Quantum-state measurement through ballistic expansion of matter waves

In this paper, a method for state measurement in atomic waveguides is presented. Matter waves exiting a terminated waveguide are allowed to expand ballistically. Measurement is performed by spatially resolved detection of laser-induced fluorescence. We describe in detail the motion of wave packets both in the guiding potential and in the region of free expansion. It is shown that different modes can be distinguished in a straightforward manner and that the same is true for coherent superpositions after introduction of a controlled phase shift. The sensitivity of the transition from adiabatic guiding to free expansion is investigated in detail. It is found that adiabatic readjustment, which will distort the original state, can be considerable but may be avoided by proper choice of potential parameters. The method proposed here is shown to be feasible for experiments in atom optics through utilizing numerical estimates.