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Cold Atoms in Space and Atomic Clocks: ACES Ch. SALOMON , Laboratoire Kastler-Brossel [ENS-LKB] N. DIMARCQ , Laboratoire de l’Horloge Atomique [LHA] M. ABGRALL, A. CLAIRON, P. LAURENT, P. LEMONDE, G. SANTARELLI, P. UHRICH , Laboratoire Primaire du Temps et des Fréquences [BNM-LPTF] L.G. BERNIER, G. BUSCA, A. JORNOD, P. THOMANN , Observatoire Cantonal de Neuchâtel [ON] E. SAMAIN , Observatoire de la Côte d’Azur [OCA – CERGA] P. WOLF , Bureau International des Poids et Mesures [BIPM] F. GONZALEZ, Ph. GUILLEMOT, S. LEON, F. NOUEL, Ch. SIRMAIN, Centre National d’Etudes Spatiales [CNES] S. FELTHAM , European Space Agency – [ESTEC]

ENS-LKB, Laboratoire Kastler Brossel, Ecole Normale Supérieure, 24 rue Lhomond, 75231, Paris, France LHA, Observatoire de Paris, 61 avenue de l�Observatoire 75014 Paris, France BNM-LPTF, Observatoire de Paris, 61 avenue de l�Observatoire 75014 Paris, France ON, rue de l�Observatoire 58, 2000 Neuchâtel, Switzerland OCA-CERGA, 2130 route de l�Observatoire 06460 Caussols, France BIPM, Pavillon de Breteuil, 92312 Sèvres cedex, France CNES, 18 Avenue Edouard Belin, 31402 Toulouse, France ESA / ESTEC, Keplerlaan, 2200 AG Noordwijk, The Netherlands

1) Introduction The field of atom manipulation using laser light has experienced a considerable growth over the last 20 years. From the initial demonstration experiments in the early 1980's, the research field has evolved into a mature domain with a wealth of new applications as testified by the 1997 Nobel prize in Physics awarded to S. Chu, C. Cohen-Tannoudji and W. Phillips [1]. Applications such as ultra-stable clocks, matter-wave interferometers, Bose-Einstein condensation and atom lasers develop rapidly and it is now conceivable to fly such systems in space. For cold atoms, space brings two major ingredients. First, space offers weightlessness: atoms can indeed be cooled to such low temperatures that the Earth gravity represents a major perturbation to their motion. Take for instance a gaseous ensemble of rubidium atoms cooled in an atom trap to a temperature sufficiently low that Bose-Einstein condensation

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occurs (Figure 1) : in this spectacular quantum phenomenon, nearly all atoms accumulate in the lowest energy state of the trap and they behave exactly all in the same way. In this system, the atoms have, on average, a mere speed of less than 30 micrometers per second. As soon as the trap is switched off, in only one tenth of a second, the atoms acquire on Earth a speed of 1 meter per second which exceeds their initial velocity by a factor 33 000 ! In a second, these atoms have dropped by 5 meters and have usually hit the bottom of the vacuum chamber in which they were cooled. In space, on the contrary, the microgravity conditions allows one to keep these atoms in the observation volume for several seconds to tens of seconds.

Figure 1: An atom laser. Rubidium atoms are extracted from a cold rubidium gas (left) and from a Bose-Einstein condensate(right). An intense low divergence atomic beam falls under the effect of gravity. (courtesy of the university of Münich, [2]) Second, space constitutes a unique laboratory to test fundamental physics laws with great precision. It is well known that a conflict exists today between

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general relativity, that describes well gravitation classically, and quantum mechanics which describes well microscopic phenomena [3]. Today there is no satisfying quantum theory of gravitation and theoreticians seek to unify all four fundamental interactions of nature in a single theory. In space, the Equivalence Principle (the universality of free fall), which forms the basis of Einstein�s general relativity theory, can be tested with orders of magnitude improvements over ground-based experiments. Similarly the famous redshift effect (Clocks in Earth orbit run at a different rate than on the Earth surface) can be tested with unprecedented accuracy by comparing ultra-stable clocks orbiting around the earth with companion clocks on Earth [3,4]. Other fundamental predictions of general relativity and of modern physical theories can be tested in space and will constitute a crucial search for new interactions or new forces. In this article, we will illustrate these two aspects in a specific example : the case of atomic clocks and the ACES mission [5]. We first briefly review the main methods for cooling atomic gases. We then introduce the principle of an atomic clock and discuss the advantages of space. The current PHARAO and ACES projects which will fly on the ISS in 2005 are then described. Finally we outline some perspectives for cold atoms for other future space missions. 2) Cooling methods 1) Laser cooling In laser cooling experiments, photons are used to exert forces on the atoms : when an atom absorbs or emits a photon, its speed changes so that the total (atom+photon) momentum is conserved. This change is called the recoil velocity and is usually very small : for cesium atoms illuminated with light at a wavelength of 0.852 micrometer, the recoil velocity is 3.5 millimeters per second. However the atom is able to absorb and emit at a rate which is typically 10 million times per second so that the net force that a laser beam can exert on an atom can be very large, exceeding typically the force of gravity by five orders of magnitude. This force exerted by a laser beam is called radiation pressure. Cooling a gas of atoms consists in reducing the thermal fluctuations of the atom�s velocity around their mean velocity.This mean velocity can be zero : the gas is at rest in the laboratory. In the case of an atomic beam, the mean velocity is non zero and can be adjusted. Several laser cooling mechanisms have been invented and the simplest of them is called Doppler cooling because it relies on the Doppler effect. It was proposed by T. Hänsch and A. Schawlow in 1975 [6]. The atoms are illuminated by two counterpropagating lasers of equal intensities and same frequency νL (Figure 2 a).

