales, interpretation of neutrino physics data, and the potential reach of future large-scale experiments.