  In the field of atom optics, the basis of many experiments is a two level
atom coupled to a light field. The evolution of this system is governed by a
master equation. The irreversible components of this master equation describe
the spontaneous emission of photons from the atom. For many applications, it is
necessary to minimize the effect of this irreversible evolution. This can be
achieved by having a far detuned light field. The drawback of this regime is
that making the detuning very large makes the timestep required to solve the
master equation very small, much smaller than the timescale of any significant
evolution. This makes the problem very numerically intensive. For this reason,
approximations are used to simulate the master equation which are more
numerically tractable to solve. This paper analyses four approximations: The
standard adiabatic approximation; a more sophisticated adiabatic approximation
(not used before); a secular approximation; and a fully quantum dressed-state
approximation. The advantages and disadvantages of each are investigated with
respect to accuracy, complexity and the resources required to simulate. In a
parameter regime of particular experimental interest, only the sophisticated
adiabatic and dressed-state approximations agree well with the exact evolution.
