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The strong-coupling limit of molecule formation in an atomic Bose-Einsteincondensate via two-mode one-color photoassociation or sweep across a Feshbachresonance is examined using a basic nonlinear time-dependent two-state model.For the general class of term-crossing models with constant coupling, a commonstrategy for attacking the problem is developed based on the reduction of theinitial system of semiclassical equations for atom-molecule amplitudes to athird order nonlinear differential equation for the molecular stateprobability. This equation provides deriving exact solution for a class ofperiodic level-crossing models. These models reveal much in common with theRabi problem. Discussing the strong-coupling limit for the general case ofvariable detuning, the equation is further truncated to a limit first-ordernonlinear equation. Using this equation, the strong nonlinearity regime for thefirst Nikitin exponential-crossing model is analyzed and accurate asymptoticexpressions for the nonlinear transition probability to the molecular state arederived. It is shown that, because of a finite final detuning involved, thismodel displays essential deviations from the Landau-Zener behavior. Inparticular, it is shown that in the limit of strong coupling the finalconversion probability tends to 1/6. Thus, in this case the strong interactionlimit is not optimal for molecule formation. We have found that if optimalfield intensity is applied the molecular probability is increased up to 1/4(i.e., the half of the initial atomic population).

Strong-coupling limit in cold-molecule formation via photoassociation or Feshbach resonance through Nikitin exponential resonance crossing