We first give a detailed account of the theory of atom interferometers
based on a sequence of laser pulses projecting the atomic wave packet
s onto a spatially separating dark superposition state. We then descri
be the experimental realization of a multiple beam atom interferometer
based on this method. In our experiment, we observe an interference s
ignal that shows the sharply peaked Airy-function like pattern charact
eristic for multiple beam interference. Besides this fringe sharpening
effect, we observe a further significant difference compared to the s
ignal of a conventional two-beam atom interferometer. When the time be
tween the beamsplitting pulses is varied, we observe collapse and revi
val of the fringe pattern, which is caused by a recoil phase shift inc
reasing quadratically with the transverse atomic momentum.