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IAF-01-J.1.04

HIGH PRECISION ATOM INTERFEROMETRY IN SPACE : THEHYPER PROJECT

G. Bagnasco(1), R. Bingham(2), C. Bordé(3), P. Bouyer(4), M. Caldwell(2), A. Clairon(5),

K. Danzmann(6), N. Dimarcq(7), W. Ertmer(8), L. Gerlach(1), J. Helmcke(9), C. Jentsch(8),

B. Kent(2), C. Lämmerzhal(10), A. Landragin(7), M. Novara(1), I. Percival(11), E.M. Rasel(8),

R. Reinhard(1), C. Salomon(12), M. Sanford(2), W. Schleich(13), P. Teyssandier(14) P. Tourrenc(15),

S. Vitale(16), P. Wolf(5)

(1) ESTEC, ESA, The Netherlands(2) Rutherford Appleton Laboratory , United Kingdom(3) Laboratoire de Physique des lasers, France(4) Laboratoire Charles Fabry, France(5) Laboratoire Primaire du Temps et des Fréquences, France(6) Institut für Atom und Molekülphysik, Germany(7) Laboratoire de l’Horloge Atomique, France(8) Institut für Quantenoptik, Germany(9) Physikalisch-Technische Bundesanstalt, Germany(10) Universität Düsseldorf, Germany(11) Queen Mary and Westfield College, United Kingdom(12) Laboratoire Kastler-Brossel, France(13) Universität Ulm, Germany(14) DANOF Observatoire de Paris, France(15) Université Pierre et Marie Curie, France(16) University of Trento, Italy

52ND INTERNATIONAL ASTRONAUTICAL CONGRESS1-5 OCT 2001/TOULOUSE, FRANCE

For permission to copy or republish, contact the International Astronautical Federation3-5 Rue Mario-Nikis, 75016 Paris, France

Copyright © 2001 by the International Astronautical Federation or the International Academy of As-tronautics. All right reserved. 2

HIGH PRECISION ATOM INTERFEROMETRY IN SPACE : THEHYPER PROJECT

G. Bagnasco(1), R. Bingham(2), C. Bordé(3), P. Bouyer(4), M. Caldwell(2), A. Clairon(5),

K. Danzmann(6), N. Dimarcq(7), W. Ertmer(8), L. Gerlach(1), J. Helmcke(9), C. Jentsch(8),

B. Kent(2), C. Lämmerzhal(10), A. Landragin(7), M. Novara(1), I. Percival(11), E.M. Rasel(8),

R. Reinhard(1), C. Salomon(12), M. Sanford(2), W. Schleich(13), P. Teyssandier(14) P. Tourrenc(15),

S. Vitale(16), P. Wolf(5)

(1) ESTEC, ESA, The Netherlands (2) Rutherford Appleton Laboratory , United King-dom

(3) Laboratoire de Physique des lasers, France (4) Laboratoire Charles Fabry, France(5) Laboratoire Primaire du Temps et des Fréquences,

France(6) Institut für Atom und Molekülphysik, Germany

(7) Laboratoire de l’Horloge Atomique, France (8) Institut für Quantenoptik, Germany(9) Physikalisch-Technische Bundesanstalt, Germany (10) Universität Düsseldorf, Germany(11) Queen Mary and Westfield College, United Kingdom (12) Laboratoire Kastler-Brossel, France(13) Universität Ulm, Germany (14) DANOF Observatoire de Paris, France(15) Université Pierre et Marie Curie, France (16) University of Trento, Italy

We present the core technique of the HY-PER mission : the matter wave based inertialsensors. We will first briefly introduce thebasics of matter wave interferometry by fo-cusing and light pulse interferometers thatwill be used on HYPER. After reviewing dif-ferent applications of inertial sensors, wewill focus on the applications of AtomicSagnac Units (ASU) to measure the Lense &Thirring effect around the earth. We willconclude with possible other mission goalssuch as tests of QED.

