In this paper we present a mathematical procedure to analytically calculate the output signal of a pulsed atom interferometer in an inertial field. Using the wellknown ABCDξ method we take into account the full wave dynamics of the atoms with a first order treatment of the wavefront distortion by the laser pulses. Using a numerical example we study the effect of both the length of the beam splitting laser pulses and of the width of the initial spatial distribution of the atoms. First, we find that in a general inertial field the interferometer only has a limited window in terms of the initial width (centered around 100 µm in the example calculation) in which interference fringes are visible at all. This effect is caused by the inevitable statistical spread in atomic parameters, such as initial position and momentum, and the dependence of the interferometer phase on these. In the optimum case, the useful range of the initial width is formed by the range in which both the spatial distribution and the diffraction limited momentum spread are small enough to avoid large phase differences over the atomic wavefunction. As a second result we find that the interferometer phase depends strongly on the length of the laser pulses and, to a smaller extent, on the initial width of the atomic cloud. This spatial dependency is relatively small (∼10 −5 rad) and justifies semiclassical approximations, as used in other calculations, for most experiments.

We report on a technique to split an atomic beam coherently with an easily adjustable splitting angle. In our experiment metastable helium atoms in the ͉͕1s2s͖ 3 S 1 M =1͘ state diffract from a polarization gradient light field formed by counterpropagating + and − polarized laser beams in the presence of a homogeneous magnetic field. In the near-adiabatic regime, energy conservation allows the resonant exchange between magnetic energy and kinetic energy. As a consequence, symmetric diffraction of ͉M =0͘ or ͉M =−1͘ atoms in a single order is achieved, where the order can be chosen freely by tuning the magnetic field. We present experimental results up to sixth-order diffraction ͑24បk momentum splitting, i.e., 2.21 m/s in transverse velocity͒ and present a simple theoretical model that stresses the similarity with conventional Bragg scattering. The resulting device constitutes a flexible, adjustable, large-angle, three-way coherent atomic beam splitter with many potential applications in atom optics and atom interferometry.

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