# Geometric phase in entangled systems: A single-neutron interferometer experiment

## Abstract

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [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 a radiofrequency field. 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{radical}(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{radical}(2) for all settings of the geometric phase.

- Authors:

- Atominstitut der Oesterreichischen Universitaeten, A-1020 Vienna (Austria)
- Department of Physics, Eidgenoessische Technische Hochschule Zuerich, Schafmattstrasse 16, CH-8093 Zurich (Switzerland)
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)
- (France)

- Publication Date:

- OSTI Identifier:
- 21408563

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 81; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.81.042113; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; GEOMETRY; INTERACTIONS; INTERFEROMETERS; NEUTRONS; OSCILLATIONS; QUANTUM ENTANGLEMENT; RADIOWAVE RADIATION; SPIN; TIME DEPENDENCE; ANGULAR MOMENTUM; BARYONS; ELECTROMAGNETIC RADIATION; ELEMENTARY PARTICLES; FERMIONS; FUNCTIONS; HADRONS; MATHEMATICS; MEASURING INSTRUMENTS; NUCLEONS; PARTICLE PROPERTIES; RADIATIONS

### Citation Formats

```
Sponar, S., Klepp, J., Loidl, R., Durstberger-Rennhofer, K., Badurek, G., Hasegawa, Y., Filipp, S., Bertlmann, R. A., Rauch, H., and Institut Laue-Langevin, Boite Postale 156, F-38042 Grenoble CEDEX 9.
```*Geometric phase in entangled systems: A single-neutron interferometer experiment*. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVA.81.042113.

```
Sponar, S., Klepp, J., Loidl, R., Durstberger-Rennhofer, K., Badurek, G., Hasegawa, Y., Filipp, S., Bertlmann, R. A., Rauch, H., & Institut Laue-Langevin, Boite Postale 156, F-38042 Grenoble CEDEX 9.
```*Geometric phase in entangled systems: A single-neutron interferometer experiment*. United States. doi:10.1103/PHYSREVA.81.042113.

```
Sponar, S., Klepp, J., Loidl, R., Durstberger-Rennhofer, K., Badurek, G., Hasegawa, Y., Filipp, S., Bertlmann, R. A., Rauch, H., and Institut Laue-Langevin, Boite Postale 156, F-38042 Grenoble CEDEX 9. Thu .
"Geometric phase in entangled systems: A single-neutron interferometer experiment". United States. doi:10.1103/PHYSREVA.81.042113.
```

```
@article{osti_21408563,
```

title = {Geometric phase in entangled systems: A single-neutron interferometer experiment},

author = {Sponar, S. and Klepp, J. and Loidl, R. and Durstberger-Rennhofer, K. and Badurek, G. and Hasegawa, Y. and Filipp, S. and Bertlmann, R. A. and Rauch, H. and Institut Laue-Langevin, Boite Postale 156, F-38042 Grenoble CEDEX 9},

abstractNote = {The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [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 a radiofrequency field. 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{radical}(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{radical}(2) for all settings of the geometric phase.},

doi = {10.1103/PHYSREVA.81.042113},

journal = {Physical Review. A},

issn = {1050-2947},

number = 4,

volume = 81,

place = {United States},

year = {2010},

month = {4}

}