GENERAL RELATIVITY AND TESTING THE EQUIVALENCE PRINCIPLE (EP)

Microscope is a CNES project, using a micro-satellite from the Myriade series, conducted with ONERA and the Observatoire de la Côte d'Azur in cooperation with the European Space Agency. The main scientific objective is to test the equivalence principle with a resolution of 10^-15, in other words three orders of magnitude greater than the best tests conducted on Earth. However this mission will also offer the occasion for qualifying the technology necessary for building a drag-free satellite, which is indispensable for the scientific experiment.
The Equivalence Principle, in other words essentially the equality of "inert" and "gravitational" masses, and then of the identity of the physical laws in reference frames submitted to an acceleration field on the one hand, or to gravity on the other, is one of the founding principles of general relativity. While observations made up to now, to test predictions of this classical theory, have always confimed it, the unification with other interactions, taken in the context of quantum theory and the standard model, have run into very particular difficulties.
The principle of the Microscope experiment is based on freefall of two bodies of different composition, in orbit around the Earth. These two masses are protected from non-gravitational perturbations by the satellite enclosing them.

The Microscope instrument consists of two SAGE accelerometers
(SAGE stands for "Space Accelerometer for Gravitation Experiment")
each of which has two concentric and centred, electrostatic inertial sensors.
On the top right in the photo, you can see the silicon parts
which have already been made for the prototype instrument.

A validated signal of EP violation, detected by the Microscope mission, would radically challenge our understanding of gravity and would thus require investigating the explored field as quickly as possible in order to specify the conditions under which this violation occurred. On the other hand, if the equivalence principle were to be confirmed with a precision of 10^-15 this would further delay current research on the theories of gravitation. It would then be necessary to consider even more precise experiments to exploit the results from Microscope.

ELECTROMAGNETIC LINKS AND THEIR APPLICATIONS FOR TIME TRANSFER, NAVIGATION AND RELATIVITY TESTS

T2L2 (Laser-Link Time Transfer)

The Transfert de Temps Lien Laser project (T2L2 - Laser-Link Time Transfer) is a very high precision time-transfer experiment developed by CNES and the Observatoire de la Côte d'Azur (OCA), which will make it possible to improve the stability of time transfer in comparison with current experiments.
T2L2 enables the synchronisation of several terrestrial atomic clocks in separate places and the synchronisation of a satellite's onboard clock with ground-based clocks.
The terrestrial clock and the Space clock to be synchronised are respectively linked to a laser telemetry station and an onboard Space instrument. For a given laser pulse emitted by one of the stations, 3 times are recorded, namely:

time of departure
time of return to the laser station
time of arrival aboard the satellite

Using these 3 times, the difference in times registered by the station clock and a satellite clock is deduced. This is a Ground-Space time transfer.
By using several laser stations, it is possible to determine a Ground-Ground time transfer.
T2L2 was suggested for the Jason-2 mission in 2008. This project is currently being developed by CNES and OCA.
The idea of applying it to interplanetary navigation is extremely tempting and such links would be extremely useful for more ambitious future scientific missions such as TIPO, OPTIS, and LATOR which have several objectives for testing relativity theory.

COLD ATOMS AND THEIR APPLICATIONS (TO TEST RELATIVISTIC EFFECTS)

The atom as a measuring device

For about twenty years, the development of laser techniques for manipulating atoms has made it possible to determine more easily the wave nature of atoms and has yielded a whole range of applicable tools for these atomic waves. We now know how to make mirrors, beam splitters, diffraction arrays, lenses and all sorts of other tools for developing operational instruments for atomic optics. Unlike photons, atoms, due to their complex structure, interact a lot with their environment. Even though they are electrically neutral, atoms have electric and magnetic dipolar moments, which make them sensitive to external electric and magnetic fields.
Atoms also have mass, which enables them to interact with the gravitational field, just as any other body with mass. Their high thermal agitation speed (several hundreds of metres or even kilometres per second) generally means that this interaction cannot be perceived. But we now know how to slow atoms down with laser beams to speeds of a few mm.s^-1, which means that their interaction with the gravity field can now be observed. The atoms' mass also makes them sensitive to inertial fields (Coriolis force, centrifugal force) which occur in non-Galilean reference frames.
Given these many possible interactions, the atom thus appears to be an ideal tool for probing the external environment. Since it is a magnetometer, a weighing device and a clock, among others, for no matter which physical magnitude you want to determine, the atom has a property which will enable you to measure it. The fact of being able to determine the wave nature of the atom means that it is possible to imagine interferometry measurement techniques (using the atomic phase), which will thus enormously improve the sensitivity of the measurement. Atomic interferometry is made possible due to the many atomic tools referred to previously. We now know how to make atom interferometers which are equivalent to Michelson, Mac-Zehnder, Fabry-Perot interferometers and many others. These devices have already been used to measure a certain number of physical magnitudes very accurately.

