A neutron diffraction study of macroscopically entangled proton states in the high temperature phase of the KHCO3 crystal at 340 K

We utilize single-crystal neutron diffraction to study the C2/m structure of potassium hydrogen carbonate (KHCO3) and macroscopic quantum entanglement above the phase transition at Tc = 318 K. Whereas split atom sites could be due to disorder, the diffraction pattern at 340 K evidences macroscopic proton states identical to those previously observed below Tc by F. Fillaux et al., (2006 J. Phys.: Condens. Matter 18 3229). We propose a theoretical framework for decoherence-free proton states and the calculated differential cross-section accords with observations. The structural transition occurs from one ordered P21/a structure (T < Tc) to another ordered C2/m structure. There is no breakdown of the quantum regime. It is suggested that the crystal is a macroscopic quantum object which can be represented by a state vector. Raman spectroscopy and quasi-elastic neutron scattering suggest that the |C2/m〉 state vector is a superposition of the state vectors for two P21/a-like structures symmetric with respect to (a, c) planes. PACS numbers: 61.12.-9, 03.65.Ud, 63.10.+a, 82.30.Hk.