Effects of colored noise on Landau-Zener transitions: two- and three-level systems

Kenmoe, M. B., Phien, H. N., Kiselev, M. N. and Fai, L. C. (2013) Effects of colored noise on Landau-Zener transitions: two- and three-level systems. Physical Review B, 87 22: 224301.1-224301.18. doi:10.1103/PhysRevB.87.224301

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Author Kenmoe, M. B.
Phien, H. N.
Kiselev, M. N.
Fai, L. C.
Title Effects of colored noise on Landau-Zener transitions: two- and three-level systems
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
Publication date 2013-06-01
Sub-type Article (original research)
DOI 10.1103/PhysRevB.87.224301
Open Access Status File (Publisher version)
Volume 87
Issue 22
Start page 224301.1
End page 224301.18
Total pages 18
Place of publication United States
Publisher American Physical Society
Collection year 2014
Language eng
Formatted abstract
We investigate the Landau-Zener transition in two- and three-level systems subject to a classical Gaussian noise. Two complementary limits of the noise being fast and slow compared to characteristic Landau-Zener tunnel times are discussed. The analytical solution of a density matrix (Bloch) equation is given for a long-time asymptotic of transition probability. It is demonstrated that the transition probability induced or assisted by the fast noise can be obtained through a procedure of Bloch's equation averaging with further reducing it to a master equation. In contrast to the case of fast noise, the transition probability for LZ transition induced, or assisted, by the slow classical noise can be obtained by averaging the solution of Bloch's equation over the noise realization. As a result, the transition probability is described by the activation Arrhenius law. The approximate solution of the Bloch's equation at finite times is written in terms of Fresnel's integrals and interpreted in terms of interference pattern. We discuss consequences of a local isomorphism between SU(2) and SO(3) groups and connections between Schrödinger and Bloch descriptions of spin dynamics. Based on this isomorphism, we establish the relations between S = 1/2 and 1 transition probabilities influenced by the noise. A possibility to use the slow noise as a probe for tunnel time is discussed.
Keyword Nonadiabatic transitions
Energy fluctuation
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
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Citation counts: TR Web of Science Citation Count  Cited 11 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 8 times in Scopus Article | Citations
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