Manuel Rodrigues’s research while affiliated with University of Paris-Saclay and other places

The objective of the proposed MAQRO mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments at the interface with gravity. Developing the necessary technologies, achieving the required sensitivities and providing the necessary isolation of macroscopic quantum systems from their environment will lay the path for developing novel quantum sensors. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. Recent scientific and technological developments since the original proposal of MAQRO promise the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade.

The MICROSCOPE mission was designed to test the Weak Equivalence Principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of $10^{-15}$ in terms of the E\"otv\"os ratio $\eta$. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultra-sensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five-months-worth of science free-fall data, two thirds with a pair of test masses of different compositions -- Titanium and Platinum alloys -- and the last third with a reference pair of test masses of the same composition -- Platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the E\"otv\"os parameter of the Titanium and Platinum pair constrained to $\eta({\rm Ti, Pt})~=~ [-1.5 \pm 2.3~{\rm (stat)} \pm 1.5~{\rm (syst)}]~\times 10^{-15}$ at $1\sigma$ in statistical errors.

The space mission MICROSCOPE dedicated to the test of the Equivalence Principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations ($a_{\rm A}$ and $a_{\rm B}$) of two test masses in terms of the E\"otv\"os parameter $\eta({\rm{A, B}}) = 2 \frac{a_{\rm A}- a_{\rm B}}{a_{\rm A}+ a_{\rm B}}$. No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 hours down to the limit of the statistical error which is smaller than $10^{-14}$ for $\eta({\rm{Ti, Pt}})$. Accumulating data from all segments leads to $\eta({\rm{Ti, Pt}}) =[-1.5\pm{}2.3{\rm (stat)}\pm{}1.5{\rm (syst)}] \times{}10^{-15}$ showing no EP violation at the level of $2.7\times{}10^{-15}$ if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the E\"ot-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null E\"otv\"os parameter with a statistical uncertainty of $1.1\times{}10^{-15}$.

The MICROSCOPE mission was designed to test the weak equivalence principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of 10−15 in terms of the Eötvös ratio η. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultrasensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five months worth of science free-fall data, two-thirds with a pair of test masses of different compositions—titanium and platinum alloys—and the last third with a reference pair of test masses of the same composition—platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the titanium and platinum pair constrained to η(Ti,Pt)=[−1.5±2.3(stat)±1.5(syst)]×10−15 at 1σ in statistical errors.

This paper focuses on the description of the design and performance of the MICROSCOPE satellite and its drag-free and attitude control system. The satellite is derived from CNES’ Myriade platform family, albeit with significant upgrades dictated by the unprecedented MICROSCOPE’s mission requirements. The 300 kg drag-free microsatellite has completed its 2 years flight with higher-than-expected performances. Its passive thermal concept allowed for temperature variations smaller than 1 μ K at the frequency of the equivalence principle test f EP . The propulsion system provided a six-axis continuous and very low noise thrust from zero to some hundreds of micronewtons. Finally, the performance of its DFACS (aimed at compensating the disturbing forces and torques applied to the satellite) is the finest ever achieved in low Earth orbit, with residual accelerations along the three axes lower than 10 ⁻¹² m s ⁻² at f EP over 8 days.

The MICROSCOPE mission aimed to test the Weak Equivalence Principle (WEP) to a precision of 10 ⁻¹⁵ . The WEP states that two bodies fall at the same rate on a gravitational field independently of their mass or composition. In MICROSCOPE, two masses of different compositions (titanium and platinum alloys) are placed on a quasi-circular trajectory around the Earth. They are the test-masses of a double accelerometer. The measurement of their accelerations is used to extract a potential WEP violation that would occur at a frequency defined by the motion and attitude of the satellite around the Earth. This paper details the major drivers of the mission leading to the specification of the major subsystems (satellite, ground segment, instrument, orbit...). Building upon the measurement equation, we derive the objective of the test in statistical and systematic error allocation and provide the mission's expected error budget.

After performing highly sensitive acceleration measurements during two years of drag-free flight around the Earth, MICROSCOPE provided the best constraint on the weak equivalence principle (WEP) to date. Beside being a technological challenge, this experiment required a specialised data analysis pipeline to look for a potential small signal buried in the noise, possibly plagued by instrumental defects, missing data and glitches. This paper describes the frequency-domain iterative least-square technique that we developed for MICROSCOPE. In particular, using numerical simulations, we prove that our estimator is unbiased and provides correct error bars. This paper therefore justifies the robustness of the WEP measurements given by MICROSCOPE.

MICROSCOPE’s space test of the weak equivalence principle (WEP) is based on the minute measurement of the difference of accelerations experienced by two test masses as they orbit the Earth. A detection of a violation of the WEP would appear at a well-known frequency f EP depending on the satellite’s orbital and spinning frequencies. Consequently, the experiment was optimised to minimise systematic errors at f EP . Glitches are short-lived events visible in the test masses’ measured acceleration, most likely originating in cracks of the satellite’s coating. In this paper, we characterise their shape and time distribution. Although intrinsically random, their time of arrival distribution is modulated by the orbital and spinning periods. They have an impact on the WEP test that must be quantified. However, the data available prevents us from unequivocally tackling this task. We show that glitches affect the test of the WEP, up to an a priori unknown level. Discarding the perturbed data is thus the best way to reduce their effect.

This paper introduces the current special issue focussed on the MICROSCOPE mission. This mission is the first experimental test in space of the weak equivalence principle (WEP) using man-made test-masses—as opposed to astronomical tests—with the goal to reach a precision two orders of magnitude better than ground-based experiments. Selected in 1999 by CNES as part of its MYRIADE microsatellite programme, the satellite was launched in 2016 and the mission lasted 2.5 years. This paper summarises the articles of the special issue and highlights the key technological and data analysis aspects that allowed for an unprecedented precision on the test of the WEP.