Test Of Equivalence Principle Research Articles

Simultaneous dual-species matter-wave accelerometer

We report the realization of a matter-wave interferometer based on Raman transitions which simultaneously interrogates two different atomic species (${}^{87}$Rb and ${}^{85}$Rb). The simultaneous aspect of our experiment presents encouraging preliminary results for future dual-species atom interferometry projects and seems very promising by taking advantage of a differential acceleration measurement. Indeed, the resolution of our differential accelerometer remains lower than $3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{g}$ even with vibration levels up to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{g}$ thanks to common-mode vibration noise rejection. An atom-based test of the weak equivalence principle has also been carried out leading to a differential free fall measurement between both isotopes of $\ensuremath{\Delta}g/g=(1.2\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.

Status report on the GBAR CERN experiment

GBAR is a recently approved experiment at CERN/AD. Its aim is to perform the first test of the Weak Equivalence Principle with Antimatter. The objective is to measure the gravitational acceleration of antihydrogen atoms on Earth with 1% precision in a first phase, and better than a per mil in a second phase. The method is to detect the free fall of ultra-cold atoms. By sympathetic cooling of antihydrogen positive ions H̄+ with beryllium ions, and after photodetachment of the excess positron, antiatoms are formed at m/s velocities and their free fall can be directly measured. Antihydrogen ions are produced by the interaction of keV antiprotons with a dense positronium cloud, the latter being formed by dumping positrons onto a porous material. We describe here briefly the experimental techniques and report on the most recent results. In particular, a flux of around 4 × 106 e+s−1 slow positrons is now produced by the source installed at Saclay, cross sections for the production of the H̄+ ions have been computed, and a dedicated beam line for the study of positronium formation and for applications in Materials Science has been realized. The tentative schedule of the GBAR developments is given.

Improved limits on long-range parity-odd interactions of the neutron

We show that a previous polarized 3He experiment at Princeton, plus Eot-Wash equivalence-principle tests, constrain exotic, long-ranged (lambda > 0.15m) parity-violating interactions of neutrons at levels well below those inferred from a recent study of the parity-violating spin-precession of neutrons transmitted through liquid 4He. For lambda > 1.0e8 meters the bounds on gAgV are improved by a 11 orders of magnitude.

Analysis and simulation of the operation of a Kelvin probe

Experiments that measure extremely small gravitational forces are often hampered by the presence of non-gravitational forces that can neither be calculated nor separately measured. Among these spurious forces is electrostatic attraction between a test mass and its surroundings due to the presence of spatially varying surface potential known as the ‘patch effect’. In order to make surfaces with small surface potential variation, it is necessary to be able to measure it. A Kelvin probe (KP) measures contact potential difference (CPD), using the time-varying capacitance between the sample and a vibrating tip that is biased with a backing potential. Assuming that the tip remains constant, this measures the sample's surface potential variation. We examine the operation of the KP from the perspective of parameter estimation in the presence of noise. We show that, when the CPD is estimated from measurements at two separate backing potentials, the standard deviation of the optimal estimate depends on the total observing time. Further, the observing time may be unevenly divided between the two backing potentials, provided the values of those potentials are correspondingly set. We simulate a two-stage KP data analysis, including a sub-optimal estimator with advantages for real-time operation. Based on the real-time version, we present a novel approach to stabilizing the average distance of the tip from the sample. We also present the results of a series of covariance analyses that validate and bound the applicability of the suboptimal estimator, make a comparison with the results of an optimal estimator and guide the user. We discuss the application of the KP to the Laser Interferometer Space Antenna and to a test of the weak equivalence principle.

Constraints on strongly coupled chameleon fields from the experimental test of the weak equivalence principle for the neutron

The chameleon scalar field is considered as a possible cause of accelerated expansion of the Universe. The chameleon field induces an interaction potential between particle and massive body. Previous experiments with falling cold neutrons intended to measure the neutron coherent scattering lengths and verification of the weak equivalence principle for the neutron are used to constrain the parameters characterizing the strength of the scalar chameleon fields.

Design and characteristics of a WEP test in a sounding-rocket payload

We describe SR-POEM, a Galilean test of the weak equivalence principle that is to be conducted during the free fall portion of the flight of a sounding rocket payload. This test of a single pair of substances will have a measurement uncertainty of σ(η) < 2×10−17 after averaging the results of eight separate drops, each of 120 s duration. The entire payload is inverted between successive drops to cancel potential sources of systematic error. The weak equivalence principle measurement is made with a set of four of the SAO laser gauges, which have achieved an Allan deviation of 0.04 pm for an averaging time of 30 s. We discuss aspects of the current design with an emphasis on those that bear on the accuracy of the determination of η. The discovery of a violation(η ≠ 0) would have profound implications for physics, astrophysics and cosmology.

