Multipath interference in a multistate Landau-Zener-type model

Yu. N. Demkov and V. N. Ostrovsky
Phys. Rev. A 61, 032705 – Published 10 February 2000
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Abstract

The bow-tie model is a particular generalization of the famous two-state Landau-Zener model to an arbitrary number of states. Recently, solution of the bow-tie model was found by the contour integral method [V. N. Ostrovsky and H. Nakamura, J. Phys. A 30, 6939 (1997)]. However, its physical interpretation remained unclear, because the model implies simultaneous strong interaction of all the states apparently irreducible to any simpler pattern. We introduce here a generalized bow-tie model that contains an additional parameter ɛ and an additional state. It includes the conventional bow-tie model as a particular limiting case when ɛ0. In the generalized model all the state-to-state transitions are reduced to the sequence of pairwise transitions and the two-state Landau-Zener model is applied to each of them. Such a reduction is well justified at least in the opposite limit of large parameter ɛ. Several paths connect initial and final states; the contributions of different paths are summed up coherently to obtain the overall transition probability. The special ET (energy and time) symmetry intrinsic for the generalized bow-tie model results in a particular property of interference phases: only purely constructive or purely destructive interference is operative. The complete set of transition probabilities is obtained in a closed form. Importantly, the results do not depend on the parameter ɛ. In the limit of conventional bow-tie model all previously derived results are reproduced. This amounts to rationalization of the bow-tie model by its interpretation in terms of multipath successive two-state transitions.

  • Received 1 June 1999

DOI:https://doi.org/10.1103/PhysRevA.61.032705

©2000 American Physical Society

Authors & Affiliations

Yu. N. Demkov and V. N. Ostrovsky*

  • Institute of Physics, The University of St. Petersburg, 198904 St. Petersburg, Russia

  • *Electronic address: Valentin.Ostrovsky@pobox.spbu.ru

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Vol. 61, Iss. 3 — March 2000

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