v

Laser Atom

ννννL ννννL

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Figure 2: (a) Principle of laser cooling. Two counterpropagating laser beams exert a radiation pressure force on an atom. When the atom moves, because of the Doppler effect, the laser which opposes the atom’s velocity has a larger radiation pressure than the beam which co-propagates with the atom. Therefore the atom’s velocity is damped. If this beam configuration is used along three ortogonal directions of space, all three velocity components are damped. This is an optical molasses where atoms are viscously confined. The frequency of the lasers is chosen slighly below the frequency at which the atoms absorb when they are at rest. When an atom moves, it sees the frequency of the laser propagating against its motion up-shifted (just as a the sound of a police car coming towards you has a higher pitch) and it absorbs photons from this wave. Conversely, the atom sees the laser beam which propagates in the same direction with a frequency which is down-shifted (more red) : the atom absorbs then much less photons from this beam. Thus the net misbalance between the two radiation pressures leads to a slowing of the atom. This mechanism is very efficient and when the laser beams are oriented along the three directions of space the atoms are rapidly cooled and viscously confined within the laser beams ; they form an optical molasses. The average speed of the atoms is then damped to about ten centimeters per second. At this stage an even more efficient cooling mechanism takes over (Sisyphus cooling) and lowers the speed to a mere 1centimeter per second corresponding to a temperature of about one microKelvin [1]. An interesting variant of optical molasses combines the previous cooling force with a trapping force. It is called the magneto-optical trap and is the work horse in cold atom manipulation [7]. If one adds to the molasses an inhomogeneous

Figure 2b: a magneto-optical trap. In this glass cell, the red ball at center is the fluorescence of 1 billion atoms cooled and trapped by six laser beams. The two white rings hold the magnetic field coils.

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magnetic field created by two coils located on each side of the experimental cell, for a suitable choice of the laser beam polarizations, a restoring force can be created which attracts the atoms toward the point where the magnetic field is zero, at the center of the laser beams. This force accumulates the atoms in a ball of a few cubic millimeters ( Figure 2 b) at a temperature of a few microdegrees Kelvin. 2) Evaporative Cooling Cooling of dilute gases has been pushed even further by a totally different technique, well known to everybody willing to drink a cup of coffee which is too hot ! To cool down the coffee, you blow air on it ! This cooling is not due to the difference in temperature between the air and the coffee but to the evaporation of the coffee which is enhanced by blowing on it. Removing a molecule from the liquid takes up energy which is taken from the remaining liquid. The liquid then cools down. The cooling process for atoms is similar [8] : the atoms are confined in a magnetic trap in which they oscillate and collide with other trapped atoms. The magnetic trap has a bowl-shaped potential which possesses a minimum and rims at a finite height. If one reduces the height of the rims to a value which slightly exceeds the average kinetic energy of the atoms, the fastest atoms escape from the bowl while the remaining atoms rethermalize by collisions to a temperature that is lower than the initial temperature. One can show that, despite of the loss of atoms in this process, the density of atoms at the trap center increases and the temperature continuously decreases. Typically a factor of ten decrease in atom number brings a factor of ten reduction in temperature. Using this method, in 1995 the group of E. Cornell and C. Wieman at JILA and the university of Colorado (USA) succeeded in producing a very peculiar new state of matter : a Bose-Einstein condensate of rubidium atoms [9]. 3) Bose-Einstein condensation and atom lasers According to quantum mechanics, to each particle of matter one can associate a wave. The period of this wave is inversely proportional to the particle�s velocity v and is called the de Broglie wavelength :λDB= h/Mv . Here h is Planck�s constant and M the mass of the particle. When the velocity of the particle becomes very low as obtained by laser and evaporative cooling methods, the de Broglie wavelength can exceed 1 micrometer, the typical wavelength of visible light. In 1925, inspired by the work of the young Bengali physicist S. Bose, A. Einstein predicted an extraordinary property for a gas of identical particles at low temperature and high density in a confining box: When the mean separation between the particles becomes on the order of

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their de Broglie wavelength, then a large fraction of the atoms condense in the lowest energy state of the system, the state with zero velocity if the size of the box becomes arbitrarily large. In the magnetic trap of the JILA experiment, about 100 000 rubidium atoms have condensed in the lowest state of the trap forming a macroscopic quantum system at almost zero temperature. In a Bose-Einstein condensate, all atoms occupy the same quantum state : they behave exactly in the same manner. By switching off the trap, the condensed atoms are easily seen by laser imaging as they correspond to a peak of ultra-cold atoms on a background of uncondensed atoms ( figure 3).

Figure 3: Velocity distribution of a Bose-Einstein condensate of Rubidium atoms. The condensate is in blue and the non condensed atoms form the green piedestal. At very low temperature only the condensate subsists. (Courtesy of Ecole Normale Supérieure, Paris). Condensates possess very peculiar quantum properties which are now actively investigated by more than 50 groups in the world. They have interesting coherence properties which, in some aspects, are analogous to that of lasers : in a laser, a very large number of photons occupy the same mode of the electromagnetic field and this property is at the origin of the high brightness and low divergence of laser beams. Atom lasers have just been produced and figure 1 shows an atom laser developped by a group of the university of Munich led by prof . Hänsch [2]. The very low divergence of the beam of atoms extracted from a rubidium condensate is clearly visible on the figure. As mentioned above the main problem of these atom lasers on earth is that, as soon as the atoms leave the trap, they are accelerated by gravity and acquire very quickly a large speed. Obviously the microgravity of space should be able to help solving some of the fundamental questions that these quantum systems offer. A second difficulty is the relatively low flux of atoms which a condensate can currently

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produce : typically a condensate of one million atoms is produced in 30 seconds. If you wish to deposit these atoms on a square of 1 cm2 , this will require about 30 years ! New methods to improve this situation are actively investigated and evaporation ramps below one second have recently been achieved [10]. As for lasers, one can expect a considerable gain in output flux in the coming years. 4) Atomic Clocks Since the early days of atom manipulation using laser light, it was recognized that the very low velocities of laser cooled atoms would benefit to atomic clocks. As illustrated in figure 4, in an atomic clock a very stable radio-frequency source is used to probe a transition between two energy levels in an atom. Since 1967, the primary time standard relies on cesium atoms and the atomic transition is between two hyperfine states of the electronic ground-state.