Frequency measurements
The first of these magnitudes to be measured was, of course, frequency. This was done with such great precision, using atomic clocks, that the atom, which previously had been a chronometer now became a time standard. Indeed, in 1967, the 13th International Conference on Weights and Measures decided to change its definition of the second. It is no longer the Earth but the atom, which decides what time it is. This new definition is based on stable clocks with a precision of some 10^-15, in other words, which deviate by only one second every 30 million years!!!
One might wonder what such precision could be used for, however manufacturers are already asking for clocks with a precision of 10^-11 for synchronising high-speed telecommunication networks and to 10^-12 for the new European satellite navigation system, GALILEO. When the cold-atom Space clock, PHARAO, is put into orbit, it will be possible to use it to compare clocks all over the world to within 10^-16, using microwave links. Today, the best time standards are atomic fountains using laser-cooled atoms. Their frequency stability is 2.10^-16 for a measurement duration of 40,000 seconds.
The microgravity environment in Space means that the time during which these atoms interact in the microgravity chamber can be increased, which means that the resolution can be increased by a factor of ten. We are thus expecting excellent accuracy for these new atomic clocks. This progress has made it possible to conduct new tests of special and general relativity or fundamental physics research. This in turn has made it possible to develop inertial sensors by means of atomic interferometry.

The cold atom clock, PHARAO/ACES
The Projet d'Horloge Atomique par Refroidissement d'Atomes en Orbite (PHARAO – Project for an atomic clock with cooling of atoms in orbit) is being developed by CNES with the Laboratoire Kastler-Brossel (LKB) and the laboratoire Systèmes de Références Temps-Espace (SYRTE) at the Paris Observatory. The complete engineering model of the PHARAO clock was delivered to CNES in Toulouse in 2006 and has been operating satisfactorily. (see the CNES e-space&science article).
The project began in 1997 when the PHARAO clock proposal was selected by ESA to be part of the Atomic Clock Ensemble in Space (ACES) project due to be installed in 2014 on an external platform of the International Space Station (ISS), pointing towards the Nadir for a period of 18 months to 3 years.
In addition to the PHARAO clock supplied by France, the ACES project includes a hydrogen maser provided by Switzerland. The frequencies of these two clocks will be compared, as will those of different types of clocks distributed around the globe.
The objectives of PHARAO/ACES are both technological –achieving clock operation with outstanding stability and precision performances, comparing times of clocks in different places to within a few picoseconds (10^-12 seconds) - and scientific – testing relativity theory by measuring the gravitational red-shift, searching for possible deviation over time of the fine structure constant and searching for possible anisotropy of light propagation. The frequency stability of the PHARAO clock should reach 10^-16 over a few days. This will provide an ultra-stable, primary time reference with global coverage, following which clocks could be compared to within a few tens of picoseconds, i.e. about two orders of magnitudes better than current performances of the GPS and GLONASS systems. The Einstein red-shift effect could thus be verified with more precisely with a gain of a factor of 30 and possible anisotropy of the speed of light could be tested with an increased precision of a factor of 10. The aim is to achieve a level of 10^-16 per year for drifting of the fine structure constant over time. A new decision will be taken as to whether the flight model for the PHARAO clock and the ACES ensemble should be built.

PHARAO atomic clock

Outlook for cold atom clocks
Atomic clocks have profited a lot since the early 1990s from the development of laser techniques for manipulating atoms. Clocks using microwave transitions will achieve a precision of 10^-16 (PHARAO/ACES mission). New types of clocks using transitions in the optical domain should make it possible to increase precision by a few orders of magnitude in the medium term. A few tests of fundamental physics, using the precision and stability of such clocks, could then be envisaged.

