  In this work, a classical-quantum correspondence for two-level
pseudo-Hermitian systems is proposed and analyzed. We show that the presence of
a complex external field can be described by a pseudo-Hermitian Hamiltonian if
there is a suitable canonical transformation that links it to a real field. We
construct a covariant quantization scheme which maps canonically related
pseudoclassical theories to unitarily equivalent quantum realizations, such
that there is a unique metric-inducing isometry between the distinct Hilbert
spaces. In this setting, the pseudo-Hermiticity condition for the operators
induces an involution which guarantees the reality of the corresponding
symbols, even for the complex field case. We assign a physical meaning for the
dynamics in the presence of a complex field by constructing a classical
correspondence. As an application of our theoretical framework, we propose a
damped version of the Rabi problem and determine the configuration of the
parameters of the setup for which damping is completely suppressed. The
experimental viability of the proposal is studied within a specific context. We
suggest that the main theoretical results developed in the present work could
be experimentally verified.
