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Aharonov–Casher effect

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The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 by Yakir Aharonov and Aharon Casher,[1] 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 interferometer in 1989[2] and later by fluxon interference of magnetic vortices in Josephson junctions.[3] It has also been seen with electrons and atoms.

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

φ A B = q ℏ ∫ P A ⋅ d x {\displaystyle \varphi _{\rm {AB}}={\frac {q}{\hbar }}\int _{P}\mathbf {A} \cdot d\mathbf {x} } {\displaystyle \varphi _{\rm {AB}}={\frac {q}{\hbar }}\int _{P}\mathbf {A} \cdot d\mathbf {x} }

While for the Aharonov–Casher effect it is

φ A C = 1 ℏ c 2 ∫ P ( E × μ ) ⋅ d x {\displaystyle \varphi _{\rm {AC}}={\frac {1}{\hbar c^{2}}}\int _{P}(\mathbf {E} \times {\boldsymbol {\mu }})\cdot d\mathbf {x} } {\displaystyle \varphi _{\rm {AC}}={\frac {1}{\hbar c^{2}}}\int _{P}(\mathbf {E} \times {\boldsymbol {\mu }})\cdot d\mathbf {x} }

where q {\displaystyle q} {\displaystyle q} is its charge and μ {\displaystyle {\boldsymbol {\mu }}} {\displaystyle {\boldsymbol {\mu }}} is the magnetic moment. The effects have been observed together.[4]

References

  1. 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.
  2. 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.
  3. 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. Archived from the original on 2011-09-27. Retrieved 2011-09-21.

Bibliography

See also