Weak measurements [1], introduced exactly 30 years ago, underwent a metamorphosis from a theoretical curiosity to a powerful resource for exploring foundations of quantum mechanics, as well as a practical laboratory tool. However, unlike in the original textbook experiment, where an experiment with massive particles is proposed, experimental applications are realized applying photonic systems. We have overcome this gap by developing a new method to weakly measure a massive particle's spin component. Our neutron optical approach is realized by utilizing neutron interferometry, where the neutron's spin is coupled weakly to its spatial degree of freedom [1]. This scheme was then applied to study a new counter-intuitive phenomenon, the so-called quantum Cheshire Cat: If a quantum system is subject to a certain pre- and post-selection, it can behave as if a particle and its property are spatially separated, which is demonstrated in an experimental test [2,3]. State tomography, the usual approach to reconstruct a quantum state, involves a lot of computational post-processing. So in 2011 a novel more direct method was established using weak measurements. Because of this weakness the information gain is very low for each experimental run, so the measurements have to be repeated many times. Our procedure is based on the method established in 2011, without the need of computational post processing, but at the same time uses strong measurements, which makes it possible to determine the quantum state with higher precision and accuracy. We performed a neutron interferometric [4] experiment, but our results are not limited to neutrons, but are in fact completely general. Our latest experiment, using weak measurements, addresses the pigeonhole principle (also known as Dirichlet's box principle): "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole". This obvious and fundamental principle of nature basically captures the very essence of counting. However, as experimentally demonstrate in our neutron optical experiment [5], in quantum mechanics this does not hold! In addition, we construct a confined contextuality witness from weak values, which we measure experimentally, to obtain a violation of the non-contextual bound, thereby identifying which specific observables must fail the non-contextual assignment
[1] S. Sponar, T. Denkmayr, H. Geppert, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, Phys. Rev. A 92, 062121 (2015).
[2] T. Denkmayr, H. Geppert, S. Sponar, H. Lemmel, A. Matzkin, J. Tollaksen, and Y. Hasegawa, Nat Commun. 5, 4492 (2014).
[3] S. Sponar, T. Denkmayr, H. Geppert, and Y. Hasegawa, Atoms 4, 11 (2016).
[4] T. Denkmayr, H. Geppert, H. Lemmel, M. Waegell, J. Dressel, Y. Hasegawa, and S. Sponar, Phys. Rev. Lett. 118, 010402 (2017).
[5] M. Waegell, T. Denkmayr, H. Geppert, D. Ebner, T. Jenke, Y. Hasegawa, S. Sponar, J. Dressel, J. Tollaksen, Physical Review A 96, 052131 (2017).
