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arXiv:1302.1518v1 [physics.ins-det] 6 Feb 2013

Compact cold atom gravimeter for ﬁeld applications

Yannick Bidel,∗Olivier Carraz,†Ren´ee Charri`ere,‡Malo Cadoret,§Nassim Zahzam, and Alexandre Bresson

ONERA, BP 80100, 91123 Palaiseau Cedex, France

We present a cold atom gravimeter dedicated to ﬁeld applications. Despite the compactness of

our gravimeter, we obtain performances (sensitivity 42 µGal/Hz1/2, accuracy 25 µGal) close to the

best gravimeters. We report gravity measurements in an elevator which led us to the determination

of the Earth’s gravity gradient with a precision of 4 E. These measurements in a non-laboratory

environment demonstrate that our technology of gravimeter is enough compact, reliable and robust

for ﬁeld applications. Finally, we report gravity measurements in a moving elevator which open the

way to absolute gravity measurements in an aircraft or a boat.

Cold atom interferometer is a promising technology to

obtain a highly sensitive and accurate absolute gravime-

ter. Laboratory instruments [1–3] have already reached

the performances of the best classical absolute gravime-

ters [4] with a sensitivity of ∼10 µGal/Hz1/2(1 µGal =

10−8m/s2) and an accuracy of 5 µGal. Moreover, com-

pared to classical absolute gravimeters, atom gravime-

ters can achieve higher repetition rate [5] and do not

have movable mechanical parts. These qualities make

cold atom gravimeters more adapted to onboard applica-

tions like gravity measurements in a boat or in a plane.

Cold atom gravimeters could thus be very useful in geo-

physics [6] or navigation [7]. In this context, cold atom

sensors start to be tested on mobile platforms. An atom

accelerometer has been operated in a 0 g plane [8]. An

atom gradiometer has also been tested in a slow mov-

ing truck [9]. In this article, we present a compact cold

atom gravimeter dedicated to ﬁeld applications. First,

we describe our apparatus and the technologies that we

use to have a compact and reliable instrument. Then,

we present the performances of the gravimeter in a labo-

ratory environment. Finally, we report gravity measure-

ments in a static and in a moving elevator.

The principle of our cold atom gravimeter is well de-

scribed in the literature [1] and we summarize in this

letter only the basic elements. In an atom gravimeter,

the test mass is a gas of cold atoms which is obtained by

laser cooling and trapping techniques [10]. This cloud of

cold atoms is released from the trap and its acceleration

is measured by an atom interferometry technique. We

use a Mach-Zehnder type atom interferometer consisting

in a sequence of three equally spaced Raman laser pulses

which drive stimulated Raman transitions between two

stable states of the atoms. In the end, the proportion of

atoms in the two stable states depends sinusoidally on

∗yannick.bidel@onera.fr

†Present address: European Space Agency - ESTEC Future Mis-

sions Division (EOP-SF) P.O. Box 299, 2200 AG Noordwijk, The

Netherlands

‡Present address: Laboratoire Hubert Curien, UMR CNRS 5516,

Bˆatiment F 18, Rue du Professeur Benoˆıt Lauras, 42000 Saint-

Etienne

§Present address: Laboratoire Commun de M´etrologie LNE-

CNAM, 61 rue du Landy, 93210 La Plaine Saint Denis, France

the phase of the interferometer ϕwhich is proportional

to the acceleration gof the atoms along the Raman laser

direction of propagation:

ϕ=keﬀ g T 2,(1)

where keﬀ ≃4π/λ is the eﬀective wave vector associated

to the Raman transition, λis the laser wavelength and

Tis the time between the Raman laser pulses.

The description of our gravimeter setup is the follow-

ing. The cold atoms are produced and fall in a vacuum

chamber made of glass connected to a titanium part to

which are connected a 3 l/s ion pump, getters and rubid-

ium dispensers. This vacuum chamber is inside a mag-

netic shield consisting of 4 layers of mu-metal. The falling

distance of the atoms is equal to 6 cm. The sensor head

containing the vacuum chamber, the magnetic shield, the

magnetic coils and the optics for shaping the laser beams

and collecting the ﬂuorescence has a height of 40 cm and

a diameter of 33 cm. The gravimeter is placed onto a pas-

sive vibration isolation table (Minus-K). The laser system

for addressing 87 Rb atoms is similar to the one described

in reference [11]. Basically, a distributed feedback (DFB)

laser diode at 1.5 µm is ampliﬁed in a 5 W erbium doped

ﬁber ampliﬁer (EDFA) and then frequency doubled in

a periodically poled lithium niobate (PPLN) crystal. A

power of 1 W at 780 nm is available. The frequency of the

laser is controlled thanks to a beatnote with a reference

laser locked on a Rubidium transition. The Raman laser

and the repumper are generated with a ﬁber phase mod-

ulator at 1.5 µm which generates side bands at 7 GHz.

