A new method to measure an atomic wave function is discussed. It effectively solves the problem of an initially random phase of a travelling-wave laser beam. The relationship between the measured data and the atomic wave function is presented, and the wave function's reconstruction procedure is also analyzed.
We discuss a simple method to probe the wave function $\ensuremath{\psi}(x)$ 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 ${\ensuremath{\psi}}^{*}(x)\ensuremath{\psi}(x\ensuremath{-}\ensuremath{\Delta}x)$, which finally allows us to reconstruct the phase of $\ensuremath{\psi}(x)$.
A wave-packet interference technique is proposed to measure exotic atomic Rydberg wave functions. For example, the subject wave packet is excited by an arbitrary pulse or pulse sequence. The resulting wave function is probed by a well-characterized pulse that shares a phase relationship with the excitation pulse(s). The observable is the population in each eigenstate after the probe pulse. By making a series of such measurements, varying the phase between excitation and probe pulses, the wave function created by the excitation pulse can be inferred. The method is experimentally feasible for atomic systems, and the extension of the method to molecular systems also appears possible.