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The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It was observed in a gravitational neutron inferometer in 1989(Cimmino et al.) and later by fluxon interference of magnetic vortices in Josephson junctions (Elion et al.). It has also been seen with electrons and atoms.

In both effects the particle acquires a phase shift $$(\varphi)$$ while traveling along some path P. In the Aharonov–Bohm effect it is

$$\varphi_{AB} = \frac{q}{\hbar} \int_P \mathbf{A} \cdot d\mathbf{x}$$

While for the Aharonov–Casher effect it is

$$\varphi_{AC} = \frac{1}{\hbar c^2} \int_P (\mathbf{E}\times \boldsymbol \mu) \cdot d\mathbf{x}$$

where q is its charge and $$\boldsymbol \mu$$ is the magnetic moment. The effects have been observed together(Bogachek and Landman).

Bibliography

Y. Aharonov; A. Casher (1984). "Topological quantum effects for neutral particles". Phys. Rev. Lett. 53 (4): 319–321. Bibcode:1984PhRvL..53..319A. doi:10.1103/PhysRevLett.53.319.
A. Cimmino; G. I. Opat; A. G. Klein; H. Kaiser; S. A. Werner; M. Arif; R. Clothier (1989). "Observation of the topological Aharonov–Casher phase shift by neutron interferometry" (PDF). Phys. Rev. Lett. 63 (4): 380–383. Bibcode:1989PhRvL..63..380C. doi:10.1103/PhysRevLett.63.380. PMID 10041058.
W. J. Elion; J. J. Wachters; L. L. Sohn; J. D. Mooij (1993). "Observation of the Aharonov–Casher effect for vortices in Josephson-junction arrays". Phys. Rev. Lett. 71 (14): 2311–2314. Bibcode:1993PhRvL..71.2311E. doi:10.1103/PhysRevLett.71.2311. PMID 10054641.
M. Koenig; A. Tschetschetkin; E.M. Hankiewicz; Jairo Sinova; V. Hock; V. Daumer; et al. (2006). "Direct Observation of the Aharonov–Casher Phase". Phys. Rev. Lett. 96 (7). arXiv:cond-mat/0508396. Bibcode:2006PhRvL..96g6804K. doi:10.1103/PhysRevLett.96.076804.
E. N. Bogachek; U. Landman (1994). "Aharonov–Bohm and Aharonov–Casher tunneling effects and edge states in double-barrier structures" (PDF). Phys. Rev. B 50 (4): 2678. Bibcode:1994PhRvB..50.2678B. doi:10.1103/PhysRevB.50.2678.
T. Boyer (1987). "Proposed Aharonov–Casher effect: Another example of an Aharonov–Bohm effect arising from a classical lag". Phys. Rev. B 36 (10): 5083. Bibcode:1987PhRvA..36.5083B. doi:10.1103/PhysRevA.36.5083.
Rohrlich, D. (2007). "The Aharonov–Casher effect". arXiv:0708.3744 [quant-ph].
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