Atom counting in ultra-cold gases using photoionisation and ion detection

We analyse photoionisation and ion detection as a means of accurately counting ultra-cold atoms. We show that it is possible to count clouds containing many thousands of atoms with accuracies better than $N^{-1/2}$ with current technology. This allows the direct probing of sub-Poissonian number statistics of atomic samples. The scheme can also be used for efficient single atom detection with high spatio-temporal resolution. All aspects of a realistic detection scheme are considered, and we discuss experimental situations in which such a scheme could be implemented.