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

TL;DR

This study uses neutron diffraction to reveal that KHCO3 crystals maintain macroscopic quantum proton states above the phase transition, suggesting the crystal acts as a macroscopic quantum object with superposition states.

Contribution

It provides experimental evidence and a theoretical framework for macroscopic quantum entanglement of protons in KHCO3 at high temperature, extending previous low-temperature findings.

Findings

Proton states remain entangled above T_c at 340 K

Structural transition occurs between ordered phases without quantum regime breakdown

The crystal can be described as a superposition of proton state vectors

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 F. Fillaux et al., (2006 \textit{J. Phys.: Condens. Matter} \textbf{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.