  A strongly-driven ($\Omega >> \gamma$) two level atom relaxes towards an
equilibrium state rho which is almost completely mixed. One interpretation of
this state is that it represents an ensemble average, and that an individual
atom is at any time in one of the eigenstates of $\rho$. The theory of Teich
and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete,
with an individual atom jumping stochastically between the two eigenstates when
a photon is emitted. The dressed atom theory is also supposed to describe the
quantum jumps of an individual atom due to photo-emissions. But the two
pictures are contradictory because the dressed states of the atom are almost
orthogonal to the eigenstates of $\rho$. In this paper we investigate three
ways of measuring the field radiated by the atom, which attempt to reproduce
the simple quantum jump dynamics of the dressed state or Teich and Mahler
models. These are: spectral detection (using optical filters), two-state jumps
(using adaptive homodyne detection) and orthogonal jumps (another adaptive
homodyne scheme). We find that the three schemes closely mimic the jumps of the
dressed state model, with errors of order $(3/4) (\gamma/\Omega)^{2/3}$, $(1/4)
(\gamma/\Omega)^{2}$, and $(3/4) (\gamma/\Omega)^{2}$ respectively. The
significance of this result to the program of environmentally-induced
superselection is discussed.
