Matter-wave interferometers utilizing different isotopes or chemical elements intrinsically have different sensitivities, and the analysis tools available until now are insufficient for accurately estimating the atomic phase difference under many experimental conditions. In this work, we describe and demonstrate two new methods for extracting the differential phase between dual-species atom interferometers for precise tests of the weak equivalence principle. The first method is a generalized Bayesian analysis, which uses knowledge of the system noise to estimate the differential phase based on a statistical model. The second method utilizes a mechanical accelerometer to reconstruct single-sensor interference fringes based on measurements of the vibration-induced phase. An improved ellipse-fitting algorithm is also implemented as a third method for comparison. These analysis tools are investigated using both numerical simulations and experimental data from simultaneous $^{87}$Rb and $^{39}$K interferometers, and both new techniques are shown to produce bias-free estimates of the differential phase. We also report observations of phase correlations between atom interferometers composed of different chemical species. This correlation enables us to reject common-mode vibration noise by a factor of 730, and to make preliminary tests of the weak equivalence principle with a sensitivity of $1.6 \times 10^{-6}$ per measurement with an interrogation time of $T = 10$ ms. We study the level of vibration rejection by varying the temporal overlap between interferometers in a symmetric timing sequence. Finally, we discuss the limitations of the new analysis methods for future applications of differential atom interferometry.
Evaluation of the systematic error induced by quadratic Zeeman effect using hyperfine ground state exchange method in a long-baseline dual-species atom interferometer
In-orbit Test of the Weak Equivalence Principle with Atom Interferometry
Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院武汉物理与数学研究所精密测量科学与技术创新院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Hefei National Laboratory（合肥国家实验室）；Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences（中国航天科技集团空间应用工程与技术中心）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）
