About 300 experiments tried to determine the value of the Newtonian gravitational constant G to date but large discrepancies in the results prevent from knowing its value precisely 1 . The weakness of the gravitational interaction and the impossibility of shielding the effects of gravity make it very difficult to measure G keeping systematic effects under control. Most of the experiments performed so far were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish 2 in 1798 and in all cases they used macroscopic masses.Here we report on the first precise determination of G using laser-cooled atoms and quantum interferometry to probe gravity. We obtain the value G= 6.67191(99) × 10 −11 m 3 kg −1 s −2with a relative uncertainty of 150 ppm. Our value is at 1.5 combined standard deviations from the current recommended value of the Committee on Data for Science and Technology (CODATA) 3 . Such a conceptually different experiment is important to identify the so far elusive systematic errors thus improving the confidence in the value of G. There is no definitive relationship indeed between G and the other fundamental constants and no theoretical pre-1 diction for its value to test the experimental results. Improving the knowledge of G has not only a pure metrological interest, but is also important for the key role that this fundamental constant plays in theories of gravitation, cosmology, particle physics, astrophysics, and geophysical models.The basic idea of our experiment is to use an atom interferometer as gravity sensor and a well-characterized mass as source of a gravitational field. From the precise measurement of the atoms' acceleration produced by the source mass and from the knowledge of the mass distribution, it is possible to extract the value of the gravitational constant G using the well-known formulaAtom interferometers 4, 5 are new tools for experimental gravitation as, for example, in precision measurements of gravity acceleration 6 and gravity gradients 7 , as gyroscopes based on the Sagnac effect 8 , for testing the 1/r 2 law 9 , general relativity 10 and quantum gravity models 11 , and for applications in geophysics 12 . Proof-of-principle experiments to measure G using atom interferometry were reported [13][14][15] . Ongoing studies show that future experiments in space will allow to take full advantage of the potential sensitivity of atom interferometers for fundamental physics tests 16 .The possibility of using atom interferometry for gravitational waves detection is being studied 17 .Since the problem in the determination of G depends on the presence of unidentified systematic errors, our experiment was designed with a double-differential configuration in order to be as immune as possible from such effects: the atomic sensor was a double interferometer in a gravity-2 gradiometer configuration, in order to subtract common-mode spurious signals, and we used two sets of well-characterized tungsten masses as source of the gravitational field that were placed in t...
We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long-term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short term sensitivity of 3 × 10 −9 g/ √ Hz to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows to reach a resolution of 5 × 10 −11 g after 8000 s on the measurement of differential gravity acceleration. The long term stability is compatible with a measurement of the gravitational constant G at the level of 10 −4 after an integration time of about 100 hours.
The Einstein equivalence principle (EEP) has a central role in the understanding of gravity and space–time. In its weak form, or weak equivalence principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms: a Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eötvös ratio of atoms in two hyperfine levels with relative uncertainty in the low 10−9, improving previous results by almost two orders of magnitude.
We present the first direct measurement of the gravity-field curvature based on three conjugated atom interferometers. Three atomic clouds launched in the vertical direction are simultaneously interrogated by the same atom interferometry sequence and used to probe the gravity field at three equally spaced positions. The vertical component of the gravity-field curvature generated by nearby source masses is measured from the difference between adjacent gravity gradient values. Curvature measurements are of interest in geodesy studies and for the validation of gravitational models of the surrounding environment. The possibility of using such a scheme for a new determination of the Newtonian constant of gravity is also discussed.In the last two decades, atom interferometry [1] has profoundly changed precision inertial sensing, leading to major advances in metrology and fundamental and applied physics. The outstanding stability and accuracy levels [2,3] combined with the possibility of easily implementing new measurement schemes [4][5][6][7] are the main reasons for the rapid progress of these instruments. Matter-wave interferometry has been successfully used to measure local gravity [8], gravity gradient [9-11], the Sagnac effect [12], the Newtonian gravitational constant [13][14][15][16], the fine structure constant [17], and for tests of general relativity [18,19]. Accelerometers based on atom interferometry have been developed for many practical applications including geodesy, geophysics, engineering prospecting, and inertial navigation [20][21][22]. Instruments for space-based research are being conceived for different applications ranging from weak equivalence principle tests and gravitational-wave detection to geodesy [23,24].One of the most attractive features of atom interferometry sensors is the ability to perform differential acceleration measurements by simultaneously interrogating two separated atomic clouds with high rejection of common-mode vibration noise, as demonstrated in gravity gradiometry applications [3,9]. In principle, such a scheme can be extended to an arbitrary number of samples, thus, providing a measurement of higher-order spatial derivatives of the gravity field. Geophysical models of the Earth's interior rely on the inversion of gravity and gravity gradient data collected at or above the surface [25]. The solution to this problem, which is, in general, not unique, leads to images of the subsurface mass distribution over different scale lengths [26]. In this context,
The proposed mission "Space Atomic Gravity Explorer" (SAGE) has the scientific objective to investigate gravitational waves, dark matter, and other fundamental aspects of gravity as well as the connection between gravitational physics and quantum physics using new quantum sensors, namely, optical atomic clocks and atom interferometers based on ultracold strontium atoms.
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