Abstract Neutrons interacting with protons in Compton scattering is here chosen as an example of a non-trivial quantum measurement. It illustrates a situation where a probe particle makes an observation (a weak measurement) of the studied protons, preparing for a final state in which one of them takes up the recoil in the collision. The proton is ejected during a strong (projective) measurement that selects one particular momentum value out of the proton’s initial distribution of momentum states. This course of events in the measurement process is evidenced by the observation that destructive interference appears during the weak interaction stage which leads to a strongly reduced neutron cross section for the proton system.
Abstract Neutrons interacting with protons in Compton scattering is here chosen as an example of a non-trivial quantum measurement. It illustrates a situation where a probe particle makes an observation (a weak measurement) of the studied protons, preparing for a final state in which one of them takes up the recoil in the collision. The proton is ejected during a strong (projective) measurement that selects one particular momentum value out of the proton’s initial distribution of momentum states. This course of events in the measurement process is evidenced by the observation that destructive interference appears during the weak interaction stage which leads to a strongly reduced neutron cross section for the proton system.
The notions of weak measurement, weak value, and two-state-vector formalism provide a new quantum-theoretical frame for extracting additional information from a system in the limit of small disturbances to its state. Here, we provide an application to the case of two-body scattering with one body weakly interacting with an environment. The direct connection to real scattering experiments is pointed out by making contact with the field of impulsive incoherent neutron scattering from molecules and condensed systems. In particular, we predict a new quantum effect in neutron-atom collisions, namely an observable momentum transfer deficit; or equivalently, a reduction of effective mass below that of the free scattering atom. Two corroborative experimental findings are shortly presented. Implications for current and further experiments are mentioned. An interpretation of this effect and the associated experimental results within conventional theory is currently unavailable. Quanta 2016; 5: 61–84.
Abstract Quantum entanglement is a basic ingredient in the formalism of quantum mechanics and was held by Heisenberg as its most emblematic feature. But although all its consequences could be foreseen from the start, it took half a century before experiments were carried out to test its more intriguing predictions. One reason was that sufficiently sensitive tools, like lasers, were not yet available, but there was also a lack of interest and imagination among theoreticians, who did not realize its full potential. When experiments were finally realized and opened a ‘weird and ghostlike quantum world’, they were first met with surprise and doubt. In the first experiments on entanglement it was purposely created (using chain-decays or down-conversion), but entanglement is actually a ubiquitous phenomenon appearing in most physical processes, although surviving over so short time-scales that it is usually not observed. The present work deals with ‘measurement-induced entanglement’ in scattering, and starts with a process where its effects can actually be studied in the sub-femtosecond range in a time-resolved manner, the Compton scattering of neutrons. Based on results from this method, the conditions for observing similar effects in other scattering processes are discussed. First, the mechanisms for entanglement creation by a scattering particle are mentioned, then the conditions for observing measurable consequences of it on scattering cross-sections: a very limited number of scattering centers, large zero-point motions of the scatterers and no strong interaction with environment which leads to decoherence.
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.
Summary form only given. Measurements are the very basis of Physics, especially in Quantum Mechanics, where they assume even a more fundamental role because of wave function collapse after a “strong” (projective) measurement. Furthermore, measuring a quantum-mechanical observable completely erases the information on its conjugate one (e.g. measurement of position erases information on momentum, and vice-versa). Nevertheless, in Quantum Mechanics other kinds of measurement are possible. For example, wave function collapse can be overcome through Weak Measurements, i.e. measurements performed with an interaction sufficiently weak not to collapse the original state, featuring several interesting properties. An example of these are weak values [1-3], realised for the first time in [4-6], that have been used for addressing fundamental questions [7-12] as Contextuality and are also a tool for Quantum Metrology [13-19]. One of the most intriguing properties of Weak Measurements is that, since they are not affected by wave function collapse, they can allow gathering simultaneous information on non-commuting observables [20], impossible with the standard (projective) measurement protocols. A second example is offered by Protective Measurements [21], a new technique able to extract information on the expectation value of an observable even measuring a single particle. In this talk, after a general introduction to WMs, we present the first realisation of sequential weak value measurements [22], i.e. a joint measurement of the weak value of (incompatible) polarizations on a single photon. Then, we present an experiment addressed to explore the connection between anomalous weak values and Contextuality [23], showing a clear violation of the inequality proposed in [12] while satisfying all the additional theoretical requests, unequivocally demonstrating the contextual nature of weak values. Finally, we present and discuss the first implementation of Protective Measurements, showing unprecedented measurement capability and demonstrating how the expectation value of an observable can be obtained with a single measurement on a single particle.
Abstract The conventional theory of non-relativistic neutron beam scattering from many-body systems treats the beam essentially as a classical system, because the neutron dynamical variables are captured in the main theoretical formulas (e.g. time-correlation functions) not as quantum mechanical operators but as c-numbers only. This simplification results in the full decoupling of the probe particles’ dynamics from the quantum dynamics of the scatterer. Further, neutrons’ wavefunctions are represented with plane waves, and thus the concept of neutron’s finite coherence length in momentum space becomes irrelevant. Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, Feynman paths, “which-path information” versus interference, Weak Values theory) new observable effects of non-relativistic quantum beam scattering may be exposed and/or predicted, such as a surprising intensity deficit in neutron Compton scattering (NCS) of epithermal neutrons from protons of H-containing materials. Here, the NCS-intensity deficit observed in scattering from liquid C6H6 is discussed and interpreted from first principles, in the general frame of Weak Values theory. Moreover, based on Feynman’s didactical argument that there isn’t any interference between distinguishable neutron paths, we show that this NCS-effect cannot be interpreted as being caused by destructive interference of neutron paths scattered from entangled (two or a few) protons, as was earlier proposed by some authors.
Abstract One of the common conceptions of nature, typically derived from the experiences with classical systems, is that attributes of the matter coexist with the substance. In the quantum regime, however, the quantum particle itself and its physical property may be in spatial separation, known as the quantum Cheshire cat effect. While there have been several reports to date on the observation of the quantum Cheshire cat effect, all such experiments are based on first-order interferometry and destructive projection measurement, thus allowing simple interpretation due to measurement-induced disturbance and also subject to trivial interpretation based on classical waves. In this work, we report an experimental observation of the quantum Cheshire cat effect with noninvasive weak quantum measurement as originally proposed. The use of the weak-measurement probe has allowed us to identify the location of the single photon and that of the disembodied polarization state in a quantum interferometer. The weak-measurement probe based on two-photon interference makes our observation unable to be explained by classical physics. We furthermore elucidate the quantum Cheshire cat effect as quantum interference of the transition amplitudes for the photon and the polarization state which are directly obtained from the measurement outcomes or the weak values. Our work not only reveals the true quantum nature of Cheshire cat effect but also sheds light on a comprehensive understanding for the counter-intuitive quantum phenomena.