Aharonov–Casher effect explained

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 (

\varphi ) while traveling along some path P. In the Aharonov–Bohm effect it is\varphi _{\rm} = (q)/(\hbar) \int _{P} A ⋅ d x

While for the Aharonov–Casher effect it is

\varphi _{\rm} = (1)/(\hbar c ^{2}) \int _{P} ( E x \boldsymbol \mu) ⋅ d x

where

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

References

1. Y. Aharonov . A. Casher . Topological quantum effects for neutral particles . Phys. Rev. Lett. . 1984 . 53 . 319–321 . 10.1103/PhysRevLett.53.319 . 4. 1984PhRvL..53..319A .
2. A. Cimmino . G. I. Opat . A. G. Klein. H. Kaiser . S. A. Werner . M. Arif . R. Clothier . Observation of the topological Aharonov–Casher phase shift by neutron interferometry . Phys. Rev. Lett. . 1989 . 63 . 380–383 . 10.1103/PhysRevLett.63.380 . 4 . 10041058. 1989PhRvL..63..380C .
3. W. J. Elion . J. J. Wachters . L. L. Sohn. J. D. Mooij . Observation of the Aharonov–Casher effect for vortices in Josephson-junction arrays . Phys. Rev. Lett. . 1993 . 71 . 2311–2314 . 10.1103/PhysRevLett.71.2311 . 14 . 10054641. 1993PhRvL..71.2311E .
4. • E. N. Bogachek . U. Landman . Aharonov–Bohm and Aharonov–Casher tunneling effects and edge states in double-barrier structures . Phys. Rev. B . 1994 . 50 . 10.1103/PhysRevB.50.2678 . 4 . 2678–2680. 9976496 . 1994PhRvB..50.2678B .

Bibliography

• Book: Commins, Eugene D.. Quantum Mechanics; an experimentalist's approach. 2014. Cambridge University Press. 83–96.
• 6 . M. Koenig . A. Tschetschetkin . E.M. Hankiewicz . Jairo Sinova . V. Hock . V. Daumer . M. Schaefer . C.R. Becker . H. Buhmann. L.W. Molenkamp . Direct Observation of the Aharonov–Casher Phase . Phys. Rev. Lett. . 2006 . 96 . 10.1103/PhysRevLett.96.076804 . cond-mat/0508396 . 7 . 2006PhRvL..96g6804K . 16606124 . 076804. 7934918 .
• T. Boyer . Proposed Aharonov–Casher effect: Another example of an Aharonov–Bohm effect arising from a classical lag . Phys. Rev. B . 1987 . 36 . 10.1103/PhysRevA.36.5083 . 10 . 5083–5086. 9898771 . 1987PhRvA..36.5083B .
• D. . Rohrlich . 2007 . The Aharonov–Casher effect . 0708.3744 . quant-ph.
• Meier . Florian . Loss . Daniel . Magnetization Transport and Quantized Spin Conductance . Physical Review Letters . 90 . 16 . 22 April 2003 . 0031-9007 . 10.1103/physrevlett.90.167204 . 167204. 12732002 . cond-mat/0209521 . 2003PhRvL..90p7204M . 22378460 .
• Nakata . Kouki . van Hoogdalem . Kevin A. . Simon . Pascal . Loss . Daniel . Josephson and persistent spin currents in Bose-Einstein condensates of magnons . Physical Review B . 90 . 14 . 15 October 2014 . 1098-0121 . 10.1103/physrevb.90.144419 . 144419. 1406.7004 . 2014PhRvB..90n4419N . 119214217 .

See also

• Duality (electricity and magnetism)