Direct Experimental Constraints on the Spatial Extent of a Neutrino Wavepacket

Despite their high relative abundance in our Universe, neutrinos are theleast understood fundamental particles of nature. They also provide a uniquesystem to study quantum coherence in fundamental systems due to their extremelyweak interaction probabilities. The quantum properties of neutrinos emitted inexperimentally relevant sources are virtually unknown and theoreticalpredictions for the spatial width of neutrino wavepackets vary by many ordersof magnitude. In weak nuclear decay, the size of a neutrino wavepacket,σ_ν,x, is related to the spatial wavefunction of its parent atproduction. Here, we present the first direct limits of this quantity through anew 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 theircreation. The ^7Li energy spectrum is measured to high precision by directlyembedding ^7Be radioisotopes into a high resolution superconducting tunneljunction that is operated as a cryogenic charge sensitive detector. The lowerlimit on the spatial coherence of the recoil daughter was found to beσ_N, x≥ 6.2 pm, which implies the system remains in aspatially coherent state much larger than the nuclear scale. Further, thisimplies a lower limit on the size of a neutrino wavepacket, σ_ν,x≥ 35 nm, which is more than five orders of magnitude more stringent thanthe limits from all combined reactor oscillation experiments. These resultshave wide-reaching implications in several areas including quantum coherence,the nature of spatial localization at sub-atomic scales, interpretation ofneutrino physics data, and the potential reach of future large-scaleexperiments.