Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree well with the predictions derived from the Pauli -Schrödinger equation.

A miniaturised versatile spin rotator for application in neutron interferometer experiments is developed. The coil design without material in the beam path allows for a magnetic field adjustable to an arbitrary direction perpendicular to the neutron beam. The field simulations show a homogeneous field over the beam cross-section of 8 mm×5 mm and a field transition 20 mm from inside to outside. The performance of the fabricated miniaturised coil was quantified by carrying out the polarimeter experiment of Demirel et al (New J. Phys., 17:023065, 2015) regarding spin-rotation coupling. The high efficiency spin manipulations by the implemented rotating magnetic field results in a linear dependence between the phase shift and the rotation frequency. In near future, the spin rotator will be used to investigate spin-rotation coupling in a related interferometer experiment.

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The well-known Robertson-Schrödinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state dependence. Therefore, Abbott et al. introduced a general approach to derive tight state-independent uncertainty relations for qubit measurements [Mathematics 4, 8 (2016)]. The relations are expressed in two measures of uncertainty, which are standard deviation and entropy, both functions of the expectation value. Here, we present a neutron polarimetric test of the tight state-independent preparation uncertainty relations for orthogonal, as well as nonorthogonal, Pauli spin observables. The final results, obtained with pure and mixed spin states, reproduce the theoretical predictions clearly for arbitrary initial states of variable degree of polarization.

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