Degenerate Landau-Zener model: Analytical solution

G. S. Vasilev, S. S. Ivanov, and N. V. Vitanov
Phys. Rev. A 75, 013417 – Published 23 January 2007

Abstract

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1.

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  • Received 19 September 2006

DOI:https://doi.org/10.1103/PhysRevA.75.013417

©2007 American Physical Society

Authors & Affiliations

G. S. Vasilev and S. S. Ivanov

  • Department of Physics, Sofia University, James Bourchier 5 Boulevard, 1164 Sofia, Bulgaria

N. V. Vitanov

  • Department of Physics, Sofia University, James Bourchier 5 Boulevard, 1164 Sofia, Bulgaria and Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko Chaussée 72, 1784 Sofia, Bulgaria

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Vol. 75, Iss. 1 — January 2007

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