Abstract
The crystal structures of KHCO 3 and KDCO 3 at 14 K were determined with the single-crystal neutron-diffraction technique. There is no evidence for proton/deuteron disorder. The diffraction pattern of KHCO 3 reveals rods of intensity separate from the Bragg peaks. These rods are not observed for KDCO 3 . They are attributed to diffraction by the sublattice of protons forming regular arrays of double slits parallel to the dimer planes. They reveal quantum coherence in two dimensions for the proton dynamics. It is shown that quantum statistics for fermions impose quantum entanglement and strict separation of the H dynamics from the lattice. The main decoherence mechanism for the vibrational states is thus canceled out. The vibrational ground state is a superposition of fully entangled macroscopic wave functions with long-lived quantum coherence.
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