  Unit-efficiency homodyne detection of the resonance fluorescence of a
two-level atom collapses the quantum state of the atom to a stochastically
moving point on the Bloch sphere. Recently,Hofmann, Mahler, and Hess [Phys.
Rev. A {\bf 57}, 4877 (1998)] showed that by making part of the coherent
driving proportional to the homodyne photocurrent can stabilize the state to
any point on the bottom half of the sphere. Here we reanalyze their proposal
using the technique of stochastic master equations, allowing their results to
be generalized in two ways. First, we show that any point on the upper or lower
half, but not the equator, of the sphere may be stabilized. Second, we consider
non-unit-efficiency detection, and quantify the effectiveness of the feedback
by calculating the maximal purity obtainable in any particular direction in
Bloch space.