‘Galileo Galilei’ (GG): space test of the weak equivalence principle to 10−17 and laboratory demonstrations

The small satellite ‘Galileo Galilei’ (GG) will test the universality of free fall and hence the weak equivalence principle which is the founding pillar of general relativity to 1 part in 1017. It will use proof masses whose atoms differ substantially from one another in their mass energy content, so as to maximize the chance of violation. GG will improve by four orders of magnitude the current best ‘Eöt-Wash’ tests based on slowly rotating torsion balances, which have been able to reach their thermal noise level. In GG, the expected violation signal is a relative displacement between the proof masses of ≃ 0.6 pm caused by a differential acceleration aGG ≃ 8 × 10−17 ms−2 pointing to the center of mass of the Earth as the satellite orbits around it at νGG ≃ 1.7 × 10−4 Hz. GG will fly an innovative acceleration sensor based on rapidly rotating macroscopic test masses weakly coupled in 2D which up-converts the signal to νspin ≃ 1 Hz, a value well above the frequency of natural oscillations of the masses relative to each other νd = 1/Td ≃ 1/(540 s). The sensor is unique in that it ensures high rotation frequency, low thermal noise and no attenuation of the signal strength (Pegna et al 2011 Phys. Rev. Lett. 107 200801). A readout based on a very low noise laser interferometry gauge developed at Jet Propulsion Laboratory (≃ 1 pm Hz−1/2 at 1 Hz demonstrated) allows the short integration time to be fully exploited. A full scale sensor with the same degrees of freedom and the same dynamical features as the one to fly in GG has been setup on ground (GGG). The proof masses of GGG are affected by acceleration and tilt noise acting on the rotating shaft because of ball bearings and terrain microseismicity (both absent in space). Overall, by means of appropriate 2D flexure joints, these noise sources have been reduced by a factor almost 105 down to a differential acceleration between the proof masses of ≃ 7 × 10−11 m s−2 (at 1.7 × 10−4 Hz up-converted by rotation to ≃ 0.2 Hz). The corresponding noise in the relative displacements of the proof masses, read by co-rotating capacitance bridges, is ≃ 180 pm, which is 300 times larger than the target in space. GGG error budget shows that it can reach a differential acceleration sensitivity aGGGgoal ≃ 8 × 10−16 m s−2, not limited by thermal noise. This value is only a factor 10 larger than what GG must reach in space to meet its target, and slightly smaller than the acceleration noise of the torsion balance. It can be achieved partly by means of weaker joints and an optimized mechanical design—so as to improve the attenuation factor—and partly by replacing the current ball bearings with much less noisy air bearings (also used in torsion balance tests) so as to reduce input noise. A laser gauge readout with noise level rlaser-ro ≃ 30 pm Hz−1/2 at 0.2÷3 Hz will be implemented.

Test masses for the G-POEM test of the weak equivalence principle

We describe the design of the test masses that are used in the ‘ground-based principle of equivalence measurement’ test of the weak equivalence principle. The main features of the design are the incorporation of corner cubes and the use of mass removal and replacement to create pairs of test masses with different test substances. The corner cubes allow for the vertical separation of the test masses to be measured with picometer accuracy by SAO's unique tracking frequency laser gauge, while the mass removal and replacement operations are arranged so that the test masses incorporating different test substances have nominally identical gravitational properties.

Constraining variations in the fine structure constant in the presence of early dark energy

We discuss present and future cosmological constraints on variations of the fine structure constant $\alpha$ induced by an early dark energy component having the simplest allowed (linear) coupling to electromagnetism. We find that current cosmological data show no variation of the fine structure constant at recombination respect to the present-day value, with $\alpha$ / $\alpha_0$ = 0.975 \pm 0.020 at 95 % c.l., constraining the energy density in early dark energy to $\Omega_e$ < 0.060 at 95 % c.l.. Moreover, we consider constraints on the parameter quantifying the strength of the coupling by the scalar field. We find that current cosmological constraints on the coupling are about 20 times weaker than those obtainable locally (which come from Equivalence Principle tests). However forthcoming or future missions, such as Planck Surveyor and CMBPol, can match and possibly even surpass the sensitivity of current local tests.

