  Recently, D. Gottesman et al. [Phys. Rev. A 64, 012310 (2001)] showed how to
encode a qubit into a continuous variable quantum system. This encoding was
realized by using non-normalizable quantum codewords, which therefore can only
be approximated in any real physical setup. Here we show how a neutral atom,
falling through an optical cavity and interacting with a single mode of the
intracavity electromagnetic field, can be used to safely encode a qubit into
its external degrees of freedom. In fact, the localization induced by a
homodyne detection of the cavity field is able to project the near-field atomic
motional state into an approximate quantum codeword. The performance of this
encoding process is then analyzed by evaluating the intrinsic errors induced in
the recovery process by the approximated form of the generated codeword.
