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

Abstract

We utilize single-crystal neutron diffraction to study theC 2/m structure of potassiumhydrogen carbonate (KHCO3) and macroscopic quantum entanglement above the phase transition atTc = 318 K. Whereas split atom sites could be due to disorder, the diffraction pattern at 340 Kevidences macroscopic proton states identical to those previously observed belowTc by Fillaux et al (2006 J. Phys.: Condens. Matter 18 3229). We propose a theoreticalframework for decoherence-free proton states and the calculated differential cross-sectionaccords with observations. The structural transition occurs from one orderedP 21/a structure(T<Tc) to anotherordered C 2/m structure. There is no breakdown of the quantum regime. It is suggested that the crystal isa macroscopic quantum object which can be represented by a state vector. Ramanspectroscopy and quasi-elastic neutron scattering suggest that the state vector is a superposition of the state vectors for twoP 21/a-like structuressymmetric with respect to (a,c) planes.