Photon exchange and entanglement formation during the transmission through a rectangular quantum barrier

When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present analytic results for the transition amplitudes of any possible photon exchange processes for an incoming plane wave and initial Fock, thermal and coherent field states. We show that for coherent field states the entanglement correlates the particle's position to the photon number in the field instead of the particle's energy as usual. Besides entanglement formation, remarkable differences to the classical field treatment also appear with respect to the symmetry between photon emission and absorption, resonance effects and if the field initially occupies the vacuum state.Comment: 6 pages (double column), 6 figure

Invasions of isotopes and of neobiota

We report on invasions with low diffusivity: one in materials science and one in ecology. What is interesting in materials science is to describe diffusivities in order to model technological important materials. In ecology on the other hand predictions into the future appear the most challenging issue

Engineering of triply entangled states in a single-neutron system

We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated the spin, path, and energy degrees of freedom in a single neutron system. The GHZ-like state was analyzed with an inequality derived by Mermin: we determined the four expectation values and finally obtained M = 2.558 +/- 0.004 > 2, which exhibits a clear violation of the noncontextual assumption and confirms quantum contextuality.Comment: 4 pages, 2figure

Energy entanglement in neutron interferometry

Entanglement between degrees of freedom, namely between the spin, path and (total) energy degrees of freedom, for single neutrons is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated relative phases of two-level quantum subsystems. An inequality derived by Mermin was applied to analyze the generated GHZ-like state: we determined the four expectation values and finally obtained M=2.558 +/- 0.004 which is clearly above the threshold of 2. This demonstrates the violation of a Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, exhibits a clear inconsistency between noncontextual assumptions and quantum mechanics and confirms quantum contextuality.Comment: 4 pages, 3 figure

Kochen-Specker theorem studied with neutron interferometer

The Kochen-Specker theorem theoretically shows evidence of 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 by 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 in a single neutron system. Here entanglement is achieved not between different particles, but between degrees of freedom, 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 of the Kochen-Specker theorem. The observed value of (2.291 +/- 0.008), which is above the threshold of 1, clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.Comment: 5 pages, 3 figure

New Aspects of Geometric Phases in Experiments with polarized Neutrons

Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.Comment: 17 pages, 9 figure

Geometric Phase in Entangled Systems: A Single-Neutron Interferometer Experiment

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. in [Phys. Rev. A 69, 032112 (2004)], and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time dependent interaction with two radio-frequency (rf) fields. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme, yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2\sqrt{2} and, therefore, always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like-CHSH inequality, where S remains 2\sqrt2 for all settings of the geometric phase.Comment: 10 pages 9 figure