How to estimate the differential acceleration in a two-species atom interferometer to test the equivalence principle

We propose a scheme for testing the weak equivalence principle (Universality of Free Fall) using an atom-interferometric measurement of the local differential acceleration between two atomic species with a large mass ratio as test masses. A apparatus in free fall can be used to track atomic free-fall trajectories over large distances. We show how the differential acceleration can be extracted from the interferometric signal using Bayesian statistical estimation, even in the case of a large mass and laser wavelength difference. We show that this statistical estimation method does not suffer from acceleration noise of the platform and does not require repeatable experimental conditions. We specialize our discussion to a dual potassium/rubidium interferometer and extend our protocol with other atomic mixtures. Finally, we discuss the performances of the UFF test developed for the free-fall (0-g) airplane in the ICE project (\verb"http://www.ice-space.fr"

Correlation Clustering with Low-Rank Matrices

Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature focuses on finding approximation algorithms. In this paper we explore how to solve the correlation clustering objective exactly when the data to be clustered can be represented by a low-rank matrix. We prove in particular that correlation clustering can be solved in polynomial time when the underlying matrix is positive semidefinite with small constant rank, but that the task remains NP-hard in the presence of even one negative eigenvalue. Based on our theoretical results, we develop an algorithm for efficiently "solving" low-rank positive semidefinite correlation clustering by employing a procedure for zonotope vertex enumeration. We demonstrate the effectiveness and speed of our algorithm by using it to solve several clustering problems on both synthetic and real-world data

Oceanic lithosphere-asthenosphere boundaryfrom surface wave dispersion data

International audienceAbstract According to different types of observations, the nature of lithosphere-asthenosphereboundary (LAB) is controversial. Using a massive data set of surface wave dispersions in a broad periodrange (15–300 s), we have developed a three-dimensional upper mantle tomographic model (first-orderperturbation theory) at the global scale. This is used to derive maps of the LAB from the resolved elasticparameters. The key effects of shallow layers and anisotropy are taken into account in the inversion process.We investigate LAB distribution primarily below the oceans, according to different kinds of proxies thatcorrespond to the base of the lithosphere from the shear velocity variation at depth, the amplituderadial anisotropy, and the changes in azimuthal anisotropy G orientation. The estimations of the LAB depthbased on the shear velocity increase from a thin lithosphere (∼20 km) in the ridges, to a thick old-oceanlithosphere (∼120–130 km). The radial anisotropy proxy shows a very fast increase in the LAB depth fromthe ridges, from ∼50 km to the older ocean where it reaches a remarkable monotonic subhorizontal profile(∼70–80 km). The LAB depths inferred from the azimuthal anisotropy proxy show deeper values for theincreasing oceanic lithosphere (∼130–135 km). The difference between the evolution of the LAB depth withthe age of the oceanic lithosphere computed from the shear velocity and azimuthal anisotropy proxies andfrom the radial anisotropy proxy raises questions about the nature of the LAB in the oceanic regions and ofthe formation of the oceanic plate

I.C.E.: a Transportable Atomic Inertial Sensor for Test in Microgravity

We present our the construction of an atom interferometer for inertial sensing in microgravity, as part of the I.C.E. (\textit{Interf\'{e}rom\'{e}trie Coh\'{e}rente pour l'Espace}) collaboration. On-board laser systems have been developed based on fibre-optic components, which are insensitive to mechanical vibrations and acoustic noise, have sub-MHz linewidth, and remain frequency stabilised for weeks at a time. A compact, transportable vacuum system has been built, and used for laser cooling and magneto-optical trapping. We will use a mixture of quantum degenerate gases, bosonic $^{87}$Rb and fermionic $^{40}$K, in order to find the optimal conditions for precision and sensitivity of inertial measurements. Microgravity will be realised in parabolic flights lasting up to 20s in an Airbus. We show that the factors limiting the sensitivity of a long-interrogation-time atomic inertial sensor are the phase noise in reference frequency generation for Raman-pulse atomic beam-splitters and acceleration fluctuations during free fall