  Bohmian mechanics is an alternative to standard quantum mechanics that does
not suffer from the measurement problem. While it agrees with standard quantum
mechanics concerning its experimental predictions, it offers novel types of
approximations not suggested by the latter. Of particular interest are
semi-classical approximations, where part of the system is treated classically.
Bohmian semi-classical approximations have been explored before for systems
without electromagnetic interactions. Here, the Rabi model is considered as a
simple model involving light-matter interaction. This model describes a single
mode electromagnetic field interacting with a two-level atom. As is well-known,
the quantum treatment and the semi-classical treatment (where the field is
treated classically rather than quantum mechanically) give qualitatively
different results. We analyse the Rabi model using a different semi-classical
approximation based on Bohmian mechanics. In this approximation, the
back-reaction from the two-level atom onto the classical field is mediated by
the Bohmian configuration of the two-level atom. We find that the Bohmian
semi-classical approximation gives results comparable to the usual mean field
one for the transition between ground and first excited state. Both
semi-classical approximations tend to reproduce the collapse of the population
inversion, but fail to reproduce the revival, which is characteristic of the
full quantum description. Also an example of a higher excited state is
presented where the Bohmian approximation does not perform so well.
