Quantum state reconstruction of an atomic matter wave

We present a simple method! to reconstruct the wave function psi(x) describ ing the transverse center-of-mass motion of an atomic beam. Our method is b ased on a dispersive interaction between a classical electromagnetic field and two-level atoms. Behind the interaction region the atomic position dist ributions are detected. These position distributions allow us to reconstruc t the phase of psi(x) due to the phase information contained in interferenc e terms of the form psi(x)psi*(x + Delta x). Moreover, the influence of sev eral experimental parameters on the reconstruction quality is studied numer ically.