Macroscopic quantum entanglement and 'super-rigidity' of protons in the KHCO3 crystal from 30 to 300 K

We utilize neutron diffraction techniques to study dynamical correlation of protons in the ionic crystal of potassium hydrogen carbonate (KHCO3). Protons are found in small planar centrosymmetric dimer entities (HCO3-)2, linked by moderately strong hydrogen bonds and well separated by the stacking of potassium atoms. There is no disordering at low temperature and rods of diffuse scattering in (a*,c*) planes, not observed for KDCO3, reveal macroscopic entanglement. We propose a theoretical framework for the degenerate lattice of indistinguishable protons, treated as fermions. Entangled centrosymmetric pairs are superpositions of singlet-like and triplet-like pseudoproton states and the sublattice is a superposition of nonlocal macroscopic single-pseudoproton states, adiabatically separated from the lattice of heavy atoms. The sublattice has no internal dynamics (super-rigidity) and is decoherence free. The energy-free quantum entanglement is a consequence of the crystal structure, irrespective of proton-proton interaction. The differential cross-section calculated for the super-rigid lattice accounts for the observed rods of intensity. Between 150 and 300 K, protons are progressively transferred to secondary sites at ∼0.6 A from the main position, via tunnelling along hydrogen bonds. Quantum entanglement, still observed at 300 K, indicates that proton transfer is a thermally activated coherent superposition of macroscopic tunnelling states. This work adds a crystalline solid to the list of systems with 'super' properties