A neutron diffraction study of macroscopically entangled proton states in the high temperature phase of the KHCO₃crystal at 340 K

Abstract

We utilize single-crystal neutron diffraction to study the C2/m structure of potassium hydrogen carbonate (KHCO 3 ) 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 |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.

Evidence of macroscopically entangled protons in a mixed isotope crystal of KHpD1−pCO3

“…Above T c , dimers split into two centrosymmetric entities, symmetric with respect to the plane (a, c). It is quite remarkable that the enhanced features of the scattering function, as well as proton dynamics and quantum interference, do not show any discontinuity at T c [14]. There is no evidence of classical disorder above T c .…”

“…Admittedly the enhanced features are an evidence of quantum correlations, but different mechanisms have been envisaged: symmetry related entanglement [12,13,14,15]; quantum exchange [23]; spin-spin interaction [24]. They will be compared.…”

“…The super-rigidity along z is necessarily destroyed by measurements and intensities are proportional to exp −U zz Q 2 z . On the other hand, since z 0 = z ′ 0 = 0 for planar dimers, the spin-symmetry holds only in the (x, y) planes, so the differential cross-section for enhanced diffraction can be written as [14] dσ c dΩ ∝…”

“…This has been exemplified with the crystal of KHCO 3 made of hydrogen bonded dimers, (HCO − 3 ) 2 [12,13,14,15]. Below 150 K, only those proton sites (L), corresponding to a unique configuration for dimers (LL), are occupied.…”

“…In Sec. 3, the quantum theory [14,15] applied to the mixed crystal accounts for macroscopic proton and deuteron states, each of which being a superposition of LL and RR states. A detailed interpretation of the enhanced features is proposed.…”