Interferometric measurement of an atomic wave function

We discuss a simple method to probe the wave function $\psi \mathrm{}\left(x\right)\mathrm{}$ describing the transverse center-of-mass motion of an atomic beam. We detect position distributions of the atoms after they have interacted with two counterpropagating laser beams. The resulting interference pattern depends crucially on the cross term ${\psi }^{*}\mathrm{}\left(x\right)\mathrm{}\psi \left(x-\Delta x\right)$, which finally allows us to reconstruct the phase of $\psi \mathrm{}\left(x\right)\mathrm{}$.