  We present a unique matter-wave interferometer whose phase scales with the
cube of the time the atom spends in the interferometer. Our scheme is based on
a full-loop Stern-Gerlach interferometer incorporating four magnetic field
gradient pulses to create a state-dependent force. In contrast to typical atom
interferometers which make use of laser light for the splitting and
recombination of the wave packets, this realization uses no light and can
therefore serve as a high-precision surface probe at very close distances.
