Macroscopic Quantum Entanglement in the KHCO₃ Crystal

Abstract

After a brief introduction to neutron scattering techniques, illustrated with the scattering function for harmonic oscillators, some new aspects of proton dynamics in the KHCO₃ crystal are presented. The full scattering function for the proton modes measured on single crystals provides a graphic view of proton dynamics. Vibrational states are fully characterized with three quantum numbers. The effective oscillator mass of 1 amu confirms the decoupling of protons from the lattice. Combining infrared, Raman and inelastic neutron scattering techniques, the double minimum potential for the transfer of a single proton along hydrogen bonds is totally determined. An outstanding advantage of elastic neutron scattering techniques is to probe vibrational dynamics in the fully-degenerate ground state, which cannot be studied with optical spectroscopy. Decoherence-free quantum entanglement arising from symmetry-related normal coordinates gives rise to quantum interference effectively observed by spectroscopic measurements of elastic scattering. They are due to lines of entangled protons analogous to double slits. With the transversal coherence length of the neutron beam quantum coherence of protons scales to the crystal size, namely ∼ 1 cm. With diffraction techniques, the dynamical structure arising from large-scale quantum coherence gives ridges of intensity, in addition to Bragg’s peaks. These ridges are fingerprint for macroscopic quantum coherence in two dimensions. The vibrational wave function in the ground state is a superposition of non-factorable macroscopic wave functions. Time independent quantum entanglement, up to macroscopic scale, appears as a natural consequence of the crystal symmetry.