  We introduce a method to dispersively detect alkali atoms in radio-frequency
dressed states. In particular, we use dressed detection to measure populations
and population differences of atoms prepared in their clock states. Linear
birefringence of the atomic medium enables atom number detection via
polarisation homodyning, a form of common path interferometry. In order to
achieve low technical noise levels, we perform optical sideband detection after
adiabatic transformation of bare states into dressed states. The balanced
homodyne signal then oscillates independently of field fluctuations at twice
the dressing frequency, thus allowing for robust, phase-locked detection that
circumvents low-frequency noise. Using probe pulses of two optical frequencies,
we can detect both clock states simultaneously and obtain population difference
as well as the total atom number. The scheme also allows for difference
measurements by direct subtraction of the homodyne signals at the balanced
detector, which should technically enable quantum noise limited measurements
with prospects for the preparation of spin squeezed states. The method extends
to other Zeeman sublevels and can be employed in a range of atomic clock
schemes, atom interferometers, and other experiments using dressed atoms.