All the electronics and the optics of the gravimeter ﬁt in

one 19” rack (0.6 x 0.7 x 1.9 m).

The experimental sequence of the gravimeter consists

in the following. First, 87 Rb atoms are loaded from a

background vapor in a 3D magneto-optical trap. The

atoms are then further cooled down in an optical mo-

lasses to a temperature of 1.8µK. Then, the atoms are

selected in the state F= 1, mF= 0 thanks to a mi-

crowave selection. After 10 ms of free fall, we apply the

atom interferometer sequence consisting in three Raman

laser pulses of duration 10, 20 and 10 µs. The Raman

laser pulses couple the state F= 1, mF= 0 to the state

F= 2, mF= 0. The time between the Raman pulses is

equal to T= 48 ms. During the interferometer sequence,

a vertical uniform magnetic ﬁeld of 28 mG is applied.

2

A radio frequency chirp of α/2π∼25.1MHz/s is also

applied to the Raman frequency in order to compensate

the time-dependant Doppler shift induced by gravity. Fi-

nally, the proportion of atoms in the state F=2 and F=1

is measured by collecting the ﬂuorescence of the atoms

illuminated with three pulses of a vertical retro-reﬂected

beam of durations of 2, 0.1, and 2 ms. The ﬁrst and

the last pulses resonant with the F= 2 →F′= 3 transi-

tion give a ﬂuorescence signal proportional to the number

of atoms in the state F=2 and the middle pulse resonant

with F= 1 →F′= 2 transition transfers the atoms from

the state F=1 to the state F=2. A rms noise of 0.2% on

the measured proportion of atoms is obtained with this

detection scheme limited by the frequency noise of the

laser. The repetition rate of the experimental sequence

is equal to 4 Hz. The measurement of the proportion of

atoms Pin the state F= 2 versus the radio frequency

chirp αleads to interference fringes given by the formula:

P=Pm−C

2cos (keﬀ g−α)T2,(2)

where Pmis the mean proportion of atoms in the state

F= 2, Cis the contrast which is equal in our case to

C= 0.36.

The protocol of the gravity measurements is the fol-

lowing. The gravity is measured by acquiring Pfrom

each side of the central fringe i.e. for α≃keﬀ g±π/2T2.

The sign of αand thus the sign of keﬀ is also changed

every two drops in order to eliminate systematic eﬀects

which change of sign with keﬀ. In order to follow slow

variations of gravity, the central value of αis also numer-

ically locked to the central fringe. For each atom drop,

the gravity is determined with the last 4 measurements

using the following relations :

αn=sα0

n+ (−1)nπ

2T2

gn=

3

X

i=0

α0

n−i

4|keﬀ|−1

|keﬀ|T2arcsin 3

X

i=0

(−1)n−iPn−i

2C!

α0

n+1 =α0

n−G(α0

n− |keﬀ|gn) (3)

where αnis the radio frequency chirp applied at the n-th

drop of the atoms, α0

nis the value of the central fringe

used at the n-th drop of the atoms, s=±1 is the sign of

radiofrequency chirp which changes every two drops, Pn

is the proportion of atoms in the state F=2 measured at

the n-th drop, gnis the gravity measurement at the n-th

drop and Gis the gain of the lock of the central value of

α.

The gravimeter was tested in our laboratory by ac-

quiring continuously gravity during ﬁve days. The mea-

surements averaged over 15 minutes are shown on Fig.

1. A good agreement is obtained with our tide model

[12] with a rms diﬀerence of 7 µGal. The Allan stan-

dard deviation on the gravity measurements corrected

for the tides is shown on Fig. 2. A short term sensitiv-

ity of 65 µGal/Hz1/2is obtained during the ﬁve days of

gravity measurements. During the night, when the level

of vibration is lower, one gets a better sensitivity of 42

µGal/Hz1/2.