INTRODUCTION

Inertial Sensors are useful device in bothscience and industry. Higher precision sen-sors could find practical scientific applica-tions in the areas of general relativity1, geod-esy and geology. Important applications ofsuch devices occur also in the field of naviga-tion, surveying and analysis of structures.

Matter-wave interferometry has recentlyshown its potential to be an extremely sensi-

tive probe for inertial forces2. For example,neutron interferometers have been used tomeasure the rotation of the earth3 and theacceleration due to gravity4. More recently,atom interference techniques have been usedin proof-of-principle work to measure rota-tions5 and accelerations6.

ATOM INTERFEROMETER-BASED INERTIAL SENSORS :

BASIC PRINCIPLE

We present here a summary of recent workwith light-pulse interferometer-based inertialsensors. We first outline the general princi-ples of operation of light-pulse inter-ferometers. This atomic state interferome-ter7 uses two-photon velocity selective Ra-man transitions8,9 to manipulate atoms whilekeeping them in long-lived ground states. Inthese interferometers, the atomic internalstates plays the role of polarization in pho-tonic optics.


Principle of a light pulse matter-waveinterferometer

Light-pulse interferometers work on theprinciple that when an atom absorbs or emitsa photon momentum must be conserved be-tween the atom and the light field. Conse-quently, an atom which emits (absorbs) aphoton of momentumi hk will receive amomentum impulse of ( )δp k k= − +h h . Whena resonant traveling wave is used to excitethe atom, the internal state of the atom be-comes correlated with its momentum: anatom is in its ground state 1 with momen-tum p (labeled 1, p ) is coupled to an excited

state 2 of momentum p k+ h ( 2,p k+ h )7.

This is analogous to, for example, a polariz-ing beam splitter (PBS) in optics, where eachoutpout port of the PBS (i.e. the photonmomentum) is correlated to the laser polari-zation (i.e. the photon state). In the opticalcase, a precise control of the input beam po-larization allows for controlling the balancebetween the output ports. In the case of at-oms, a precise control of the light-pulse du-ration plays the role of the polarization con-trol, allowing a complete transfer from onestate (for example 1, p ) to the other

( 2,p k+ h ) in the case of a π pulse and a

50/50 splitting between the 2 states in thecase of a π 2 pulse (half the duration of a πpulse).

We use a π π π2 2− − pulse sequence10 tocoherently divide, deflect and finally recom-bine an atomic wavepacketii. The first π 2

i Even though photon has no mass, it carries momen-tum which is proportional to the radiation frequency.This property, foreseen by A. Einstein, was alreadyused in 1933 by Frisch to explain the direction of thetail of the comets.ii A wavepacket is the quantum mechanics equivalentof a partially coherent light vibration. The wavepacket

pulse excites an atom initially in the 1, p

state into a coherent superposition of states1, p and 2,p k+ h . If state 2 is stable

against spontaneous decay, the twowavepackets will drift apart by a distance

hkT m in time T . Each wavepacket is redi-rected by a π pulse which induces the transi-tions 1 2, ,p p k→ + h and 2 1, ,p k p+ →h .

After another interval T the wavepacketsonce again overlap. A final π 2 pulse causesthe two wavepackets to interfere. The inter-ference is detected, for example, by measur-ing the number of atoms in the 2 state.

We obtain large wavepacket separation byusing laser cooled atoms and velocity sensi-tive stimulated Raman transitions8 to drivethe transitions. it gives large recoil kicks

hk m in transition between ground-state hy-perfine levels.

Applications to inertial force sensors

Inertial forces manifest themselves bychanging the relative phase of the de Brogliematter waves with respect to the phase ofthe driving light field, which is anchored tothe local reference frame. The physical mani-festation of the phase shift is a change in thenumber of atoms in, for example, the state2 , after the interferometer pulse sequence

as described above.

