  Realising and probing topological superfluids is a key goal for fundamental
science, with exciting technological promises. Here, we show that chiral
$p_x+ip_y$ pairing in a two-dimensional topological superfluid can be detected
through circular dichroism, namely, as a difference in the excitation rates
induced by a clockwise and counter-clockwise circular drive. For weak pairing,
this difference is to a very good approximation determined by the Chern number
of the superfluid, whereas there is a non-topological contribution scaling as
the superfluid gap squared that becomes signifiant for stronger pairing. This
gives rise to a competition between the experimentally driven goal to maximise
the critical temperature of the superfluid, and observing a signal given by the
underlying topology. Using a combination of strong coupling Eliashberg and
Berezinskii-Kosterlitz-Thouless theory, we analyse this tension for an atomic
Bose-Fermi gas, which represents a promising platform for realising a chiral
superfluid. We identify a wide range of system parameters where both the
critical temperature is high and the topological contribution to the dichroic
signal is dominant.
