Correlative methods for dual-species quantum tests of the weak equivalence principle

TL;DR

This paper introduces two new analysis methods for dual-species atom interferometers to accurately estimate differential phases, enabling more precise tests of the weak equivalence principle by effectively rejecting vibration noise.

Contribution

The work presents a generalized Bayesian analysis and a vibration-based fringe reconstruction method, improving differential phase estimation in dual-species atom interferometry.

Findings

Bias-free differential phase estimates achieved

Vibration noise rejected by a factor of 730

Preliminary weak equivalence principle test with sensitivity of 1.6e-6

Abstract

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.