Attosecond Quantum Entanglement of Protons and Electrons in Condensed Matter – Neutron and Electron Compton Scattering

Abstract. The “anomalous ” scattering of neutrons and electrons from protons in the electron-volt energy range is described, and related experimental results are presented. Due to the very short characteristic scattering time, there is no well defined separation of time scales of electronic and protonic motions. An outline of a proposed theoretical interpretation is presented, which is based on the fact that scattering protons represent open quantum systems. PACS number: 03.65.Ud 1 Introductory Remarks The counter-intuitive phenomenon of entanglement [1] between two or more quantum systems has emerged as the most emblematic feature of quantum me-chanics. Experiments investigating entanglement, however, are mainly focused on collections of few simple (two- or three-level) quantum systems thoroughly isolated from their environment (e.g., atoms in high-Q cavities and optical lat-tices). These experimental conditions are necessary due to the decoherence of entangled states [2, 3]. In short, decoherence refers to the suppression of quan-tum superpositions caused by the environment. By contrast, quantum entanglement (QE) in condensed and/or molecular mat-ter at ambient conditions is usually assumed to be inaccessible experimentally. However, applying two new scattering techniques (NCS and ECS, see below) which operate in the sub-femtosecond time scale, we provided results indicating that short-lived entangled states may affect measurements in condensed matter even at room temperature [4–6]. The first direct experimental evidence of short-lived (that is, attosecond) QE involving protons in condensed matter was provided by means of the novel neu-tron Compton scattering (NCS) method. Starting in 1995, our experiments on 1310–0157 c © 2006 Heron Press Ltd. 19