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We provide an introduction into the field of atom optics and review our work on interferometry with cold atoms, and in particular with Bose-Einstein condensates. Here we emphasize applications of atom interferometry with sources of this kind. We discuss tests of the equivalence principle, a quantum tiltmeter, and a gravimeter. We acknowledge the support by the CRC 1227 DQmat, the CRC 1128 geo-Q, and the QUEST-LFS. The German Space Agency (DLR) with funds provided by the Fed- eral Ministry of Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grant No. DLR 50WM1137 (QUANTUS-IV-Fallturm), and 50WM1641 (PRIMUS-III) was central to our work. We also acknowledge support by the Federal Ministry of Education and Research (BMBF), by ”Wege in die Forschung (II)” of Leibniz Universit ̈at Hannover, and ”Nieders ̈achsisches Vorab” through the ”Quantum- and Nano-Metrology (QUANOMET)” initiative M.A.E. thanks the Center for Integrated Quantum Science and Technology (IQST ) for financial support. W.P.S. is most grateful to Texas A&M University for a Faculty Fellowship at the Hagler Institute for Advanced Study at the Texas A&M University as well as to Texas A&M AgriLife Research. F.A.N. acknowledges a generous grant from the Office of the Secretary of Defense (OSD) in the Quantum Science and Engineering Program (qSEP). We acknowledge the support by the CRC 1227 DQmat, the CRC 1128 geo-Q, and the QUEST-LFS. The German Space Agency (DLR) with funds provided by the Fed- eral Ministry of Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grant No. DLR 50WM1137 (QUANTUS-IV-Fallturm), and 50WM1641 (PRIMUS-III) was central to our work. We also acknowledge support by the Federal Ministry of Education and Research (BMBF), by ”Wege in die Forschung (II)” of Leibniz Universit ̈at Hannover, and ”Nieders ̈achsisches Vorab” through the ”Quantum- and Nano-Metrology (QUANOMET)” initiative M.A.E. thanks the Center for Integrated Quantum Science and Technology (IQST ) for financial support. W.P.S. is most grateful to Texas A&M University for a Faculty Fellowship at the Hagler Institute for Advanced Study at the Texas A&M University as well as to Texas A&M AgriLife Research. F.A.N. acknowledges a generous grant from the Office of the Secretary of Defense (OSD) in the Quantum Science and Engineering Program (qSEP).

We present a source engineering concept for a binary quantum mixture suitable as input for differential, precision atom interferometry with drift times of several seconds. To solve the non-linear dynamics of the mixture, we develop a set of scaling approach equations and verify their validity contrasting it to the one of a system of coupled Gross-Pitaevskii equations. This scaling approach is a generalization of the standard approach commonly used for single species. Its validity range is discussed with respect to intra- and inter-species interaction regimes. We propose a multi-stage, non-linear atomic lens sequence to simultaneously create dual ensembles with ultra-slow kinetic expansion energies, below 15 pK. Our scheme has the advantage of mitigating wave front aberrations, a leading systematic effect in precision atom interferometry.

The article of record as published may be found at https://doi.org/10.1103/PhysRevLett.123.083601 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. 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.

Recent proposals for space-borne gravitational wave detectors based on atom interferometry rely on extremely narrow single-photon transition lines as featured by alkaline-earth metals or atomic species with similar electronic configuration. Despite their similarity, these species differ in key parameters such as abundance of isotopes, atomic flux, density and temperature regimes, achievable expansion rates, density limitations set by interactions, as well as technological and operational requirements. In this study, we compare viable candidates for gravitational wave detection with atom interferometry, contrast the most promising atomic species, identify the relevant technological milestones and investigate potential source concepts towards a future gravitational wave detector in space.