Macroscopic quantum entanglement at the scale and temperature of our everyday world enlightens the foundations of quantum mechanics and reveals unforeseen mechanisms for proton transfer across hydrogen bonds in the solid state. We utilize neutron scattering techniques to study dynamical correlation of protons in potassiumhydrogencarbonate (KHCO₃) and benzoic acid (C₆H₅COOH) crystals, both composed of planar centrosymmetric dimer entities linked by moderately strong hydrogen bonds.

All protons are indistinguishable, they behave as fermions, and they are degenerate. We define pseudoprotons to account for proton dynamics. As a consequence of the symmetrization postulate of quantum mechanics, the sublattice of protons is a superposition of macroscopic single-particle states such that each pseudoproton occupies simultaneously all sites. The sublattice has no internal dynamics and decoherence is forbidden. Coherent elastic neutron scattering gives rise to quantum interferences, in addition to Bragg's peaks.

Between 15 and 300 K, protons are progressively transferred, to secondary sites at ~ 0.6 Å from the main position, via tunneling along hydrogen bonds. The macroscopic quantum entanglement, still observed at 300 K, reveals that proton transfer is a coherent process throughout the crystal arising from a superposition of macroscopic tunneling states.

References:

[1] F. Fillaux, M. H. Limage, F. Romain, Chem. Phys. 2002, 276, 181.

[2] F. Fillaux, A. Cousson, D. Keen, Phys. Rev. B 2003, 67, 054301.

[3] F. Fillaux, A. Cousson, M. J. Gutmann, J. Phys.: Cond. Matter 2006, 18, 3229.

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1. Crystal Growth and Neutron Diffraction Studies of LiCoO₂ Bulk Single Crystals