Multipath interference in a multistate Landau-Zener-type model

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 $\ensuremath{\varepsilon}$ and an additional state. It includes the conventional bow-tie model as a particular limiting case when $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varepsilon}}0.$ 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 $\ensuremath{\varepsilon}.$ Several paths connect initial and final states; the contributions of different paths are summed up coherently to obtain the overall transition probability. The special $\mathrm{ET}$ (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 $\ensuremath{\varepsilon}.$ 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.