νννν0000

Cs D 1/∆∆∆∆t

Cs DΤΤΤΤ

Ramsey method

1/2T

E1

E2

νννν0000

ATOM

h ν ν ν ν0000 ==== ΕΕΕΕ2222 − Ε − Ε − Ε − Ε1111

RADIATION

∆∆∆∆t

∆∆∆∆t ∆∆∆∆tνννν0000

Figure 4 : Principle of an atomic clock. An electromagnetic radiation of frequency ν is tuned near the atomic frequency ν0 and transfers atom from the ground state E1 to the excited state E2 . The width of the resonance curve is inversely

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proportional to the duration ∆t that the atoms spend in the interaction zone with the radiation. The method proposed by N. Ramsey uses two separated zones. In this case, the width of the resonance is inversely proportional to the time of flight T of the atoms between the two zones. Slow atoms produce longer T. By definition the frequency of this transition is ν = 9 192 631 770 Hertz and the Second is simply the inverse of the Hertz. When the radio-frequency is scanned around the atomic transition, it excites the atoms and one obtains a resonance curve. The narrower the resonance curve the better will be the clock and in practice, the radio-frequency is electronically locked to the peak of the resonance. As the width of this resonance is simply the inverse of the time taken by the atoms to cross the radiofrequency interaction zone, slow atoms will allow longer transit times and a narrower width. Commercial clocks use atoms at an average speed of 100 meter per second. Laser cooled cesium atoms move at a speed of 1 centimeter per second : the gain in interaction time for a fixed length of the device could reach a factor 10 000 ! Because of gravity, on Earth this gain is « only » 100 and one uses a fountain geometry as shown in figure 5[11,12]. In space, a gain of another factor of 10 is expected.

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Figure 5 : An atomic fountain. Cesium atoms are cooled to 1 micro degree Kelvin and launched upwards at a velocity of 4 meters per second. They cross twice a microwave cavity fed with a frequency close to the hyperfine transition frequency in cesium, once on the way up, once on the way down. The time separation between the two interactions with the microwave field is about 0.5 second. Atoms which are excited by the field are detected below by a laser beam in which they fluoresce. Atomic fountains have already improved the accuracy of the atomic time by a factor of ten and rapid progress on the stability and accuracy are currently expected [13]. The best fountains have a relative frequency instability of only 6 part in 1016 [14]. This means that these clocks make an error of about 1 second every 50 million years ! Today, 10 atomic fountains are in operation worldwide and about 20 others are under construction. 6) Atomic Clocks in microgravity : PHARAO In an atomic fountain, gravity obviously imposes a limit to the interaction time which is on the order of 1 second. Increasing this duration by a factor of ten imposes a clock height of 125 meters, a size which is not realistic, considering technical aspects such as shielding of residual magnetic fields and thermal stability. On the contrary, in microgravity, long interaction times can be achieved in a reduced volume [15]. It suffices to launch the atoms slowly in the clock device. One returns to the scheme of normal clocks of figure 4 but with a launch velocity 1000 times smaller. The principle of the PHARAO microgravity clock is described in figure 6 and the resonance curves in a conventional clock, a cold atom fountain and a microgravity clock are compared in figure 7. It illustrates clearly the gain in resolution made possible by laser cooling and microgravity environment.

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Figure 6 : Principle of PHARAO , a cold atom clock in microgravity. An optical bench (top) provides light to a cesium tube for cooling and detecting the atoms using optical fibers. Atoms are collected in optical molasses in a first chamber (left), cooled below 1 microKelvin and launched into a second chamber. They enter a cavity in which they experience the two successive Ramsey interactions with a microwave field tuned near the 9.192 631 770 Hz cesium frequency. Atoms excited by this field are detected downstream by fluorescence. The resonance signal is used to lock the oscillator’s central frequency to the cesium transition. For a launch velocity of 5 cm/s , the expected resonance width is 0.1 Hz, ten times narrower than in Earth fountains.

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Figure 7 : Interest of cold atoms in microgravity. (a) measured resonance signal in a conventional thermal beam cesium clock. The resonance width is 100 Hz. (b) measured resonance signal with laser cooled atoms in a fountain ; width : 1 Hz. (c) Expected signal in PHARAO clock for a launch velocity of 5cm/s ; width : 0.1 Hz. The relative frequency stability of the PHARAO clock onboard the International Space Station (ISS) is expected to be better than 10-13 for one second measurement time, 3 10-16 for one day and 1 10-16 for ten days. This is three orders of magnitude beyond the clocks which are currently flying in GPS satellites. A prototype of a cold atom clock developped by french laboratories with CNES support has been tested in the reduced gravity of jet plane parabolic flights in 1997 (figures 8 and 9 ) [16]. This prototype is now a transportable cold atom clock with an accuracy of 1 10-15 , presently the best accuracy among atomic clocks [17]. The satellite version of PHARAO, developed by CNES, has entered in industrial development in June 2001.

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Figure 9 : The cesium tube of PHARAO. Bottom:cooling zone, middle:interaction zone, top: detection zone and vacuum pump. Total length : 1m.

Figure 8: The PHARAO prototype under test in parabolic flights in the Zero G Airbus, in 1997.

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7) ACES : Atomic Clock Ensemble in Space 7.1 The ACES mission PHARAO has been proposed to the European Space Agency in 1997 in the frame of a more general mission, ACES [6]. ACES has been selected by ESA to fly on the International Space Station (ISS) in the frame of its early utilization. The initial ACES payload consisted of two clocks, PHARAO (developed by CNES) and a hydrogen maser (SHM developed by Neuchâtel observatory, Switzerland), together with optical (T2L2) and microwave (MWL) communication links for time and frequency transfer to users on the Earth (figure 10). Both links are high performance systems designed to be able to communicate the very high stability of the space clocks to the ground without the degradation induced by propagation through the atmosphere. The projected performance of the links is a time stability below 10 picoseconds over one day, more than two orders of magnitude beyond the present GPS timing signal accuracy. Figure 10 : Principle of ACES

ACESACES :

New clocks on board the ISSA

PHARAOH-MASER

LASER LINK (T2L2)

30 ps/day

µµµµwave-link

two-ways

Universal time reference Worldwide access

Validation of space clocks

Fundamental Physics tests

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The optical communication link is developed by the observatory of côte d'azur and CNES (FR). Its name is T2L2 (Time Transfer by Laser Link). T2L2 is based on laser pulses which are synchronized to a ground clock and emitted using a telescope towards the satellite. The arrival time of the laser pulses are dated onboard the ISS and part of the light is retroreflected towards the emitting ground station by cornercubes located on the ACES platform. The retroreflected signal is also dated in the ground clock time scale. This round-trip of the light pulses enables one to cancel the fluctuations of the atmosphere in the comparison between the ground time scale and the ISS time scale. The microwave link is a system which transmits high frequency microwave signals between the Earth and the ISS. As for T2L2, these signals are synchronized to the ground and space clocks respectively and allow one to compare these clocks. Contrarily to the optical link which cannot operate by cloudy conditions, the microwave link is weather independent. These equipments will fit on a nadir oriented express pallet of dimensions 863 : 1168 : 1240 mm attached to the European Columbus module. The total mass will not exceed 227 kg and the electrical power 500 Watts. A mock-up of the ACES pallet is shown in figure 11.

