Quantum-nondemolition measurement of small photon numbers and the preparation of number states

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Abstract
We analyze in detail the quantum-nondemolition (QND) scheme of Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. It is shown that the quantum treatment of the scheme based on the density-matrix formalism is fully equivalent to an information-theoretical description. In this context, it is explicitly seen that the scheme works well even with a low detection efficiency. We show further that a careful choice of the atomic velocities can significantly reduce the number of atoms needed to perform a measurement. It is also possible to use a monoenergetic atomic beam, although in this case the number of atoms needed increases. Finally we discuss how the results are modified if the atomic velocities are only known approximately.