Exotic quantum holonomy in Hamiltonian systems

Taksu Cheon; Atushi Tanaka; Sang Wook Kim

doi:10.1016/j.physleta.2009.10.064

Exotic quantum holonomy in Hamiltonian systems

Taksu Cheon
, Atushi Tanaka
, Sang Wook Kim

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.

Original language	English
Pages (from-to)	144-149
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	374
Issue number	2
DOIs	https://doi.org/10.1016/j.physleta.2009.10.064
Publication status	Published - 28 Dec 2009

Bibliographical note

Funding Information:
We acknowledge the financial support by the Grant-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science and Technology , Japan (Grant number 21540402 ), and by Korea Research Foundation Grant ( KRF-2008-314-C00144 ).

Keywords

Adiabatic quantum control
Geometric phase
Non-Abelian gauge potential

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10.1016/j.physleta.2009.10.064

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title = "Exotic quantum holonomy in Hamiltonian systems",

abstract = "We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.",

keywords = "Adiabatic quantum control, Geometric phase, Non-Abelian gauge potential",

author = "Taksu Cheon and Atushi Tanaka and Kim, \{Sang Wook\}",

note = "Funding Information: We acknowledge the financial support by the Grant-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science and Technology , Japan (Grant number 21540402 ), and by Korea Research Foundation Grant ( KRF-2008-314-C00144 ).",

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AU - Cheon, Taksu

AU - Tanaka, Atushi

AU - Kim, Sang Wook

N1 - Funding Information: We acknowledge the financial support by the Grant-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science and Technology , Japan (Grant number 21540402 ), and by Korea Research Foundation Grant ( KRF-2008-314-C00144 ).

PY - 2009/12/28

Y1 - 2009/12/28

N2 - We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.

AB - We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.

KW - Adiabatic quantum control

KW - Geometric phase

KW - Non-Abelian gauge potential

UR - https://www.scopus.com/pages/publications/71849118973

U2 - 10.1016/j.physleta.2009.10.064

DO - 10.1016/j.physleta.2009.10.064

M3 - Article

AN - SCOPUS:71849118973

SN - 0375-9601

VL - 374

SP - 144

EP - 149

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 2

ER -

Exotic quantum holonomy in Hamiltonian systems

Abstract

Bibliographical note

Keywords

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