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

M. B. Kenmoe, H. N. Phien, M. N. Kiselev, and L. C. Fai
Phys. Rev. B 87, 224301 – Published 6 June 2013

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.

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  • Received 15 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.224301

©2013 American Physical Society

Authors & Affiliations

M. B. Kenmoe1,2, H. N. Phien3, M. N. Kiselev2, and L. C. Fai1,2,4

  • 1Mesoscopic and Multilayer Structures Laboratory, Faculty of Science, Department of Physics, University of Dschang, Cameroon
  • 2The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
  • 3Center for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane 4072, Australia
  • 4Higher Teachers' Training College, Department of Physics, The University of Bamenda, Cameroon

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Issue

Vol. 87, Iss. 22 — 1 June 2013

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