PHARAO optics

POD T2L2

PHARAO Tube

POD T2LMWL

PHARAO USO

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Figure 11 : Mock-up of the ACES platform 7.2 ACES scientific objectives Scientific objectives of ACES are both of technical and fundamental nature. The first objective is to operate the PHARAO clock at the level of performance mentioned above ( frequency stability better than 3 10-16 for one day ) and to

Figure 12 : Expected Allan standard deviation of PHARAO and SHM on the ISS make frequency comparisons onboard the ISS between the two types of atomic clocks, PHARAO and SHM. While the SHM operation is not affected by the effect of the reduced gravity, PHARAO operation takes advantage of the reduced gravity environment. The expected frequency stability of PHARAO and SHM in ACES as a function of averaging time is depicted in figure 12. Between 10 seconds and 103 seconds the maser stability is better than that of PHARAO while beyond 103 the reverse is true. Thanks to its excellent medium term stability, SHM will be used for the evaluation of some frequency shifts

100 101 102 103 104 105 10610-17

10-16

10-15

10-14

10-13

10-12

PHARAO

SHM

1 day

σσσσy(ττττ)

ττττ (s)

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affecting PHARAO accuracy such as the collisional shift, micro-wave cavity phase shift, magnetic field shift,� The second objective is to use the very high stability of the PHARAO-SHM combined time scale onboard the ISS to perform time comparisons between ground clocks with a precision of 30 picoseconds through the communication links, T2L2 and MWL. This represents an improvement over the best current GPS comparisons by a factor of 100. Frequency comparisons between these clocks will be performed with a relative accuracy of 10-16 while present frequency comparisons between distant clocks have not been performed below 10-15 [18]. The third objective is to perform several fundamental physics tests with increased precision. The gravitational red-shift will be measured with 3 10-6 accuracy, a 25-fold improvement over the NASA 1976 Gravity Probe A mission [4]. A better tests of the isotropy of speed of light and a new search for a possible drift of one of the fundamental physical constants, the fine structure constant, alpha, will also be performed. These test are detailed below in section 7.4 after a short description of the requirements associated with the communication links . 7. 3 Time and frequency transfer between ISS and Earth a) Required T&F link performance

In order to perform time and frequency comparisons between space-clocks and Earth-based clocks, ACES T&F links must exhibit a very low phase noise compatible with the clock stability of 10-16. The acceptable degradation introduced by the links is assumed to be less than 20 % of the ISS clock stability, and the required time fluctuations expected for T2L2 and MWL as a function of the integration time τ are presented in Figure 13.

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Figure 13: Expected time fluctuations for MWL and T2L2

Two caracteristic times are important in these comparisons : • 300 s, which is the mean duration of an ISS pass over a given point on Earth.

Depending on the elevation of the ISS above the horizon for a given ground terminal, the duration of contact between ISS and the ground terminal will be between 250 and 500 seconds per orbital period. The T&F links must exhibit rms time fluctuations below 0.3 ps over 300 s.

• 90 min, which is the ISS orbital period. The dead time between two successive comparison sessions will be about 90 min. Depending on the longitude of the groud terminal and the minimum elevation at which space-ground connection can be made , between 3 and 6 frequency comparison sessions per day will occur. Larger dead times may also occur. This requires a T&F link with a very good long term time stability, typically better than 6 ps over 1 day and the capability to recover the phase of the transmitted signal from one ISS path to the next.

b) The optical link : T2L2

T2L2 is designed by the Observatoire de la Côte d�Azur (OCA-CERGA) with the technical and financial support of CNES.

The operation principle of T2L2 is simple. A laser station on the ground emits short light pulses towards the ISS. On the ACES payload, part of the laser

100 101 102 103 104 105 1060,01

0,1

1

10

100

T2L2MWL

1 day

σσσσx(ττττ)

(ps)

ττττ (s)

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pulse is detected and part is reflected towards the ground terminal with a corner cube reflector. For each pulse, three datations are performed : • date T0 of pulse emission from the ground terminal (date in ground clock

time scale) • date T1� of pulse detection on the ACES payload (date in space clock time

scale) • date T2 of reflected pulse detection at the ground terminal (date in ground

time scale).

The comparison of ground and space clock time scales relies on the knowledge of the ensemble of date triplets (T1, T2�, T3) corresponding to a large number of detected laser pulses. The « Two-way » operation of T2L2 (up and down link) rejects many common mode noise sources, especially the tropospheric delay. The ionospheric delay is extremely small at optical frequencies and is also cancelled by this Two-Way scheme. Fluctuations of instrumental delays are the main noise sources in T2L2. Preliminary experiments have been already carried out at OCA and have demonstrated instrumental delay fluctuations with time standard deviation σx at the required picosecond level between 100 and several thousand seconds.

c) The microwave link : MWL

No existing microwave link (GPS, TWSTFT) can reach today the required performance for ACES. In 1999, ESA initiated two independent industrial studies for the development of a new microwave link with adequate performance for ACES. Two different concepts have been proposed by two compagnies which have already a long experience in T&F transfer techniques : Timetech, in Germany (designer of PRARE and SATRE systems) and Thalès-Detexis in France (designer of T2L2 datation device). Both proposals share a common point: unlike the GPS system where ground equipments are only receivers, the proposed methods are two-way systems in which the ground terminal both emits and receives microwave signals in order to remove first order Doppler and tropospheric fluctuations. In essence they are upgraded versions of the Vessot Two-Way technique used for the GP-A experiment in 1976 [4]. In this pionneering experiment, a two-way link with 3 frequencies in S band (one signal up, two signals down) allowed the frequency comparison during two hours between two H-masers (one on the ground and one in a sounding rocket) at the level of 8. 10-15 at 1000 seconds. This Two-Way / 3 frequencies method allowed : • the complete rejection of tropospheric delay and 1rst order Doppler effect • a partial rejection of ionospheric delay ; the up and down frequency are not

equal to avoid interference effects and they do not lead to equal ionospheric delays. The evaluation of this residual ionospheric delay required the knowledge of the ionosphere Total Electronic Content (TEC) which was evaluated using the second down link at different frequency.

