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

T^3-Stern-Gerlach Matter-Wave Interferometer