  We demonstrate that there is a fundamental limit to the sensitivity of
phase-based detection of atoms with light for a given maximum level of
allowable spontaneous emission. This is a generalisation of previous results
for two-level and three-level atoms. The limit is due to an upper bound on the
phase shift that can be imparted on a laser beam for a given excited state
population. Specifially, we show that no single-pass optical technique using
classical light, based on any number of lasers or coherences between any number
of levels, can exceed the limit imposed by the two-level atom. This puts
significant restrictions on potential non-destructive optical measurement
schemes.