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Vessot�s technique was a frequency comparison technique : it required the

clocks to be in permanent visibility during the comparison. Moreover, it did not offer multi-user capability which is mandatory for ACES mission to allow common view comparisons of ground clocks.

The two MWL concepts proposed for ACES are improved versions of

Vessot�s technique and their main characteristics are (see Table 1) : • the carrier frequency fc is increased to Ku band (about 15 GHz) ; this leads to

a noticeable reduction of the inospheric delay which varies as 1/(fc)2. Timetech technique uses a third frequency in S band to determine ionosphere TEC. In Thalès technique, up and down links have the same frequency : the ionospheric delay is thus completely rejected by the two-way scheme.

• the operation of Timetech system is continuous whereas Thalès one is pulsed to avoid interference effects (equal up and down link frequencies)

• a Pseudo random modulation code is used to remove 2π phase ambiguity between two successive comparisons sessions separated by large dead times. This code modulation is applied to the phase (Timetech) or the amplitude (Thalès) of the carrier.

• both systems allow multi-user capability : different ground users are distinguished by different codes and different Doppler shifts.

Timetech

Technique Thalès

Technique Concept

- Two-Way (up and down link)

- 3 frequencies

- Two-Way (up and down link)

- 1 frequency

Carrier frequency

- Ku band (one up and one down link)

- S band (one down link) for TEC determination

- Ku band

Operation mode

Continuous Pulsed

PN-code

on carrier phase of Ku and S signals

on carrier amplitude

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Code rate

- 100 Mchip/s for Ku signals

- 1 Mchip/s for S signal

- 100 MHz

Multi-users capability

YES (4 simultaneous users)

YES (2 simultaneous users)

Table 1 Main characteristics of proposed

MWL concepts Relativistics effects affecting time or frequency transfer (gravitational shift, 2nd order Doppler effect, Sagnac effect, �) will be corrected using the orbitography data. Preliminary studies have already been performed on these two MWL concepts. Today they bring sufficient confidence in the feasibility of this high stability microwave T&F link for ACES. ESA selection of the industrial contractor for MWL will occur in october 2001.

Orbitography requirements The Scientific objectives of ACES rely on comparisons between clocks in space and clocks on the ground. As the separation between the two clocks in on the order of 400 kms, relativistic effects occuring in the comparison can exceed 10-11, five orders of magnitude above the expected clock stability and accuracy. Thus a precise knowledge of the orbit of the ISS is required because both the gravitational potential seen by the clocks and the ISS altitude and velocity are involved in the calculation of these relativistic effects. A relativistic theory for time and frequency transfer to order c-3 order has recently been developped to provide a time-keeping accuracy of the order of 5 10-17 in fractional frequency [19,20].These two papers show that currently known relativistic corrections to order c-2 for frequency transfer (first and second order Doppler contributions, Einstein gravitational red-shift) are not sufficient at this frequency stability level. At third order, the standard formula is modified by a simple correction factor involving the first order Doppler effect. It is also shown that at the level of 5 10-17, this third order calculation is sufficient. In a geocentric isotropic inertial (non rotating) reference frame (GRS), the fractional frequency difference between the space clock (coordinate Sw! , velocity

Sv! ) and a ground clock ( Ew! , Ev! ) measured on the ground by a two-way frequency transfer is given by:

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( ) ( )2

2

1 (1 . )2

E S S EE S E E SE E SE

v v v vf U w U w r a nf cc

− −∆ = − + − − ⋅ +

! ! ! !! ! ! ! !

where UE is the gravitational potential at clock locations (with U ≥ O following the International Astronomical Union convention). UE(wS) is the Earth gravitational potential applied to the ISS clock at the coordinate position Sw! in the GRS. UE( Ew! ) is the Earth gravitational potential applied to the clock on the ground located at the coordinate position Ew! in the GRS. c is the velocity of the light, Ev! is the GRS cooordinate velocity of the clock on ground, Sv! is the GRS coordinate velocity of the ISS clock. SEr

! is the range between the ground clock

and the space clock, SEn! a unit vector along SEr! and Ea

! is the Earth acceleration in the GRS. The first term of equation (1) [ ] 2)()( cwUwU EESE

!! +− is the red-shift effect (Einstein effect) induced by of the Earth gravitational potential. As the ISS is a low orbiting satellite, the influence of other bodies (e.g. the Moon) is negligible at the expected 10-17 level. For an ISS orbit of 400 km, this term is +4.6 10-11. The second term - 22

SE c2vv!!

−−−− describes the second order Doppler effect between two moving clocks and has a value of �3.3 10-10.

The third term 2ESE c)a.r(!! includes the effect of the rotation of the Earth

(Sagnac 1/c2 effect). It is maximal for a ground station on the equator and is lower than 7 10-13. The last term [[[[ ]]]]SEESSE

1 r/)vv.(r.c1!!!

−−−−++++ −−−− does not appear at order 1/c2 and was not known before. This c-1 correction term can be interpreted as a Doppler correction to the three relativistic terms in equation (1). During the two-way frequency comparison, this correction is maximum at low elevation and antisymetric around zenith. Its magnitude is smaller than 2.7 10-5 or 1.2 10-15 in relative frequency. For frequency comparisons at 10-16 this correction must be taken into account and it is sufficient to calculate its value at the 5 % level.

In order to evaluate the relativistic frequency shifts with a precision compatible with clock stability and accuracy, the whole orbit of both ground and space clocks must be known with uncertainties lower than : • 1.7 m (averaged over 1 day) for the altitude • 1.9 mm .s-1 (averaged over 1 day) for the velocity

For a single ISS path of mean duration 300 s, these uncertainties must be less than 24 m for the altitude and 26 mm .s-1 for the velocity. These orbitography requirements are currently easily fulfilled with DORIS and GPS devices but on satellites which are considerably smaller than the ISS . The orbitography models apply to the satellite center of gravity where, for instance, the air drag is modelled. As the orbitography requirements apply to the clock location and not the COG, the knowledge of ISS attitude and structural deformations will be needed .

