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 T-c = 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 T-c by 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 P2(1)/a structure (T < T-c) 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 vertical bar C2/m > state vector is a superposition of the state vectors for two P2(1)/a-like structures symmetric with respect to (a, c) planes.