If the 3 light pulses of the pulse sequenceare only separated in time, and not separatedin space (i.e. if the velocity of the atoms isparallel to the laser beams), the interferome-

denotes the spatial extension over which all mono-chromatic “atomic” vibrations will interfere construc-tively and the size of this wavepacket can therefore beseen as the coherent length of the atomic source.Colder atoms lead to longer coherence length. Forexample, atoms cooled at 1 µK have a coherencelength of about 1 µm.


ter is in a gravimeter or accelerometer con-figuration11. In a uniformely acceleratingframe with the atoms, the frequency of thedriving laser changes linearly with time at therate of − ⋅k aeff t because of the Doppler ef-fect. The phase shift arises from the interac-tion between the light and the atoms12 andcan be written

∆φ φ φ φ≡ + +1 1 2 2 3 3( ) ( ) ( )t t t

where φ δi i t

tt t dt

i

( ) ( )= ∫0

is the phase of light

pulse I at time t1 relative to the atoms (δ isthe laser detuning : the difference betweenthe chirped frequency of the laser vibrationand the atomic transition frequencyiii). If thelaser beams are vertical, the gravitationallyinduced chirp can be written:

∆φ ≡ − ⋅k geff T2

It should be noted that this phase shift doesnot depend on the atomic initial velocity oron the mass of the particle. A first experi-ment demonstrated a sensitivity of 3 parts in108 after integrating for 2000 sec11. Morerecently, accuracy comparable to the preci-sion obtained by measuring g with a fallingcorner cube under the best seismic conditionshas been achieved13.

iii The atomic transition frequency ω0 represents theenergy hω0 that one photon from the laser has tocommunicate to the atom to allow the change of elec-tronic state. Since the photon energy is related to thelaser wavelength and hence its frequency, the atomictransition can be driven by laser light only if the laserfrequency is equal to the atomic transition.

Principle of the atom-fountain-based atomgravimeter achieved in S. Chu (Nobel 1998)group at Stanford. Left shows a two days re-cording showing the variation of gravity. Theaccuracy allowed to resolve ocean loadingeffects.

Gravimetric survey using gravimeters doesnot yield the spatial resolution and the accu-racy that is typically needed. The major rea-sons for the shortfall are associated withspurious acceleration from the platform thesensor is mounted on. Altitude uncertaintiescan also lead to errors in the reference gravityfield. In principle, such problems disappearif the gravity field gradient is measured ratherthan the gravity field itself. The use of twoindependant atom-interferometer based ac-celerometers, as described above, can providegravity gradient measurement by comparingacceleration measurements at two locationsseparated by a fixed distance. In this geome-try, the light pulses propagate along a direc-tion passing through two spatially separatedensembles of laser cooled atoms. Following athree-pulse interferometer sequence, thenumber of atoms making the transition atboth regions is recorded, and the gravitation-ally induced phase shifts are extracted. Thechange of the projection of along the direc-tion of the beams may then be derived fromthe difference of the two phase shifts and thedistance between the sources. The designsensitivity of ~ 10 9 2− −s Hz competes fa-


vorably with the existing instruments.

Photo of the atomic gradiometer built inYale University. One clearly sees 2 cold atomsources (Magneto-Optical Traps).

If the laser beams are now separated inspace (i.e. if the atomic velocity is perpen-dicular to the direction of the laser beams),the interferometer which is formed is in aMach-Zenhder configuration. In this case,the interferometer is sensitive to rotations, asin the Sagnac geometry14. For a Sagnac loopenclosing area A, a rotation ΩΩΩΩ produces ashift:

∆φπ

λ= ⋅

4

vΩΩΩΩ A

where λ is the particle wavelength and v itsvelocityiv.

iv The atomic wavelength, or de Broglie wavelength,has been introduced by Louis de Broglie in 1918. Itdenotes the quantum behavior of matter via its wave-particule duality, namely the fact that matter can be-have like waves (with the “matter” or “atomic” radia-tion having a frequency proportional to its velocity)and vice versa (light radiation gives rise to photons,pressure or sonic vibrations give rise to phonons).

