General limit to non-destructive optical detection of atoms

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.