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7.4 ACES science objectives The first part of ACES mission will be a 6 months characterization phase: performance evaluation of the clocks and T&F links. Then, the utilization phase (12 to 30 months duration) will take place. ACES user groups have identified experiments in the following domains : • physics of cold atoms • relativistic effects • precise orbit determination • laser time transfer • microwave link technologies • T&F metrology • geodesy • earth observation Thanks to its 51 degree orbit inclination, the ISS will fly above most primary time and frequency metrology laboratories worldwide. Thus ACES has obvious objectives in T&F metrology: comparisons between primary standards, comparisons between clocks in the microwave domain and in the optical domain, time scales,� ). ACES tests in Fundamental Physics play a fundamental role and are further detailed below. a) Measurement of the gravitational frequency shift As outlined above in the time and frequency transfer section, a direct consequence of Einstein�s equivalence principle, is that a source of radiation in a gravitational potential Us appears to an observer in a different gravitational potential Uo shifted in frequency by an amount ∆f/f = -∆U/c2 where ∆U=Us-Uo is the gravitational potential difference between the source « s » and the observer « o » positions. Pound and Rebka made a direct laboratory determination of this effect in 1960 using the Mossbauer effect. The result confirmed the prediction of general relativity to within +/-1%. The most precise measurement of this gravitational shift is presently the Gravitational Probe A experiment performed in 1978 by Vessot, Levine and colleagues [4].

The ACES red-shift measurement will use a different technique. Instead of modulating the red shift by changing the altitude of satellite as done in GP A, ACES will use the high accuracy of the PHARAO clock ( 10-16) and ground clocks (10-16 or better) to make an absolute measurement of the frequency difference between PHARAO and ground cesium fountains. Knowing precisely the orbital parameters of the space station (position and velocity), the frequency difference between the ground clocks and the PHARAO clock will be calculated and compared to theory. As the ISS orbit slowly changes as a function of time,

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the gravitational redshift will also be modulated but only by about 10% of its magnitude. If both the ground and space clocks used in the frequency comparison have an accuracy of 10-16 and, if the link does not degrade clock performance, the Einstein effect can be determined with a relative uncertainty of 3 10-6. This represents a factor 25 improvement over the GPA experiment. b) Search for a possible time variation of the fine structure constant

The fine structure constant c4e 02 "πεα ==== =1/137.0359895(61) characterises

the strength of the electromagnetic interaction in an atom or a molecule. In 1937 Dirac suggested that it was worth checking if the fundamental

constants of physics were indeed constant in time and a great deal of effort has been devoted to this goal with increasing precision. In General Relativity as in other metric theories of gravitation, a time change of non-gravitational constants is forbidden. This is a direct consequence of Einstein�s equivalence principle. However a number of modern theories predict the existence of new interactions which violates Einstein's equivalence principle. Damour and Polyakov for instance predict time variation of fundamental constants and in particular of the fine structure constant [21].

Among the numerous experiments designed to check the equivalence principle, methods utilising space (STEP, MICROSCOPE), and stable clocks have a long history. The high stability and accuracy of ACES clocks and cold atom ground clocks makes the search for a drift in α with atomic frequency standards a promising route. As compared to astrophysical tests such as the absorption of quasar light by interstellar clouds [22] or the Oklo test [23], laboratory tests can be repeated in different locations and cross-checked to a relatively high degree. In addition these test check the stability of a at the present time.

The principle underlying these tests involves the comparison of the frequencies given by clocks using different elements as a function of time. Any change of the frequency difference between two clocks might be attributed to a change of fundamental constants or to imperfections in long term behaviour of the clocks. Therefore to make a convincing test, it is mandatory to involve a large number of clocks and to make cross-correlation between the measurements. ACES will provide access to a large number of laboratories world-wide. This will involve clocks operating with many different atoms, e.g. cesium, rubidium, hydrogen, mercury ion, ytterbium ion, etc, etc. These frequency standards operate either in the microwave domain (caesium and rubidium fountains, H, Hg+, Yb+, Cd+,...) or in the visible part of the spectrum. For an alkali atom with atomic number Z and having an hyperfine transition in the microwave domain, Prestage et al [24] calculated the effect of a possible drift of α upon the hyperfine energy as a function of Z. The calculation showed

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that relativistic corrections to the hyperfine energy become important for high Z values and can be as large as 40% of the main effect. If one makes the ratio between the hyperfine energies of two (or more) atoms having very different Z numbers, one finds the sensitivity of the test of the constancy of α . For instance, if (dα/dt)/α = 1. 10-14/year, then a frequency drift of 1.4 10-14/year would occur between a cesium clock (Z=55) and a mercury ion clock (Z=80). For cesium and rubidium (Z=35) this figure is 0.45 10-14/year. The best laboratory experiment to date is based on the comparison between cesium and rubidium fountains and gives the upper limit for (dα /dt)/α < 6.9 10-15/year [25]. Since both the ACES cesium clock and ground rubidium clocks have a projected accuracy of 10-16, any frequency drift can be determined with a resolution as low as year/10.2 16−−−− giving an improvement of a factor 20 / year. For a 3 year mission the gain would be close to 100. The Z dependence means that the signature of a drift of α, if found, would be unambiguous. Such a discovery would constitute a major breakthrough and have profound implications on our understanding of the laws of physics. c) Test of special relativity A number of relativity theories allow for violations of special relativity (see [26] for a review). Such theories all postulate some �universal rest frame� Σ in which the basic postulates of special relativity are valid : in particular, slow clock transport and Einstein synchronization procedures [27] for distant clocks are equivalent. In special relativity this is also valid in any inertial frame S moving at constant velocity v in Σ but this is not the case in some alternative theories. This implies, for example, that for a light signal transmitted one-way between two distant points its speed, as measured by clocks that were synchronised using slow clock transport, is a constant in Σ (i.e. independent of the direction of signal transmission), but not in S.