Schematic of the atomic Sagnac interferome-ter at Yale [27]. The figure shows an atomicSagnac interferometer based on thermal at-oms. Two atomic beams are emerging fromtwo ovens on the left and right side andcounter propagate to each other. The atomicwaves are coherently split by the same laserbeams and independently detected by observ-ing the fluorescence. Due to highly symmetricset-up many disturbances due to the environ-ment could be ruled out. This Sagnac interfer-ometer is almost shot-noise limited.

Consequently, the inherent sensitivity of amatter-wave gyroscope exceeds that of aphoton-based system by a factor ofmc 2 1110hω ~ (m is the particle mass, ω thephoton frequency)v. Although optical gyro-scopes have higher particle fluxes and largerenclosed areas, atom-based systems still out-perform optical systems by several orders ofmagnitude.

The minimal rotation rate which can be re-solved is in the best case limited by the shot-noise. In that case the noise amplitude of theatomic beam scales with the square root ofthe averaged flux (i.e. the square root of thestandard deviation of the flux from the mean)and, thus, a high atomic flux is essential. For1010 atoms/s the white shot noise would bee.g. 105 atoms/s at a 1Hz frequency band-width.

∆Φ ∆Sagancatoms atm

hA

N

N,min = ⋅22π

v This ratio is simply the ratio of relativistic energiesmc2 for the atoms and hω for the light.


In the case of the caesium Sagnac interfer-

ometer described above the resolution Ω∂Φ∂

is

about 10-5 rad/s for an enclosed surface of

0.2 cm2. In the shot noise limit the sensitiv-

ity is 2⋅10-10 rad/s⋅√Hz for a signal ampli-

tude of 1010 atoms/s.

The individual signals at the output of the two counter-propagating atom interferometers (doted and broken lines)and the difference of both signals. Unlike phase shifts due toaccellerations, the Sagnac phases measured by the twocounter-propagating interferometer have opposite sign:

SI.AI ~ cos (ΦL + ΦSag + ΦAcc)SII.AI ~ cos (ΦL - ΦSag + ΦAcc)

Further increases of this impressive sensi-tivity can be achieved by changing the atomicflux and the enclosed area. While the atomicflux is already considerable, the enclosed sur-face is rather small compared to the overalllength of the apparatus of 2 m. Caesium isone of the best choices, because it has a highvapour pressure even at room temperaturesand a rather large atomic mass (133 u). Thus,atomic beams with a high atomic flux andslow velocities (a couple of 100 m/s) can berealised. In addition, caesium can be ma-nipulated easily with laser light generated bysolid state lasers (laser diodes). The atomicmass is however less important as one mightconclude from the preceding discussion.Nevertheless, the achievable surface in anatom interferometer depends also on the

atomic mass. The size of the surface is de-termined by the ratio of the atomic beamvelocity vL to the velocity vT of both atomicwaves relative to each other due to the beamsplitting process. The recoil velocity trans-ferred to the atom by the atom light interac-tion scales inversely with the atomic massfor a given photon momentum hk, while thevelocity of the atomic beam scales for a giventemperature T of the atomic ensemble withthe square root of the mass.

A Lm

k

m

k T

m

at

at

B

at

= ⋅ ∝

= ∝

2 1

2

vv

v

T

L

T

h

The highest potential for further improve-ments of an atomic Sagnac interferometerrelies therefore on the increase of the en-closed surface: Using cold atoms with alower velocity, one can achieve a ratio ofvT/vL close to unity. The improvements withHYPER will follow precisely this philoso-phy keeping the atomic flux at the same timeas high as possible. Presently first proto-types based on atomic fountains of lasercooled atoms are under construction in ajoint project of LPTF , IOTA and LHA inParis as well as at the IQO in Hanover.

