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Atom interferometry is an emerging high-precision tool for inertial sensing. Compared to optical interferometers,matter waves are manipulated by light to propagate in superposition of two trajectories through space-time. Theenclosed space-time area determines the observed interference signal and allows to measure inertial forces likethe gravitational acceleration. In addition, differential setups, for example, can be used to test the various facets ofthe Einstein equivalence principle [1] or detect gravitational waves. For the latter, the decihertz range is at the focusof current efforts and has initiated the construction of long baseline sites (such as MAGIS, AION, MIGA, ZAIGA) tocomplement conventional detection capabilities over the whole frequency range. Besides these applications, atominterferometers can be used to test physics beyond the Standard Model [2]. There are several possibilities, oneof which is ultra-light dark matter coupled to the internal degrees of freedom of atoms. These applications makeatom interferometry a testbed for the interface of relativity and quantum mechanics or the detection of ultralightdark-matter candidates [3, 4]. The talk gives an introduction into the main concepts of atom interferometry and the toolbox necessary to manipulateatoms. While we explain basic examples of atom interferometers, we also discuss current and ambitiousproposals for high-precision tests of fundamental physics and current developments in the field aiming at largescalequantum detectors of gravitational waves and dark matter. [1] F. Di Pumpo, A. Friedrich, C. Ufrecht & E. Giese, Universality-of-clock-rates test using atom interferometry with T³scaling. Phys. Rev. D 107, 064007 (2023). [2] A. Bott, F. Di Pumpo & E. Giese, Atomic diffraction from single-photon transitions in gravity and Standard-Modelextensions. AVS Quantum Sci. 5, 044402 (2023). [3] D. Derr & E. Giese, Clock transitions versus Bragg diffraction in atom-interferometric dark-matter detection. AVSQuantum Sci. 5, 044404 (2023). [4] F. Di Pumpo, A. Friedrich & E. Giese, Optimal baseline exploitation in vertical dark-matter detectors based on atominterferometry. AVS Quantum Sci. 6, 014404 (2024). Followed by Talk by Local LANL Scientist:
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