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Atoms

Fundamental Features of Quantum Dynamics Studied in Matter-Wave Interferometry—Spin Weak Values and the Quantum Cheshire-Cat

Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Yuji Hasegawa

Published Mar 11, 2016• 11 citations
Publisher

Abstract

The validity of quantum-mechanical predictions has been confirmed with a high degree of accuracy in a wide range of experiments. Although the statistics of the outcomes of a measuring apparatus have been studied intensively, little has been explored and is known regarding the accessibility of quantum dynamics. For these sorts of fundamental studies of quantum mechanics, interferometry using neutron matter-waves in particular, provides almost ideal experimental circumstances. In this device quantum interference between spatially separated beams occurs on a macroscopic scale. Recently, the full determination of weak-values of neutrons 1 2 - spin adds a new aspect to the study of quantum dynamics. Moreover, a new counter-intuitive phenomenon, called quantum Cheshire Cat, is observed in an interference experiment. In this article, we present an overview of these experiments.

DOI
10.3390/atoms4010011

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Comment on: Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment

W. M. Stuckey, Michael Silberstein, Timothy J. McDevitt

In a July 2014 Nature Communications paper, Denkmayr et al. claim to have instantiated so-called quantum Cheshire Cat experiment using neutron interferometry. Crucial to this claim are weak values which must imply quantum Cheshire Cat interpretation, i.e., the neutron and its spin are spatially separated in their experiment. While they measured correct weak values for quantum Cheshire Cat interpretation, corresponding implications do not obtain because, as we show, those weak values were measured with both a quadratic and a linear magnetic field Bz interaction. We show explicitly how those weak values imply quantum Cheshire Cat if Bz interaction is linear and then we show how quadratic Bz interaction destroys quantum Cheshire Cat implications of those weak values. Since both linear and quadratic Bz interactions contribute equally to neutron intensity in this experiment, deviant weak value implications are unavoidable. Because weak values were used successfully to compute neutron intensities for weak Bz in this experiment, it is clearly case that one cannot make ontological inferences from weak values without taking into account corresponding interaction strength.

•Oct 5, 2014•1 citation
The validity of quantum-mechanical predictions has been confirmed with a high degree of accuracy in a wide range of experiments. Although the statistics of the outcomes of a measuring apparatus have been studied intensively, little has been explored and is known regarding the accessibility of quantum dynamics. For these sorts of fundamental studies of quantum mechanics, interferometry using neutron matter-waves in particular, provides almost ideal experimental circumstances. In this device quantum interference between spatially separated beams occurs on a macroscopic scale. Recently, the full determination of weak-values of neutrons 1 2 - spin adds a new aspect to the study of quantum dynamics. Moreover, a new counter-intuitive phenomenon, called quantum Cheshire Cat, is observed in an interference experiment. In this article, we present an overview of these experiments.
Quantum theory provides us with the best account of microscopic components of matter as well as of radiation. It was introduced in the twentieth century and has experienced a wide range of success. Although the theory’s probabilistic predictions of final experimental outcomes is found to be correct with high precision, there is no general consensus regarding what is actually going on with a quantum system “en route”, or rather the perceivable intermediate behavior of a quantum system, e.g., the particle’s behavior in the double-slit experiment. Neutron interferometry using single silicon perfect crystals is established as a versatile tool to test fundamental phenomena in quantum mechanics, where an incident neutron beam is coherently split in two or three beam paths with macroscopic separation of several centimeters. Here, we present quantum optical experiments with these matter-wave interferometers, studying the effect of the quantum Cheshire Cat in some variants, the neutron’s presence in the paths of the interferometer as well as the direct test of a commutation relation. To reduce disturbances induced by the measurement, the interaction strength is lessened and so-called weak interactions are exploited by employing pre- and post-selection procedures. All results of the experiments confirm the predictions of quantum theory; the observed behaviors of the neutron between the pre- and post-selection in space and time emphasize striking and counter-intuitive aspects of quantum theory.
From its very beginning, quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schrödinger cats and quantum non-locality. Another paradoxical phenomenon found within the framework of quantum mechanics is the 'quantum Cheshire Cat': if a quantum system is subject to a certain pre- and postselection, it can behave as if a particle and its property are spatially separated. It has been suggested to employ weak measurements in order to explore the Cheshire Cat's nature. Here we report an experiment in which we send neutrons through a perfect silicon crystal interferometer and perform weak measurements to probe the location of the particle and its magnetic moment. The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other.
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.
Fundamental phenomena in quantum mechanics are investigated by the use of matter-wave optics: in the studies neutron polarimeter and interferometer are exploited. Successive measurements of 1/2-spin of the neutron are carried out to test the error-disturbance uncertainty relation. The experimental results confirm the violation of Heisenberg's original reciprocal relation for measurement error and disturbance, and the validity of the reformulated generally valid relation. In addition, as an example of a counterfactual phenomenon of quantum mechanics, interferometric experiment is performed to observe the so-called quantum Cheshire-Cat: a particle and its magnetic moment travel through the interferometer along different beam paths. The results of our experiment suggest that, with suitable pre- and post-selections, neutrons travel along one of the arms of the interferometer, while their spin is located in the other arm.
Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.
In a July 2014 Nature Communications paper, Denkmayr et al. claim to have instantiated so-called quantum Cheshire Cat experiment using neutron interferometry. Crucial to this claim are weak values which must imply quantum Cheshire Cat interpretation, i.e., the neutron and its spin are spatially separated in their experiment. While they measured correct weak values for quantum Cheshire Cat interpretation, corresponding implications do not obtain because, as we show, those weak values were measured with both a quadratic and a linear magnetic field Bz interaction. We show explicitly how those weak values imply quantum Cheshire Cat if Bz interaction is linear and then we show how quadratic Bz interaction destroys quantum Cheshire Cat implications of those weak values. Since both linear and quadratic Bz interactions contribute equally to neutron intensity in this experiment, deviant weak value implications are unavoidable. Because weak values were used successfully to compute neutron intensities for weak Bz in this experiment, it is clearly case that one cannot make ontological inferences from weak values without taking into account corresponding interaction strength.