Violation of a Leggett-Garg Inequality Using Ideal Negative Measurements in Neutron Interferometry.

Leggett-Garg inequalities (LGIs) have been proposed in order to assess how far the predictions of quantum mechanics defy "macroscopic realism." With LGIs, correlations of measurements performed on a single system at different times are described. We report on an experiment that demonstrates the violation of an LGI with neutrons. The final measured value of the Leggett-Garg correlator K=1.120±0.007(stat)±0.019(sys), obtained in a neutron interferometric experiment, is clearly above the limit K=1 predicted by macrorealistic theories. The experimental results are analyzed within the framework of dynamical theory of neutron diffraction, evidently reproducing the obtained values.

Quantum causality emerging in a delayed-choice quantum Cheshire Cat experiment with neutrons.

We report an experiment with neutrons in a silicon perfect crystal interferometer, that realizes a quantum Cheshire Cat in a delayed choice setting. In our setup the quantum Cheshire Cat is established by spatially separating the particle and its property (i.e. the neutron and its spin) into the two different paths of the interferometer. The condition for a delayed choice setting is achieved by postponing the choice of path assignment for the quantum Cheshire Cat, i.e. which path is taken by the particle and which by its property, until the point in time when the neutron wave function has already split and entered the interferometer. The results of the experiment suggest not only the fact that the neutrons and its spin are separated and take different paths in the interferometer, but also quantum-mechanical causality is implied, insomuch that the behavior of a quantum system is affected by the choice of the selection at a later point in time.

Phase vortex lattices in neutron interferometry.

Neutron Orbital Angular Momentum (OAM) is an additional quantum mechanical degree of freedom, useful in quantum information, and may provide more complete information on the neutron scattering amplitude of nuclei. Various methods for producing OAM in neutrons have been discussed. In this work we generalize magnetic methods which employ coherent averaging and apply this to neutron interferometry. Two aluminium prisms are inserted into a nested loop interferometer to generate a phase vortex lattice with significant extrinsic OAM, 〈Lz〉 ≈ 0.35, on a length scale of ≈ 220 µm, transverse to the propagation direction. Our generalized method exploits the strong nuclear interaction, enabling a tighter lattice. Combined with recent advances in neutron compound optics and split crystal interferometry our method may be applied to generate intrinsic neutron OAM states. Finally, we assert that, in its current state, our setup is directly applicable to anisotropic ultra small angle neutron scattering.

Experimental Demonstration of Direct Path State Characterization by Strongly Measuring Weak Values in a Matter-Wave Interferometer.

A method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently, Vallone and Dequal [Phys. Rev. Lett. 116, 040502 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.040502] showed theoretically that weak measurements are not a necessary condition to determine the weak value. Here, we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system's quantum state was characterized via direct measurements, using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones for tomographic accuracy. Our results are not limited to neutron interferometry, but can be used in a wide range of quantum systems.

Experimental Test of Residual Error-Disturbance Uncertainty Relations for Mixed Spin-½ States.

The indeterminacy inherent in quantum measurements is an outstanding character of quantum theory, which manifests itself typically in the uncertainty principle. In the last decade, several universally valid forms of error-disturbance uncertainty relations were derived for completely general quantum measurements for arbitrary states. Subsequently, Branciard established a form that is optimal for spin measurements for some pure states. However, the bound in his inequality is not stringent for mixed states. One of the present authors recently derived a new bound tight in the corresponding mixed state case. Here, a neutron-optical experiment is carried out to investigate this new relation: it is tested whether error and disturbance of quantum measurements disappear or persist in mixing up the measured ensemble. The attainability of the new bound is experimentally observed, falsifying the tightness of Branciard's bound for mixed spin states.

Erratum: Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Spin-1/2 Measurements [Phys. Rev. Lett. 115, 030401 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.115.030401.

Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Spin-1/2 Measurements.

Information-theoretic definitions for noise and disturbance in quantum measurements were given in [Phys. Rev. Lett. 112, 050401 (2014)] and a state-independent noise-disturbance uncertainty relation was obtained. Here, we derive a tight noise-disturbance uncertainty relation for complementary qubit observables and carry out an experimental test. Successive projective measurements on the neutron's spin-1/2 system, together with a correction procedure which reduces the disturbance, are performed. Our experimental results saturate the tight noise-disturbance uncertainty relation for qubits when an optimal correction procedure is applied.

Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment.

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.

Kochen-Specker theorem studied with neutron interferometer.

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Observation of nonadditive mixed-state phases with polarized neutrons.

In a neutron polarimetry experiment the mixed-state relative phases between spin eigenstates are determined from the maxima and minima of measured intensity oscillations. We consider evolutions leading to purely geometric, purely dynamical, and combined phases. It is experimentally demonstrated that the sum of the individually determined geometric and dynamical phases is not equal to the associated total phase which is obtained from a single measurement, unless the system is in a pure state.