The article of record as published may be found at https://doi.org/10.1103/PhysRevLett.123.083601We 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.This work is funded in part by the Israel Science Foundation (grant No. 856/18) and the German- Israeli DIP projects (Hybrid devices: FO 703/2-1, AR 924/1-1, DU 1086/2-1) supported by the DFG. We also acknowledge support from the Israeli Council for Higher Education (Israel). M.A.E. is thankful to the Center for Integrated Quantum Science and Technology (IQST ) for its generous financial support. W.P.S. is grateful to Texas A&M University for a Faculty Fellowship at the Hagler Institute for Advanced Study at Texas A&M University, and to Texas A&M AgriLife Research for the support of this work. The research of the IQST is financially supported by the Ministry of Science, Research and Arts, Baden-Wurttemberg. F.A.N. is grateful for a generous Laboratory University Collaboration Initiative (LUCI) grant from the Office of the Secretary of Defense.This work is funded in part by the Israel Science Foundation (grant No. 856/18) and the German- Israeli DIP projects (Hybrid devices: FO 703/2-1, AR 924/1-1, DU 1086/2-1) supported by the DFG. We also acknowledge support from the Israeli Council for Higher Education (Israel). M.A.E. is thankful to the Center for Integrated Quantum Science and Technology (IQST ) for its generous financial support. W.P.S. is grateful to Texas A&M University for a Faculty Fellowship at the Hagler Institute for Advanced Study at Texas A&M University, and to Texas A&M AgriLife Research for the support of this work. The research of the IQST is financially supported by the Ministry of Science, Research and Arts, Baden-Wurttemberg. F.A.N. is grateful for a generous Laboratory University Collaboration Initiative (LUCI) grant from the Office of the Secretary of Defense
