Aharonov–Casher effect

The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 by Yakir Aharonov and Aharon Casher,{{cite journal | author=Y. Aharonov | author2=A. Casher | title=Topological quantum effects for neutral particles | journal=Phys. Rev. Lett. | date=1984 | volume=53 | pages=319–321 | doi=10.1103/PhysRevLett.53.319 | url=http://www.tau.ac.il/~yakir/yahp/yh98 | issue=4|bibcode = 1984PhRvL..53..319A }} 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 {{cite journal | author=A. Cimmino | author2=G. I. Opat | author3=A. G. Klein| author4=H. Kaiser | author5=S. A. Werner | author6= M. Arif | author7=R. Clothier | title=Observation of the topological Aharonov–Casher phase shift by neutron interferometry | journal=Phys. Rev. Lett. | date=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 | issue=4 | pmid=10041058|bibcode = 1989PhRvL..63..380C }} and later by fluxon interference of magnetic vortices in Josephson junctions.{{cite journal | author=W. J. Elion | author2=J. J. Wachters | author3=L. L. Sohn| author4=J. D. Mooij | title=Observation of the Aharonov–Casher effect for vortices in Josephson-junction arrays | journal=Phys. Rev. Lett. | date=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/ | issue=14 | pmid=10054641|bibcode = 1993PhRvL..71.2311E }} 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

: $\varphi_{\rm AB} = \frac{q}{\hbar} \int_P \mathbf{A} \cdot d\mathbf{x}$

While for the Aharonov–Casher effect it is

: $\varphi_{\rm AC} = \frac{1}{\hbar c^2} \int_P (\mathbf{E}\times \boldsymbol \mu) \cdot d\mathbf{x}$

where $q$ is its charge and $\boldsymbol \mu$ is the magnetic moment. The effects have been observed together.* {{cite journal | author=E. N. Bogachek | author2=U. Landman | title=Aharonov–Bohm and Aharonov–Casher tunneling effects and edge states in double-barrier structures | journal=Phys. Rev. B | date=1994 | volume=50 | doi=10.1103/PhysRevB.50.2678 | url=http://www.physics.gatech.edu/files/u26/papers/0164.pdf | issue=4 | pages=2678–2680| pmid=9976496 |bibcode = 1994PhRvB..50.2678B }}

References

Bibliography

{{cite book|last= Commins|first=Eugene D.|title=Quantum Mechanics; an experimentalist's approach|year=2014|publisher=Cambridge University Press|pages=83–96}}
{{cite journal | display-authors=6 | author=M. Koenig | author2=A. Tschetschetkin | author3=E.M. Hankiewicz | author4=Jairo Sinova | author5=V. Hock | author6=V. Daumer | author7=M. Schaefer | author8=C.R. Becker | author9=H. Buhmann| author10=L.W. Molenkamp

| title=Direct Observation of the Aharonov–Casher Phase | journal=Phys. Rev. Lett. | date=2006 | volume=96 | doi=10.1103/PhysRevLett.96.076804 | arxiv=cond-mat/0508396 | issue=7 |bibcode = 2006PhRvL..96g6804K | pmid=16606124 | pages=076804| s2cid=7934918 }}

{{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 | date=1987 | volume=36 | doi=10.1103/PhysRevA.36.5083 | issue=10 | pages=5083–5086| pmid=9898771 |bibcode = 1987PhRvA..36.5083B }}
{{cite arXiv | first = D. | last = Rohrlich |date=2007 | title = The Aharonov–Casher effect | eprint = 0708.3744 |class=quant-ph}}
{{cite journal | last1=Meier | first1=Florian | last2=Loss | first2=Daniel | title=Magnetization Transport and Quantized Spin Conductance | journal=Physical Review Letters | volume=90 | issue=16 | date=22 April 2003 | issn=0031-9007 | doi=10.1103/physrevlett.90.167204 | page=167204| pmid=12732002 | arxiv=cond-mat/0209521 | bibcode=2003PhRvL..90p7204M | s2cid=22378460 }}
{{cite journal | last1=Nakata | first1=Kouki | last2=van Hoogdalem | first2=Kevin A. | last3=Simon | first3=Pascal | last4=Loss | first4=Daniel | title=Josephson and persistent spin currents in Bose-Einstein condensates of magnons | journal=Physical Review B | volume=90 | issue=14 | date=15 October 2014 | issn=1098-0121 | doi=10.1103/physrevb.90.144419 | page=144419| arxiv=1406.7004 | bibcode=2014PhRvB..90n4419N | s2cid=119214217 }}
{{citation |last1=Frydman |first1=Aviad |title=Aharonov-casher Effect With Vortices In An Amorphous Superconductor |date=6 Mar 2020 |work=Bulletin of the American Physical Society |volume=65 |issue=1 |last2=Arnab |first2=Roy |url=https://meetings.aps.org/Meeting/MAR20/Session/W58.1}}

Aharonov–Casher effect

References

Bibliography

See also