Aharonov–Casher effect

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

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.
4. • 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.

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.
• 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].
• Meier, Florian; Loss, Daniel (22 April 2003). "Magnetization Transport and Quantized Spin Conductance". Physical Review Letters. American Physical Society (APS). 90 (16): 167204. arXiv:cond-mat/0209521. doi:10.1103/physrevlett.90.167204. ISSN 0031-9007.
• 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. American Physical Society (APS). 90 (14): 144419. arXiv:1406.7004. doi:10.1103/physrevb.90.144419. ISSN 1098-0121.

See also

• Duality (electricity and magnetism)