Abstract
We derive the analytical solution of the model of a two-state system interacting with an external coherent field, in which the Hamiltonian is pseudo-Hermitian. We describe in detail the non-Hermitian generalization of the famed Landau-Zener-St\uckelberg-Majorana model, but similar generalizations can be derived in a very simple fashion for the other analytically soluble two-state models. The analytical solutions possess a non-Hermitian dynamical invariant, which replaces the probability conservation condition in the Hermitian case. Implementations in waveguide optics and nonlinear frequency conversion are suggested.
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