Picture of the cold atom inertial base (gyro-scope and accelerometer) in fabrication inObservatoire de Paris (France)


LATITUDINAL MAPPING OFTHE GRAVITOMAGNETIC EF-

FECT WITH HYPER

The high sensitivity of atomic Sagnac inter-ferometer for rotation rates will enable HY-PER to measure even the latitudinal structureof the gravitomagnetic or Lense-Thirring ef-fect while the satellite orbits around theEarth. In terms of atom interferometry therotation ΩLT induced by the gravitomagneticeffect of the spinning Earth induces an addi-tional Sagnac phase ∆ΦSagnac:

LTat

Sagnac Ah

mΩ⋅=∆Φrr2

2π

where

( )5

2

2

)(3

r

rrr

c

GIrLT

ωωrrrrr −⋅=Ω

is the Lense & Thirring effect.

Entering the interferometer the matter waveis coherently split by the atom-light interac-tion acting as beam splitter mechanism andtravels along two spatially separated pathsuntil it is recombined. The Earth’s drag ΩLT

bends these two distinct trajectories fol-lowed by the matter wave, while the orienta-tion of the atomic beam splitter which servesas reference remains fixed at an inertial sys-tem, a far distant guide star pursued by ahigh-performance telescope.

Schematic of the measurement of the Lense-Thirring effect. The black lines visualise the vec-

tor field of the Earth’s drag ΩLT. The satellite’sorbit is marked red. The sensitive axes (blue) ofthe two ASUs are perpendicular to the pointing ofthe telescope. The direction of the Earth’s dragvaries over the course of the orbit showing thesame structure as the field of a magnetic dipole.Due to this formal similarity the Lense-Thirringeffect is also called gravitomagnetic effect. It hasto be pointed out that there is no connection toelectromagnetism.

In a Sun-synchronous, circular orbit at 700km altitude, HYPER will detect how the di-rection of the Earth’s drag varies over thecourse of the near-polar orbit as a function ofthe latitudinal position ϑ:

ΩΩ

x

y

∝

−

3

2 13

2

2

sin

cos,

ϑϑ

with

r r r rJ e ey x, arccos ( ) rϑ ≡ ⋅ the coordinate

system, spanned by ex and ey, defines theorbital plane.


TOrbit

0rad/s-14

The rotation ΩLT due to Earth’s gravitomagnetism assensed by the two orthogonal ASUs (red and green)in the orbit around the Earth. The satellite completesone orbit in the time TOrbit.Rotation rate at pole: +1.25_10-5 nrad/sRotation rate at equator:-2.5_ 10-5 nrad/s

The drag which the matter wave experi-ences is strongest over both Earth’s poles.There, the matter wave will start to followEarth’s rotation. At the Earth’s equator thedrag has the opposite sign and half the am-plitude as on the two poles. An intuitive ex-planation for the behaviour at the equatorrefers to the dependence of the Lense-Thirring effect on the relative distance: Thematter wave experiences a stronger drag trav-elling along the trajectory closer to the Earthas on trajectory turned away from the Earth.The rotation sensed by the atoms has theopposite sign of the Earth’s rotation as inthe case of two interconnected gearwheels.The sign of the Sagnac phase shift is there-fore reversed with respect to the shift overthe two poles.

Baseline configuration of the ASUs in HYPER : Theatomic Sagnac unit (ASU) is a device to measure rota-tions and accelerations with by interferometric means.For both kind of motions the device shows a highly di-rectional sensitivity. In order to measure all accelera-tional and rotational vector components three ASUswould have to be used, arranged in orthogonal orienta-tions. The objective of HYPER is to measure the Lense-Thirring effect, for this the rotations and accelerationsin only two directions need to be measured. Hence, forHYPER, the complete payload will consist of only twoorthogonal ASUs.

HYPER carries two atomic Sagnac interfer-ometers, each of them is sensitive for rota-tions around one particular direction. Thetwo units will measure the vector compo-nents of the gravitomagnetic rotation alongthe two axes perpendicular to the telescopepointing which is directed to a guide star.The drag variation written above describesthe situation for a telescope pointing in thedirection perpendicular to the orbital planeof the satellite. The orbit, however, changesits orientation over the coarse of a yearwhich has to be compensated by a rotationof the satellite to track continuously theguide star. Consequently the pointing of thetelescope is not always directed parallel tothe normal of the orbital plane.

