Aharonov–Casher effect

The Aharonov–Casher effect is a quantum mechanical phenomenon in which a traveling magnetic dipole is affected by electric field. It is dual to Aharonov-Bohm effect, in which the quantum phase of charged particle depends on side of magnetic flux tube it comes through. In Aharonov–Casher effect, the particle has magnetic moment and the tubes are charged instead. It was used for example to observe interference of neutrons or fluxons.

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

$\varphi _{AB}={\frac {q}{\hbar }}\int _{P}\mathbf {A} \cdot d\mathbf {x}$

While for Aharonov-Casher effect it is

$\varphi _{AC}={\frac {1}{\hbar }}\int _{P}(\mathbf {E} \times \mu )\cdot d\mathbf {x}$

where $q$ is its charge and $\mu$ is the magnetic moment.

Bibliography

• Y. Aharonov, A. Casher (1984). "Topological quantum effects for neutral particles". Phys. Rev. Lett. 53: 319–321. doi:10.1103/PhysRevLett.53.319.
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• 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: 2311–2314. doi:10.1103/PhysRevLett.71.2311.{{cite journal}}: CS1 maint: multiple names: authors list (link)
• W. J. Elion, J. J. Wachters, L. L. Sohn, J. D. Mooij (2006). "Direct Observation of the Aharonov-Casher Phase" (PDF). Phys. Rev. Lett. 96. doi:10.1103/PhysRevLett.96.076804.{{cite journal}}: CS1 maint: multiple names: authors list (link)
• 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. doi:10.1103/PhysRevB.50.2678.
• D. Rohrlich, "The Aharonov-Casher effect", arXiv:0708.3744.