For certain types of experiments measuring one way signal transmissions, a simple test theory based on a parameter δc/c is often used. In this interpretation distant clocks are synchronised in S using slow clock transport. c is the round trip speed of light (independent of the chosen synchronization convention) and δc the deviation from c of the speed of light in S (measured by the transport synchronised clocks) for a signal propagating one-way along a particular direction. The experiments look for a variation of δc/c as a function of the direction of signal transmission in S. In special relativity δc/c = 0 which, of course, reflects the fact that the two synchronization conventions are equivalent. A number of experiments searching for a non zero value of δc/c have been carried out either by direct measurements of the variation of one way transmission times of light signals between distant clocks or by indirect measurements searching for the variation of the first order Doppler shift. The former used the clocks and time links in the JPL deep space tracking network

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and the GPS system [28], the latter the first order Doppler effect in Two Photon Absorption [29], Mössbauer effect [30], and frequency links of the GP-A experiment [4]. A violation of special relativity is, in this model, linked to a particular spatial direction (velocity v

! of S in Σ) and the experiments search for the modulation of the effect as the direction of signal transmission is changed. Consequently experiments that rely on the rotation of the Earth for a change of direction are only sensitive to the component of δc/c that lies in the equatorial plane. The ACES experiment is expected to improve previous limits on δc/c by about one order of magnitude. The experiment will compare the space clocks to the ground clocks continuously during the passage of ISS. The time transfer link will consist of microwave signals that are exchanged in both directions between the clocks. All emission and reception times are measured in the local space time scale and ground time scale respectively. The difference of the measured reception and emission times provides the one-way travel time of the signal plus some unknown but constant offset ∆s due to the fact that the clocks are not synchronized (by slow clock transport). Thus the difference of the up and down travel times is sensitive to a non zero value of δc/c along a preferred direction

θδ cos2 TccTT msdownup +∆+∆=−

where T is half the light round-trip time, θ is the angle between the link and a preferred direction, and ∆m are known small corrections due to path asymmetries, atmospheric delays, etc� ∆s is unknown (desynchronization) but remains constant, so adjusting a cosine to the data over the passage allows the measurement of δc/c. The sensitivity of the experiment is determined by the instabilities over one ISS pass of both the clocks and T&F links phase. The value of Τ varies during successive passes between ≈ 1.5 ms and ≈ 8 ms. With an overall time instability over one ISS pass as low as 1 ps, the expected sensitivity to δc/c should be in the low 10-10 region which is an improvement by a factor 10 or more over previous measurements. Such a performance seems even more likely when considering that several systematic error sources (atmospheric delay, orbit accuracy, clock stability) that were likely sources of uncertainty for the GPS experiment [28] will be negligible for ACES because of the two way systems used (cancellations between the up and down links) and the high stability of the ACES clocks. 8) Present status of ACES mission Due to an excess of mass, some ACES instruments and pieces of equipment have be descoped in november 2000. The new baseline proposed for ACES payload includes PHARAO, SHM, MWL and FCDP. The optical link T2L2, the Magnetic and Microvibration Measurement Device, M3D, and the DORIS receiver for the orbit determination have been removed. The most severe aspect

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of this reduction deals with the removal of T2L2. This implies to search for other flight opportunities for the demonstration of high accuracy time transfer with light pulses. As microwave time and frequency transfers are done today only at the 10-15 level, i.e. one order of magnitude below the ACES requirement, it was considered important to have two independent links to validate the operation of each of them. The removal of T2L2 will thus suppress this option and put more pressure on the MWL in terms of performance tests and reliability. The removal of DORIS orbitography system means that the precise orbitography needed for ACES must be done using the GPS receivers located on the ISS. The payload integration study made by ASTRIUM for the accomodation of the new ACES payload on the Columbus external plattform has been completed in July 2001. The study has shown the feasibility of ACES with respect to mass, electrical power and thermal dissipation with a reasonable margin being allocated for the development of the various instruments. In June 2001, the PHARAO instrument entered in industrial development (Phase C/D) and an engineering model of each of the PHARAO subsystem will be delivered to CNES at the end of 2002 for assembling. Functional and performance tests will last about 6 months. The flight model will be delivered at the end of 2003 for delivery to NASA in the summer of 2004 and launch at the end of 2004. The SHM development is also in C/D phase. The Invitation to Tender for the MWL industrial development was issued by ESA in July 2001 and closed early october 2001. Selection of the industrial company by ESA is due in october 2001. A MWL breadboard demonstrator will be delivered to ESA at the end of 2002. Negociations for the C/D phase of the ACES palett integration are ongoing between ESA and industry. Figure 14 illustrates the progress in the last forthy years of atomic clocks in the microwave and optical domains. In 2005, ACES is likely to be near the crossing point of microwave and optical clocks, a very interesting situation for comparing through space these ultra-stable clocks on the ground.

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1950 1960 1970 1980 1990 2000 201010-17

1x10-16

10-15

1x10-14

1x10-13

1x10-12

1x10-11

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1x10-9

Optical clocks

ACES

Ca PTB

H MPQ

Cold atoms

Microwave clocksSlope: gain of 10 every 10 years

ACCURACY OF THE ATOMIC TIME

NIST: Hg+

LPTF

PTBNIST

PTBNRCNBSVNIIFTRI

NPLNBSLSRH

RE

LATI

VE

AC

CU

RA

CY

YEAR

Figure 14 : evolution of the accuracy of the atomic time. Comparison between microwave clocks and optical clocks. 9) Perspectives PHARAO and ACES will probably constitute the first demonstration of the benefits of space for cold atomic gases and their application to ultra-stable atomic clocks. The performances of PHARAO could still be improved by using a better interrogation oscillator, better microgravity environment than that of

