It is shown that quantum entanglement in condensed matter can be observed with scattering experiments if the energy resolution of the experiments enables a clear separation between the elastic scattering and the scattering from the excitations in the system. These conditions are not satisfied in recent deep inelastic neutron scattering experiments from hydrogen-containing systems that have been interpreted as showing the existence of quantum entanglement for short times in, for example, water at room temperature. It is shown that the theory put forward to explain these experiments is inconsistent with the first-moment sum rule for the Van Hove scattering function and we suggest that the theory is incorrect. The experiments were performed using the unique EVS spectrometer at ISIS and suggestions are made about how the data and their interpretation should be re-examined.
It is shown that quantum entanglement in condensed matter can be observed with scattering experiments if the energy resolution of the experiments enables a clear separation between the elastic scattering and the scattering from the excitations in the system. These conditions are not satisfied in recent deep inelastic neutron scattering experiments from hydrogen-containing systems that have been interpreted as showing the existence of quantum entanglement for short times in, for example, water at room temperature. It is shown that the theory put forward to explain these experiments is inconsistent with the first-moment sum rule for the Van Hove scattering function and we suggest that the theory is incorrect. The experiments were performed using the unique EVS spectrometer at ISIS and suggestions are made about how the data and their interpretation should be re-examined.
We calculate the scattering function of neutrons, $S(\stackrel{P\vec}{q},\ensuremath{\omega})$, from a pair of nuclei in entangled states caused by the quantum-mechanical indistinguishability of particles. From the calculation, the conditions for detecting the entanglement of protons in solids by neutron scattering experiments are clarified. Our conclusion is that the entangled state of a proton pair, if it exists, can be observed by performing neutron scattering experiments at very low temperatures for elastic scattering and with high energy resolution for inelastic scattering.
In general, nuclei and electrons in condensed matter and/or molecules are entangled, due to the prevailing (electromagnetic) interactions. As a matter of fact, the "environment" interacting with a microscopic system of interest (e.g. a proton) causes the destruction of the entanglement. This process, called decoherence, has until now prevented experimenters from directly accessing atomic and/or nuclear entanglement effects in real experiments. However, our neutron and electron Compton scattering experiments from protons (H-atoms) in several condensed systems and molecules at ambient conditions demonstrated a new striking effect, i.e. an "anomalous" decrease of scattering intensity from protons, which seem to become partially "invisible" to the neutrons. This effect, which has no interpretation within conventional neutron scattering theory, is proposed to be caused by the non-unitary time evolution (due to decoherence) during the ultrashort, but finite, time-window of the neutron-proton scattering process. Due to the large energy (several eV) and momentum (20-200 Å −1 ) transfers of these experiments the collisional time between the probe particle and a struck proton is 100–1000 attoseconds long. It is shown that, due to this short timescale, the scattering process must be theoretically treated within quantum dynamics of open quantum systems. New experimental neutron Compton scattering results from a single crystal KHCO 3 are presented. They provide the first direct evidence for a connection between the momentum distribution and the "anomalous" scattering intensity of H. Additionally, recent experiments with electron-atom Compton scattering at momentum transfers are mentioned, which reveal the presence of this effect even in scattering from single H 2 molecules in the gas phase. Theoretical discussions "from first principles" are presented, also in relation to the quantum Zeno effect, which underline the crucial role of decoherence in the considered experiments. The experimental results and their qualitative interpretation show that epithermal neutrons being available at spallation sources (e.g. ISIS/UK, SNS/USA or ESS/Sweden), and electron spectrometers with large scattering angles, provide tools for investigating new physical and chemical phenomena in the sub-femtosecond timescale.
Abstract Quantum entanglement in scattering processes has most often been treated in general terms only. A few examples of detailed calculations exist for atomic systems but for nuclear processes it is an almost unexplored area, although it may be important for interpretation of some measured quantities. The present treatment is a study of the time-development of the deuteron-like compound state created in the n – p scattering process. The increase and decay of neutron–proton entanglement in this state is calculated for low transferred momenta over the atto-second range. It is well known that the very high value for the bound proton cross sections ( σ = 81.9 barns) is caused by a specific feature in the deuteron, a virtual 0+ state close to its binding level. In scattering this state causes a negative phase shift δ s in the outgoing neutron wave function, increasing linearly with the transferred momentum. This phase shift is produced during a short-lived virtual energy transfer Δ E in exciting the 0+ state and Δ E is estimated here from the ratio of the phase shift δ observed and the time Δ t it takes to create the entanglement. It is further argued that the nuclear excitation decreases after the n – p encounter in proportion to the degree of n – p entanglement calculated, i.e. as long as the scattering state has deuteron characteristics. This phase shift is neglected in low energy neutron scattering text-books (which are based on the Fermi pseudo potential) and may be negligible for thermal neutron scattering, but will be important already at epithermal energies (0.1–1 eV). The phase shift has measurable consequences in interpretation of INS (inelastic neutron scattering) since its associated energy shift increases quadratically with the transferred momentum. It explains quantitatively certain anomalies found in scattering on water, where water vibration modes are excited far below the expected transferred momentum limit. This paper ends with a short discussion about quantum entanglement in scattering processes in general, with the present example as a starting point.
Several recent observations of closely spaced hydrogen nuclei in condensed matter systems — water, polymers and metal hydrides — indicate that they cannot be considered as independent quantum objects when observed over very short time intervals. According to these measurements, pairs (or possibly small clusters) of protons or deuterons seem to be quantum correlated, and are able to preserve their mutual quantum phase relations over times of the order of femtoseconds even in strongly perturbing liquid or solid environments. These new experimental results are mainly based on scattering of neutrons with time windows in the atto- and femtosecond range, but there also exists corroborating evidence from other spectroscopies. When the width of the observational time window is increased above a characteristic value, the quantum coherence effects are seen to disappear. This time limit marks the onset of decoherence as the mutual phase relations between the particles are gradually lost. Possible reasons for short-time entanglement of nuclei in condensed matter systems, as well as mechanisms for its decoherence will be discussed.
Several recent experiments on liquid and solid samples containing protons or deuterons show an interesting anomaly, which is a shortfall in the intensity of energetic neutrons scattered by the samples. Previously we demonstrated that quantum correlations in the spatial and spin degrees of freedom of the hydrogen isotopes lead to entanglement in scattering and a reduction in the scattered intensity. The viability of short-lived quantum correlations as the cause of the observed anomalies is further explored and found to be entirely feasible. General features of the basic premiss, that quantum entanglement reduces the scattered signal, are discussed and the interpretation of the neutron scattering experiments is set in context to related work on other systems. For the experiments in question, the duration of a scattering event, τ s , is a fraction of a femtosecond which is extremely short compared to solid-state relaxation times. Increasing τ s , by suitably changing experimental conditions, restores the intensity to the standard value calculated from the single atom cross-section and concentration of particles. Our physical picture of the restoration is evolution with increasing τ s from a pure state of the particles (described by a wavefunction) to a mixed state (described by a density matrix) that is created, through decoherence, by steadily engaging the solid-state environment of the particles.