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 (${\displaystyle \varphi }$) while traveling along some path P. In the Aharonov–Bohm effect it is

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

While for the Aharonov–Casher effect it is

${\displaystyle \varphi _{\rm {AC}}={\frac {1}{\hbar c^{2}}}\int _{P}(\mathbf {E} \times {\boldsymbol {\mu }})\cdot d\mathbf {x} }$

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

References

Bibliography

• Commins, Eugene D. (2014). Quantum Mechanics; an experimentalist's approach. Cambridge University Press. pp. 83–96.

• 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): 076804. arXiv:cond-mat/0508396. Bibcode:2006PhRvL..96g6804K. doi:10.1103/PhysRevLett.96.076804. PMID 16606124. S2CID 7934918.
• T. Boyer (1987). "Proposed Aharonov–Casher effect: Another example of an Aharonov–Bohm effect arising from a classical lag". Phys. Rev. B. 36 (10): 5083–5086. Bibcode:1987PhRvA..36.5083B. doi:10.1103/PhysRevA.36.5083. PMID 9898771.
• Rohrlich, D. (2007). "The Aharonov–Casher effect". arXiv:0708.3744 [quant-ph].
• Meier, Florian; Loss, Daniel (22 April 2003). "Magnetization Transport and Quantized Spin Conductance". Physical Review Letters. 90 (16): 167204. arXiv:cond-mat/0209521. Bibcode:2003PhRvL..90p7204M. doi:10.1103/physrevlett.90.167204. ISSN 0031-9007. PMID 12732002. S2CID 22378460.
• Nakata, Kouki; van Hoogdalem, Kevin A.; Simon, Pascal; Loss, Daniel (15 October 2014). "Josephson and persistent spin currents in Bose-Einstein condensates of magnons". Physical Review B. 90 (14): 144419. arXiv:1406.7004. Bibcode:2014PhRvB..90n4419N. doi:10.1103/physrevb.90.144419. ISSN 1098-0121. S2CID 119214217.

See also

• Duality (electricity and magnetism)