As discussed before, the rotation rate willalternate between the two poles and theequator resulting in a periodically changingsignal with twice the frequency of the satel-lites revolution around the Earth. At the twopoles the rotation rate reaches the maximumvalue of -2.5⋅10-14 rad/s, while on the equa-tor the rotation rate changes its sign and be-comes 1.25⋅10-14 rad/s. The resolution of theatomic Sagnac units is about 10-12 rad/s for adrift time of about 3 s. Repeating this meas-urement all 3 seconds the ASU’s will reachafter 2 hours the level of 10-14 rad/s, in thecourse of one year the level of 10-16 rad/s, i.e.a hundredth of the expected effect.


CONCLUSION

We reviewed inertial sensors using atomicinterferometry techniques which are ex-pected to exhibit largely improved sensitivi-ties compared to those relying on optical in-terferometry. Like atomic clocks, they musttake benefit from the use of cold atoms. Pre-vious experiments measuring the gravita-tional acceleration of Earth and its gradient(in an atomic fountain) or rotations (in aSagnac interferometer) have been demon-strated to be very promising. Sensitivitiesbetter than 1 nrad.s-1.Hz-1/2 for rotationmeasurements and 10-9g.Hz-1/2 for gravitymeasurement have already been obtained.Gravity is the most fundamental impedimentto take full advantage of the superior poten-tial of cold atom physics. The sensitivity ofmatter-wave interferometers for rotationsand accelerations increases with the meas-urement time and can therefore be dramati-cally enhanced by reducing the atomic veloc-ity. Laser cooling can efficiently reduce thespeed of the atoms but cannot circumventthe acceleration due to gravity. Measures tocompensate for gravity with additionalforces perturb unavoidably the sensor. Onthe ground the 1-g environment sets clearlimitations for ultimate sensitivities.

HYPER-precision atom interferometry inspace opens up entirely new possibilities forresearch in fundamental physics with un-precedented precision. The cold atom inter-ferometers carried by HYPER will be ac-commodated in a drag-free spacecraft in alow-Earth, Sun-synchronous orbit. The pri-mary scientific objectives of the HYPERmission are to test General Relativity bymapping (latitudinal) structure (magnitudeand sign) of the Lense-Thirring effect, to de-termine the fine structure constant by meas-uring the ratio of Planck’s constant to the

atomic mass and to test the equivalence prin-ciple on individual atoms, a complement toother space tests of the equivalence principleusing massive bodies (STEP, MICRO-SCOPE)

1W. Chow et al. Rev. Mod. Phys. 57, 61 (1985).2J.F. Clauser, Physica B 151, 262 (1988)3R. Colella, A. Overhauser, and S. Werner, Phys.Rev. Lett. 34, 1472 (1975).4S.A. Werner, J.L. Staudenmann, And R. Colella,Phys. Rev. Lett. 42, 1103 (1979).5F. Riehle et al., Phys. Rev. Lett. 67, 177 (1991).6G. Stedman et al., Phys. Rev. A 51, 4944 (1995).7C.J. Bordé, Phys. Lett. A 140, 10 (1989).8M. Kasevich et al., Phys. Rev. Lett. 66, 2297(1991).9K. Moler, D.S. Weiss, M. Kasevich, and S. Chu,Phys. Rev. A 45, 342 (1992)10 See for example: L. Allen, J.H. Eberly: OpticalResonance and two level atoms, Wiley, New York(1975)11M. Kasevich and S. Chu, Appl. Phys. 67, 177(1991)12For a detailed calculation see B. Young, M.Kasevich and S. Chu, in Advances in Atomic andmolecular Physics, Atom Interferometry, edited by P.Berman (1996)13A. Peters, K. Chung and S. Chu, private comm.(1996).14M. Sagnac, Compt. Rend. Acad. Sci. 157, 708(1913).

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