Aharonov–Casher effect: Difference between revisions

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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.
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: 380–383. doi:10.1103/PhysRevLett.63.380.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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.
T. Boyer (1987). "Proposed Aharonov-Casher effect: Another example of an Aharonov-Bohm effect arising from a classical lag". Phys. Rev. B. 36. doi:10.1103/PhysRevA.36.5083.
D. Rohrlich, "The Aharonov-Casher effect", arXiv:0708.3744.

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-The '''Aharonov–Casher effect''' is a [[quantum mechanics|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 of [[neutrons]] or [[fluxons]].
+The '''Aharonov–Casher effect''' is a [[quantum mechanics|quantum mechanical]] phenomenon in which a traveling [[magnetic dipole]] is affected by [[electric field]]. It is [[Duality_%28electricity_and_magnetism%29|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 [[Double-slit experiment|interference]] of [[neutrons]] or [[fluxons]].
 In both effects particle acquires some phase shift (<math>\varphi</math>) while traveling along some path ''P''. In Aharonov–Bohm effect it is
@@ Line 12: / Line 12: @@
 ==Bibliography==
-* Y. Aharonov and A. Casher, “Topological quantum effects for neutral particles”, Phys. Rev. Lett. 53, 319-321 (1984).
+* {{cite journal | author=Y. Aharonov, A. Casher | title=Topological quantum effects for neutral particles | journal=Phys. Rev. Lett. | year=1984 | volume=53 | pages=319-321 | doi=10.1103/PhysRevLett.53.319 | url=http://www.tau.ac.il/~yakir/yahp/yh98}}
-* A. Cimmino, G. I. Opat, A. G. Klein, H. Kaiser, S. A. Werner, M. Arif and R. Clothier, “Observation of the topological Aharonov-Casher phase shift by neutron interferometry”, Phys. Rev. Lett. 63, 380-383 (1989).
+* {{cite journal | author=A. Cimmino, G. I. Opat, A. G. Klein, H. Kaiser, S. A. Werner, M. Arif, R. Clothier | title=Observation of the topological Aharonov-Casher phase shift by neutron interferometry | journal=Phys. Rev. Lett. | year=1989 | volume=63 | pages=380-383 | doi=10.1103/PhysRevLett.63.380 | url=http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/Topological%20phases/a-c%20effect%20expts/Cimmino_PRL_1989.pdf}}
-* W. J. Elion, J. J. Wachters, L. L. Sohn and J. D. Mooij, “Observation of the Aharonov-Casher effect for vortices in Josephson-junction arrays”, Phys. Rev.Lett. 71, 2311-2314 (1993).
+* {{cite journal | author=W. J. Elion, J. J. Wachters, L. L. Sohn, J. D. Mooij | title=Observation of the Aharonov-Casher effect for vortices in Josephson-junction arrays | journal=Phys. Rev. Lett. | year=1993 | volume=71 | pages=2311-2314 | doi=10.1103/PhysRevLett.71.2311 | url=http://repository.tudelft.nl/view/ir/uuid%3A1fc70550-ac87-49fd-af97-bf0372b260f0/}}
-* M. Konig et al., “Direct Observation of the Aharonov-Casher Phase”, Phys.Rev. Lett. 96, 076804 (2006).
+* {{cite journal | author=W. J. Elion, J. J. Wachters, L. L. Sohn, J. D. Mooij | title=Direct Observation of the Aharonov-Casher Phase | journal=Phys. Rev. Lett. | year=2006 | volume=96 |  doi=10.1103/PhysRevLett.96.076804 | url=http://arxiv.org/PS_cache/cond-mat/pdf/0508/0508396v1.pdf}}
+* {{cite journal | author=E. N. Bogachek, U. Landman | title=Aharonov-Bohm and Aharonov-Casher tunneling effects and edge states in double-barrier structures | journal=Phys. Rev. B | year=1994 | volume=50 |  doi=10.1103/PhysRevB.50.2678 | url=http://www.physics.gatech.edu/files/u26/papers/0164.pdf}}
-* D. Rohrlich, "The Aharonov-Casher effect", arXiv:0708.3744.
+* {{cite journal | author=T. Boyer | title=Proposed Aharonov-Casher effect: Another example of an Aharonov-Bohm effect arising from a classical lag | journal=Phys. Rev. B | year=1987 | volume=36 |  doi=10.1103/PhysRevA.36.5083}}
-* E. N. Bogachek, U. Landman, "Aharonov-Bohm and Aharonov-Casher tunneling effects and edge states in double-barrier structures", Phys. Rev. B 50, 2678–2680 (1994).
+* D. Rohrlich, "The Aharonov-Casher effect", [http://arxiv.org/PS_cache/arxiv/pdf/0708/0708.3744v1.pdf arXiv:0708.3744].
+==See also==
+[[Duality (electricity and magnetism)]]
+[[Category:Quantum mechanics]]
+[[Category:Physical phenomena]]
 {{Template:Quantum-stub}}