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.
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.
Several recent experiments on liquid and solid samples containing protons or deuterons have shown an interesting anomaly, which is apparently absent when the hydrogen isotopes are replaced by heavier particles. The anomaly is a shortfall in the intensity of energetic neutrons scattered by the samples; specifically, the intensity per hydrogen isotope in bulk samples is smaller than the intensity for total scattering by an isolated hydrogen isotope. Short-lived correlations in the spatial and spin degrees of freedom of the hydrogen isotopes have been proposed as an explanation of the anomaly. The correlations involve entanglements of the degrees of freedom created by the requirements of quantum mechanics applied to identical particles. By using energetic neutrons to perform Compton scattering experiments on the hydrogen isotopes, the time scale of the experimental probe covers the region of ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\mathrm{s}$ where entangled states might still be expected to survive. The proposed explanation is pursued here by reporting the cross section for Compton scattering, also known as deep inelastic scattering, by two identical nuclei occupying nonequivalent states. The model reproduces the observed dependence of the cross section on energy transfer, in which intensity accumulates at the recoil energy of a single nucleus. Several features of the model demand that the intensity at the recoil energy is indeed less than the intensity for total scattering by an isolated nucleus. Although the pair approximation used here is unquestionably a first approximation to real many-body entanglements, it is a compelling explanation of all the observations, including the restoration of the normal cross section at longer observation times achieved by moving to longer scattering times.
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.
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.
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.
Several recent experiments have shown that protons, and to some extent also deuterons, show anomalous cross sections when the neutrons have energies in the range 10-100 eV (this results in a Compton scattering process where an essential part of the energy is transferred to one of the scattering particles). Here, an experiment on partially deuterated water, carried out by Chatzidimitriou-Dreismann et al., is analyzed in terms of a theory, which assumes that during the short duration (<10(-15) s) of this scattering process, protons are exchange correlated and cannot be considered as independent scattering objects. The quantum decoherence time for protons in liquid water is estimated from a simple model for the interaction of the water protons with hydrogen bonds.
Nuclei and electrons in condensed matter and/or molecules are usually entangled, due to the prevailing electromagnetic interactions. Usually, the “environment” of a microscopic scattering system (e.g., a proton) causes an ultrafast decoherence, thus making atomic and/or nuclear entanglement effects not directly accessible to experiments. However, neutron Compton scattering (NCS) and electron Compton scattering represent ultrafast techniques operating in the sub-femtosecond timescale, thus opening a way for investigation of such dehoherence and short-lived entanglement phenomena of atoms in molecules and condensed matter. The experimental context of NCS and a new striking scattering effect from protons (H-atoms) in several condensed systems and molecules are described. In short, one observes an “anomalous” decrease of scattering intensity from protons, which seem to become partially “invisible” to the neutrons. The experiments apply large energy (several electronvolts) and momentum (10–200 Å −1 transfers, and the collisional (or scattering) time between the neutron and a struck proton is only 100–1000 attoseconds long. Similar results are also obtained with electron-atom Compton scattering at large momentum transfers. As an example, we present new NCS experimental results from a single crystal, which also provide new physical insights into the attosecond quantum dynamics of protons in molecules and condensed matter. Theoretical discussions and models are presented which show that the effect under consideration is caused by the non-unitary time evolution (due to decoherence) of open quantum systems during the ultrashort, but finite, time-window of the neutron-proton scattering process. The conceptual connection with the well known Quantum Zeno Effect is pointed out. The experimental results, together with their qualitative interpretation “from first principles,” show that epithermal neutrons being available at spallation sources, and electron spectrometers providing large momentum transfers, may represent novel tools for investigation of thus far unknown physical and chemical attosecond phenomena.