Limit to non-destructive optical detection of atoms

All optical techniques used to probe the properties of Bose-Einstein condensates have been based on dispersion and absorption that can be described by a two-level atom. Both phenomena lead to spontaneous emission that is destructive. Recently, both were shown to lead to the same limit to the signal to noise ratio for a given destruction. We generalise this result to 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 measurement schemes.