A quick test of the WEP enabled by a sounding rocket

We describe SR-POEM, a Galilean test of the weak equivalence principle (WEP), which is to be conducted during the free fall portion of a sounding rocket flight. This test of a single pair of substances is aimed at a measurement uncertainty of σ(η) < 10–16 after averaging the results of eight separate drops, each of 40 s duration. The WEP measurement is made with a set of four laser gauges that are expected to achieve 0.1 pm Hz–1/2. We address the two sources of systematic error that are currently of greatest concern: magnetic force and electrostatic (patch effect) force on the test mass assemblies. The discovery of a violation (η ≠ 0) would have profound implications for physics, astrophysics and cosmology.

Development of an atom gravimeter and status of the 10-meter atom interferometer for precision gravity measurement

Experimental realizations of cold 85Rb atom interferometers in Wuhan are reviewed in this paper. The application of atom interferometers in local gravity measurement are reported. The resolutions of gravity measurement are 2.0 × 10−7g for 1 s and 4.5 × 10−9g for 1,888 s. The absolute g value was derived with a difference of 1.6 × 10−7g compared to the gravity reference value. The tidal phenomenon was observed by continuously monitoring the local gravity over 123 h. A 10-meter atom interferometer designed for precision gravity measurement and the equivalence principle test is under construction, the latest status is reported for the first time.

Antihydrogen physics: gravitation and spectroscopy in AEgISThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

AEgIS (Antimatter experiment: gravity, interferometry, spectroscopy) is an experiment approved by CERN with the goal of studying antihydrogen physics. In AEgIS, antihydrogen will be produced by charge exchange reactions of cold antiprotons with positronium atoms excited in a Rydberg state (n &gt; 20). In the first phase of the experiment, controlled acceleration by an electric field gradient (Stark effect) and subsequent measurement of free fall in a Moiré deflectometer will allow a test of the weak equivalence principle. In a second phase, the antihydrogen will be slowed, confined, and laser-cooled to perform CPT studies and detailed spectroscopy. In the present work, after a general description of the experiment, the present status of advancement will be reviewed, with special attention to the production and excitation of positronium atoms.

General Relativity Accuracy Test (GReAT): New configuration for the differential accelerometer

We presents the results of an activity concerning the test of the Einstein Weak Equivalence Principle with an accuracy of about 5×10−15. The experiment will be performed in an “Einstein elevator” using a differential accelerometer with a final sensitivity of about 10−14g⊕/Hz1/2. The differential accelerometer is spun about an horizontal axis at a frequency in the range 0.5–1Hz in order to modulate, during the free fall, the signal from a possible violation of the Equivalence Principle. In the paper the perturbing effects with the same signature of the possible violation are analyzed and constrained. The experimental results obtained in the laboratory with a first prototype of the differential accelerometer are discussed, comparing this results with those obtained using a new prototype.

DC cancellation as a method of generating a t2-response and of solving the radial position error in a concentric free-falling two-sphere equivalence-principle experiment in a drag-free satellite

This paper presents a new method for doing a free-fall equivalence-principle (EP) experiment in a satellite at ambient temperature which solves two problems that have previously blocked this approach. By using large masses to change the gravity gradient at the proof masses, the orbit dynamics of a drag-free satellite may be changed in such a way that the experiment can mimic a free-fall experiment in a constant gravitational field on the earth. An experiment using a sphere surrounded by a spherical shell both completely unsupported and free falling has previously been impractical because (1) it is not possible to distinguish between a small EP violation and a slight difference in the semi-major axes of the orbits of the two proof masses and (2) the position difference in the orbit due to an EP violation only grows as t whereas the largest disturbance grows as t3/2. Furthermore, it has not been known how to independently measure the positions of a shell and a solid sphere with sufficient accuracy. The measurement problem can be solved by using a two-color transcollimator (see the main text), and since the radial-position-error and t-response problems arise from the earth's gravity gradient and not from its gravity field, one solution is to modify the earth's gravity gradient with local masses fixed in the satellite. Since the gravity gradient at the surface of a sphere, for example, depends only on its density, the gravity gradients of laboratory masses and of the earth unlike their fields are of the same order of magnitude. In a drag-free satellite spinning perpendicular to the orbit plane, two fixed spherical masses whose connecting line parallels the satellite spin axis can generate a dc gravity gradient at test masses located between them which cancels the combined gravity gradient of the earth and differential centrifugal force. With perfect cancellation, the position-error problem vanishes and the response grows as t2 along a line which always points toward the earth. In the practical case where the cancellation is not perfect, the t2-response can hold for about 104 to 106 s (depending on the cancellation accuracy), and the position error is also suppressed proportional to the accuracy of the cancellation. Experience with a prior drag-free satellite indicates that this cancellation may be accomplished with an accuracy of at least 10−2 and possibly 10−4 to 10−6, and this ameliorates the measurement problem sufficiently that equivalence-principle tests with accuracies from 10−19 to 10−23 g may be possible. t2-response times between 105 and 106 s are equivalent to a very tall (0.1–10 AU) drop tower with an effective value of g equal to about 3.4 m s−2 which is 3/7 of the value of g at the orbital altitude.

