Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models

We consider the simplest nonintegrable model of the multistate Landau-Zener transition. In this model, two pairs of levels in two tunnel-coupled quantum dots are swept past each other by the gate voltage. Although this $2\ifmmode\times\else\texttimes\fi{}2$ model is nonintegrable, it can be solved analytically in the limit when the interlevel energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar $2\ifmmode\times\else\texttimes\fi{}1$ model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In the $2\ifmmode\times\else\texttimes\fi{}1$ model, the probability for a particle, residing at time $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ in one dot, to remain in the same dot at $t\ensuremath{\rightarrow}\ensuremath{\infty}$, falls off exponentially with tunnel coupling. By contrast, in the $2\ifmmode\times\else\texttimes\fi{}2$ model, this probability grows rapidly with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as a manifestation of the Dicke effect.