COLD-ATOM INERTIAL SENSORS

Interest in cold-atom interferometry has increased over the last few years, in particular for use with inertial sensors. Indeed, these new sensors have, a priori, increased our knowledge of the scale factor and have enabled the construction of very precise devices.
Furthermore, the operation of these sensors is based on fundamental physical principles: quantum mechanics, and in particular, the interaction between atoms and light. This "originality" means that we have a clear understanding of how they work, thus justifying their use for defining reference values (atomic clocks and Watt balance). These qualities are no less important for testing fundamental physics, in particular, for achieving the ultimate performance levels required for testing general relativity. Nevertheless, the use of cold-atom inertial sensors suffers from a severe limitation: gravity. This acceleration, even though it can be put to good use in similar configurations in fountain clocks, limits the interrogation time which in turn directly limits the sensitivity of these devices. When used in Space, the 0-g environment can be taken advantage of, thus increasing their sensitivity by several orders of magnitude. Thus, the sensitivity of an accelerometer increases in proportion to the square of the interaction time. Times then increase from a typical duration of 100 ms on Earth to several seconds or even several tens of seconds. For these significant interrogation times, another limitation may appear. For instance, cold atoms (at temperatures of the order of 1 µK) spread over about 10 cm after a few seconds of interrogation. In order to use the incredible potential of these sensors in Space, we would thus need maximum interrogation times, which would thus be based on the use, no longer of cold atoms, but of ultra-cold atoms such as Bose-Einstein condensates or atom lasers.
Inertial sensors devices are used to reveal whether the reference frames to which they are tied are inertial or not. They are thus essentially used as gyrometers and accelerometers, and by extension as gravimeters and gradiometers. For about fifteen years, many atomic inertial sensors have been made or are being made around the world. Several French teams are doing advanced work in this field in cooperation with CNES R&D studies

Atomic gravimeters and gradiometers
The phase induced by the gravity field on an atomic wave varies rapidly with the value of this field. This phase may be very precisely measured using an atomic interferometer of the temporal Mach-Zehnder type for instance. This makes it possible to measure gravity (terrestrial potential or any other gravitational potential) very precisely. The latest experiments conducted have revealed high sensitivity which corresponds typically to a variation of about one centimetre of the gravity field on the ground.

Atomic gyrometers
The Sagnac effect applied to light waves is the physical principle used for all optical gyrometers. It is possible to demonstrate that this principle, when applied to atomic waves, produces for a given "interferometry area" an effect which is intrinsically one hundred billion times more sensitive than for the optical case!!! It is easy to see how useful such inertial sensors using atomic waves would be and why they should be developed.
If the measurement is taken over a long period of time (in Space for instance) the measurement noise is averaged slowly and the sensitivity of the device can thus be further improved.

The cold-atom gyrometer at SYRTE

Atomic accelerometry; the prototype of the ICE laboratory
This is a joint project initiated in 2002 by the Laboratoire Charles Fabry de l'Institut d'Optique (LCFIO), the SYRTE and ONERA and CNES.
Ultimately, the Interférométrie Cohérente dans l'Espace (ICE – Coherent interferometry in Space) project, which is still at the R&D stage, is intended to develop a new kind of interferometer based on matter waves whose (coherent) atomic source is a Bose-Einstein condensate. This source could be used, for example, to directly read the phase offset induced by the recoiling of a photon by diffraction of a probe laser beam on the matter configuration created by the different condensates which interfere. A time analysis of the interference figure is used to directly determine the phase offset, unlike "classic" devices such as clocks for which it is necessary to sample the interference figure.

The first tests of the ICE device, which was designed to take and then analyse very precise acceleration measurements in microgravity using an atomic interferometer, made it possible to trap and cool atoms in microgravity for the first time following the first experiments undertaken during the PHARAO study. During the flight campaign on the 0-g Airbus operated by the Novespace company, between 27 and 29 March 2007, new trapping technologies were validated using telecommunication technologies. For three days, the campaign team, consisting of researchers from the Institut d'Optique from ONERA, from SYRTE-LNE and from CNES was able to observe and study the cooling and manipulation of atoms in a device which ultimately will enable them to measure acceleration very precisely using a coherent atomic source accelerometer (atom laser). The objective is to compare, during a parabolic flight on an Airbus, the accelerations undergone by these atoms to those undergone by classic accelerometers. It will in no way be possible to test the short/long term complementarity of these different sensors. For that, it would be necessary to undertake a Space mission carrying both interferometers.

