  In an atomic interferometer, the phase shift due to rotation is proportional
to the area enclosed by the split components of the atom. However, this model
is unclear for an atomic interferometer demonstrated recently by Shahriar et
al., for which the atom simply passes through a single-zone optical beam,
consisting of a pair of bichromatic counter-propagating beams. During the
passage, the atomic wave packets in two distinct internal states couple to each
other continuously. The two internal states trace out a complicated trajectory,
guided by the optical beams, with the amplitude and spread of each wavepacket
varying continuously. Yet, at the end of the single-zone excitation, there is
an interference with fringe amplitudes that can reach a visibility close to
unity. For such a situation, it is not clear how one would define the area of
the interferometer, and therefore, what the rotation sensitivity of such an
interferometer would be. In this paper we analyze this interferometer in order
to determine its rotation sensitivity, and thereby determine its effective
area. In many ways, the continuous interferometer (CI) can be thought of as a
limiting version of the Borde-Chu Interferometer (BCI). We identify a quality
factor that can be used to compare the performance of these interferometers.
Under conditions of practical interest, we show that the rotation sensitivity
of the CI can be comparable to that of the BCI. The relative simplicity of the
CI (e.g., elimination of the task of precise angular alignment of the three
zones) then makes it a potentially better candidate for practical atom
interferometry for rotation sensing.