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the ISS and by replacing cesium atoms by rubidium atoms which display less collisional interactions. Such perspectives are under development at NASA (PARCS, SUMO and RACE projects). Frequency stability and accuracy in the 10-17 range can be envisioned. The associated time and frequency transfer techniques will need to include several higher order relativistic corrections in order to compare adequately distant clocks. Of particular interest would then be a clock mission in the strong gravitational potential of the Sun rather than that of the Earth (SORT project). This mission could bring several orders of magnitude on tests of general relativity such as the Shapiro delay. Third generation navigation systems are likely to benefit from advances made on the time transfer techniques validated with ACES. Totally new concepts for global positioning systems based on a reduced set of ultra-stable space clocks in orbit associated with simple transponding satellites could be studied. More generally, clocks operating in the optical domain rather than in the microwave domain are making rapid progress on the ground. The frequency of these clocks is four to five orders of magnitude higher than the frequency of microwave standards and with an equivalent linewidth, the quality factor of the resonance exceeds that of cesium clocks by the same factor. Using laser cooled atoms or ions and ultra-stable laser sources, these optical clocks will likely open the 10-17--10-18 stability range. In this range, it is clear that fluctuations of the earth potential at the clock location induced, for instance, by the tides will affect comparisons between distant clocks. This limitation could be turned into an advantage if one installs such ultra-stable clock in space where the gravitational potential can present far reduced fluctuations compared to ground. With adequate Time and Frequency transfer technique, a new type of geodesy based on the Einstein effect could be realized. Using the wide frequency comb generated by femtosecond lasers, it becomes now possible to connect virtually all frequency standards together throughout the microwave to ultra-violet frequency domain [31]. The simplicity of this table top frequency chain makes it conceivable now to qualify it for space. Clocks are not the only devices which can benefit from space. Atom interferometers would also increase their sensitivity with increased interaction times. In these systems, the interference of matter waves rather than light waves is created, bringing an enormous gain in potential sensitivity over light interferometers. After just a few years of existence, matter wave gyroscopes on the ground have now surpassed their optical counterparts in rotation sensitivity. This opens a whole new field for inertial sensors, accelerometers, gradiometers, both on Earth and in space. In january 2000, the HYPER project was submitted to ESA in answer to the call for flexi-missions (F2/F3). HYPER aims at measuring yet another effect predicted by general relativity, the Lense-Thirring effect and at measuring the fine structure constant with at least one order of magnitude gain in precision. HYPER would also be the first satellite to be monitored by matter-wave inertial sensors rather than classical accelerometers and gyroscopes. Finally, the technology for producing Bose-Einstein condensates and atom lasers is also progressing rapidly on the ground.

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Space would offer the possibility to produce coherent atomic waves in the picokelvin temperature range. In addition to the interesting fundamental many-body physics that this quantum matter would offer on a truly macroscopic scale in space, atom lasers would constitute ideal sources for atom interferometers with long interaction times. Cold atoms open fascinating perspectives for space applications ! Support by ESA, CNES, CNRS, Region Ile de France, Bureau National de Metrologie and Paris Observatory is gratefully acknowledged. References [1] See for instance the 1997 Nobel lectures: S. Chu, Rev. Mod. Phys., 70, 685 (1998); C. Cohen-Tannoudji, ibid., p. 707; William D. Phillips, ibid., p. 721. [2] I. Bloch, T.W. Hänsch, and T. Esslinger, Nature 403, 166 (2000) [3] See for instance, contributions of T. damour and P. Fayet in this volume [4] R.F.C. Vessot and M.W. Levine, Journal of General Relativity and Gravitation, 10, 181 (1979) . [5] R.F.C. Vessot al., Phys. Rev. Lett. 45, 2081 (1980).red-shift theory [6] C. Salomon and C. veillet, Proc. of the first symposium on the utilisation of the international space station, ESA special publication SP 385, 295, (1997). C. Salomon, P. Lemonde, P. Lautrent, E. Simon, G. santarelli, A. Clairon, P. Petit, N. Dimarcq, C. audoin, F. Gonzalez, and F. Jamin-Changeart P., Proc. of the first symposium on the utilisation of the international space station, ESA special publication SP 385, 289, (1997). [6] T. W. Haensch and A. Schawlow, Opt. Comm., 13, 68 (1975) [7] E. Raab, M. Prentiss, A. Cable, S. Chu and D. Pritchard, Phys. Rev. Lett., 59, 2631 (1987) [8] H. Hess, Phys. Rev. B, 34, 3476 (1986) [9] M. Anderson et al., Science, 169, 198 (1995) [10] W. Hänsel, T. Hommelhof, T.W. Hänsch and J. Reichel, Nature, 413, 498 (2001) [11] M. Kasevich, E. Riis, S. Chu and R. de Voe, Phys.Rev. Lett., 63, 612 (1989). [12] A. Clairon, C. Salomon, S. Guellati, and W. Phillips, Europhys. Lett., 16, 165 (1991) [13] P. Lemonde et al., in Frequency measurement and control, Topics Appl. Phys., 79, 131, A. Luiten ed., Springer Verlag, (2001) [14] G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A.G. Mann, S. Chang, A.N. Luiten, C. Salomon, Phys. Rev. Lett., 82, 4619 (1999) [15] B. Lounis, J. Reichel and C. Salomon, C. R. Acad. Sc. Paris 316, 739 (1993) [16] P. Laurent, P. Lemonde, E. Simon, G. Santarelli, A. Clairon, N. Dimarcq, P.Petit, C. Audoin, and C. Salomon, Euro. Phys. J. D, 3, 201 (1998).

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[17] M. Niering, R. Holzwarth , J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, A. Clairon, Phys. Rev. Lett. 84, 5496 (2000) [18] F. Taris et al., IEEE trans. on Ultrasonics, ferroelectrics and frequency control 47, 1140, (2000) [19] L. Blanchet et al., A&A, 370, 320 (2001) [20] N. Ashby, in Proc. of the 1998 IEEE Frequency Control Symposium, p. 320 (1998). [21] T. Damour and A. Polyakov, Nucl. Phys. B, 423, 532 (1994) [22] J. Webb et al., Phys. Rev. Lett., 87, 091301 (2001) [23] T. Damour and A. Polyakov, Nucl. Phys. B, 480, 37 (1996) [24] J. Prestage, R. Tjoelker and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995) [25] C. salomon et al., in Proc. of the 17th Int. Conf. on Atomic Physics, 23, World Scientific (2001) [26] C. Will, Theory and Experiment in Gravitational Physics, revised edition, (Cambridge University Press, Cambridge) 1993. [27] Lorentz H.A., Einstein A., Minkowski H., Weyl H., The Principle of Relativity, (Dover, New York) 1923 [28] P. Wolf P., Petit G., Physical Review A 56, 4405 (1997). [29] Riis E. et al., Phys. Rev. Lett. 60, 81 (1988). [30] Turner K.C. and Hill H.A., Phys. Rev. 134, B252 (1964). [31] J. Reichert et al., Opt. Commun., 172, 59 (1999).

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