A weak equivalence principle test on a suborbital rocket

We describe a Galilean test of the weak equivalence principle, to be conducted during the free fall portion of a sounding rocket flight. The test of a single pair of substances is aimed at a measurement uncertainty of σ(η) < 10−16 after averaging the results of eight separate drops. The weak equivalence principle measurement is made with a set of four laser gauges that are expected to achieve 0.1 pm Hz−1/2. The discovery of a violation (η ≠ 0) would have profound implications for physics, astrophysics and cosmology.

Satellite Skin-Force Modelling for Atmospheric Drag Calculations

Satellites in low Earth orbits are influenced by the Earth’s atmosphere. The interactions between the molecules and the spacecraft cause the highest non-gravitational force, which in magnitude is comparable to planetary disturbances. Therefore the modelling of atmospheric drag effects is important for many missions with a scientific background like STEP (Satellite Test of Equivalence Principle). With the STEP mission variations between gravitational and inertial mass shall be measured with an accuracy of 10−18. The results are of great interest for cosmological and gravitational theories. To achieve the aimed accuracy, a precise model of external disturbances is necessary. In this article the method of Ray-Tracing is used to quantify the atmospheric drag forces and torques for spacecrafts of arbitrary shape.

Laboratory Tests of the Equivalence Principle at the University of Washington

Equivalence principle tests are probes for new fundamental physics. We have conducted several laboratory experiments to test the equivalence principle with unprecedented precision and generality using a torsion balance placed on a continuously rotating turntable. We present preliminary results comparing the differential accelerations of Ti, Be, and Al towards local masses, the earth and the center of our galaxy.

New test of the weak equivalence principle for neutrons

We describe a neutron gravity quantum experiment of a new type. The gain in kinetic energy of free-falling neutrons is compensated by a quantum of energy ℏ Ω , due to phase modulation of the neutron wave. As phase modulator a grating was used moving perpendicular with respect to the direction of the neutron wave propagation. As a result, monochromatic neutrons will have exactly the same energy after falling as before the free fall. The weak equivalence principle was tested to an accuracy of 2×10 −3. A possible future experiment of more improved accuracy is discussed as well.

LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON

A primary objective of the lunar laser ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of the highly accurate measurements of the distance between the Earth and the Moon provide unique information used to determine whether, in accordance with the equivalence principle (EP), these two celestial bodies are falling toward the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Thirty-five years since their initiation, analyses of precision laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-1.0 ± 1.4) × 10-13for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, Δ(MG/MI). This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of Δ(MG/MI)SEP= (-2.0 ± 2.0) × 10-13. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter η of (4.4 ± 4.5) × 10-4, where η = 4β - γ - 3 and both γ and β are parametrized post-Newtonian (PPN) parameters. Using the recent result for the parameter γ derived from the radiometric tracking data from the Cassini mission, the PPN parameter β (quantifying the nonlinearity of gravitational superposition) is determined to be β - 1 = (1.2 ± 1.1) × 10-4. We also present the history of the LLR effort and describe the technique that is being used. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR accuracy will further advance the research on relativistic gravity in the solar system and, most notably, will continue to provide highly accurate tests of the EP.

GAUGE: the GrAnd Unification and Gravity Explorer

The GAUGE (GrAnd Unification and Gravity Explorer) mission proposes to use a drag-free spacecraft platform onto which a number of experiments are attached. They are designed to address a number of key issues at the interface between gravity and unification with the other forces of nature. The equivalence principle is to be probed with both a high-precision test using classical macroscopic test bodies, and, to lower precision, using microscopic test bodies via cold-atom interferometry. These two equivalence principle tests will explore string-dilaton theories and the effect of space–time fluctuations respectively. The macroscopic test bodies will also be used for intermediate-range inverse-square law and an axion-like spin-coupling search. The microscopic test bodies offer the prospect of extending the range of tests to also include short-range inverse-square law and spin-coupling measurements as well as looking for evidence of quantum decoherence due to space–time fluctuations at the Planck scale.