Discriminating field mixtures from macroscopic superpositions

Atomic homodyne detection allows the field characteristic function to be reconstructed from the excitation probabilities of probe atoms that interact both with the prepared cavity field and a reference driving field. We examine the effects of retaining a full quantum description of both fields and show that the homodyne approximation limits the time of observation of the field. This in turn limits our ability to reconstruct precisely the field characteristics from the restricted data, and can make it impossible to determine fine quantum detail, and, in particular, to discriminate between field superpositions and statistical mixtures.