This project might enable scientists to design a coherent atom source (Bose-Einstein condensate or atom laser), which could be carried into Space and which would no doubt be indispensable for undertaking atomic interferometry experiments in Space. Furthermore, the recent development of compact devices (in particular "atomic chips") might enable scientists to consider integrating such devices into microsatellites or minisatellites. In a future mission configuration, it could thus carry a system for determining the position of the satellite, which could be used to compare the "local" measurements of trajectories with measurements taken on Earth. Such a device, carried for a remote mission (greater or equal to the distance between Earth and Mars) would make it possible to understand potential anomalies which would arise during measurements of the satellite's position taken from a distance.
The very long-term stability of atomic accelerometers makes it possible to alternate, without any problems arising, between inertial measurement phases and phases during which the atomic interferometer is used for more fundamental research. One might thus, to begin with, verify the potential of these sensors by measuring the fine structure constant, . This would be done by using the speed measurement (or energy measurement) of the recoil of an atom of mass M during the absorption of a given photon pulse. This measurement would then yield the fundamental constant, . The use of a coherent source in microgravity would improve our knowledge of this fundamental constant.
Another interesting opportunity might be the possibility of creating a "double species" atomic source of Rubidium and Potassium atoms without having to double the complexity of the laser system. One might then obtain a direct comparison between the acceleration undergone by two different atomic species and thus test the equivalence principle on a microscopic level. The prototype being developed should enable scientists to take the first measurements of this kind during a possible microgravity campaign. The precision of the test should be of an order of 10^-10.

Artist's view of the ICE experiment, showing only the heavy components		Artist's view of the ICE experiment, in addition to the heavy experiment elements, the red lines show the trajectories of 3D MOT (Magneto-Optic Trap) beams, emerging from the breadboard above the cube. The yellow colour shows the optical tweezer beam. The main support and optical elements are shown for each type of beam.

Other experiments are being developed.

DETECTION OF GRAVITATIONAL WAVES

The LISA Space project aims to detect gravitational waves in a frequency range of the order of 0.1 to 100 mHz as compared to the 10 Hz to 10 kHz range covered by terrestrial interferometers. It is in fact very difficult to extend the sensitivity of terrestrial interferometers to cover low frequencies (less than 1 Hz) due to seismic noise, dynamic gravity gradients and the limited size of available land on which to build them. The idea of installing a very large gravitational interferometer in Space led to a proposal for the Space project, LISA, which will not be launched before 2018.
The basic principle consists in creating optical links between very distant satellites such that the phase received is permanently measured by comparing it with a local oscillator. LISA will consist of three satellites, each of which has two inertial masses associated with two telescopes. These satellites will be positioned at the peaks of an equilateral triangle with sides of 5 million km. They will be in a sun-centred orbit with a radius of 1 AU, following the Earth with a time-lag of 20 days. The satellite navigation is done using a drag-free mode (for compensating non-gravitational forces). Their motion is dependent on the masses defining the optical reference for one of the extremities of an optical path. These paths are defined by neodyme laser benches generating about two watts for each beam, and telescopes with apertures of 38 cm. The optical paths between the satellites are compared to within 10^-12 m/Hz^½.

The scientific teams taking part in the mission definition studies and in data simulation are part of a group known as LISA-France (including APC Paris, ARTEMIS, Observatoire de la Côte d'Azur, IAP Paris, LAPP Annecy-le-Vieux, LUTH Observatoire de Paris-Meudon, SYRTE Observatoire de Paris-Meudon, ONERA/DMPh, etc.)

The LISA-Pathfinder mission
The LISA project requires particularly difficult technological development, specifically in the fields of ultra-stable lasers, telescopes, accelerometers, micro-thrusters and drag-free flight (drag compensation). It also requires perfect control of satellite formation flying. ESA has planned for an intermediary phase with the flight of the technology demonstrator, LISA-Pathfinder.
The key element to be validated is the drag-free control system, with expected performance of 10^-14 ms-²/Hz, i.e. one order of magnitude less than that for LISA. It consists of the following elements:

the LISA Technological Package (LTP);
a drag-free attitude control system;
continual thrust ionic micro-thrusters, known as FEEPs (for Field Emission Electric Propulsion), to be used as actuators for maintaining the satellite centred around a free-fall reference point.

The LTP is a scale model of one arm of the LISA interferometer (the distance between two sample masses being reduced from 5 million km to 20 cm), with a measurement precision of a picometer. As for LISA, the sample masses have a dual function: they act as an optical reference (mirrors) for the interferometer and as an inertial reference for the satellite's drag-free control system.

The LTP will be financed by the national budgets of member states. France will be financing the modulation unit (AOMU: Acousto-Optic Modulation Unit) of the interferometer laser source, jointly with the Laboratoire Astro Particule et Cosmologie (APC - CNRS-IN2P3).
LISA-Pathfinder will be launched in 2010 by a small European launcher and placed on a geostationary transfer orbit and will then use its own propulsion module to reach its operational orbit near to the Lagrange point L₁.

All of the Space instruments being developed, cold-atom clocks, inertial sensors, interferometers, optical and microwave links will be used as building blocks for future missions to be proposed in response to ESA's "cosmic vision" call for proposals in particular to test gravitation over great distances.