24 48 72 96 120 144

-20

0

20

40

60

80

100

120

140

Time (hours)

-100

-50

0

50

100

Residual (mGal)∆g (mGal)

FIG. 1. Continuous gravity measurements from 27 May to

2 June 2009. The data are averaged over 15 minutes (3600

atom drops). Top: gravity measurements uncorrected from

tides with the tide model in red solid line. Bottom: residual

between the gravity measurements and the tide model.

110 100 1000 10000 100000

1

10

100

τ (s)

s(τ) (mGal)

65 mGal/Hz1/2

42 mGal/Hz1/2

FIG. 2. Allan standard deviation of the gravity measure-

ments. The top red line corresponds to the Allan standard

deviation of data taken during ﬁve days. The bottom blue

line corresponds to data taken during one night when the vi-

bration level is lower.

This diﬀerence of sensitivity between night and day

3

indicates that the sensitivity of the gravimeter is limited

by the vibrations. This is conﬁrmed by our estimation

of the other sources of noise. The detection noise limits

the sensitivity at 15 µGal/Hz1/2. The phase noise of our

microwave source limits the sensitivity at 2 µGal/Hz1/2.

The frequency noise of the Raman laser [13] limits the

sensitivity at ∼1µGal/Hz1/2.

The main systematic eﬀects which limit the accuracy

of the gravimeter were evaluated and are listed in Table

I. Our method of generating the Raman laser by mod-

ulation induces a systematic error on the gravity mea-

surement. This eﬀect was studied in detail in reference

[14]. In our case, one obtains an uncertainty of 8 µGal.

The systematic eﬀects caused by the inhomogeneity of

the magnetic ﬁeld [1] and the ﬁrst order light shift [1]

change of sign with keﬀ. These eﬀects cancel therefore

with our protocol of measurement consisting in alternat-

ing the sign of keﬀ . The residue of these eﬀects is es-

timated to be below 1 µGal and is negligible compared

to the other systematic eﬀects. The second order light

shift [15, 16] has been calibrated by measuring gravity

versus the power of the Raman laser. Our uncertainty

on the calibration is equal to 2 µGal. The Coriolis ef-

fect gives an error equal to 2 vtΩ where Ω is the rotation

rate of the earth projected in the horizontal plane and

vtis the transverse velocity of the atoms perpendicular

to the Earth rotation vector. The uncertainty on the

transverse velocity of the atoms detected is estimated

in our case at 2 mm/s leading to an uncertainty on g

equal to 19 µGal. The wavefront curvature of the Ra-

man laser caused by imperfect optics is causing an error

equal to σ2

v/R [3] where σvis the rms width of the ve-

locity distribution of the atoms and R is the radius of

curvature of the wavefront. We estimate that our optics

induce a wavefront curvature with a radius |R|around

1.4 km leading to an uncertainty of 12 µGal. The Ra-

man laser is aligned vertically by maximizing the value

of gravity. This procedure leads to an uncertainty of 2

µGal. The uncertainty on our laser wavelength is equal

to 2 MHz giving an uncertainty of 5 µGal. The quadratic

sum of all these contributions gives a total uncertainty

of 25 µGal. This accuracy estimation of our gravime-

ter has been conﬁrmed by the comparison with a rela-

tive gravimeter (Scintrex CG-5) calibrated with an ab-

solute gravimeter. The relative gravimeter gives a mea-

surement of gravity equal to 980883499 ±6µGal. Our

atom gravimeter gives 980883165 ±25 µGal. The diﬀer-

ence of height between the two gravimeters is equal to

1.09 ±0.03 m leading to a correction due to vertical grav-

ity gradient of 347±10 µGal. Finally, one obtains a diﬀer-

ence between the two measurements equal to 13±28 µGal

in agreement with the error bar.

The gravimeter was tested in an elevator located in a

14 levels building. A gravity measurement was done at

each level with an acquisition time of 250 s (1000 drops).

The distance between the levels was measured with a

laser distance measurer pointing the top of the elevator

cage. At each level, the verticality of the gravimeter was

Eﬀect Bias Uncertainty

(µGal) (µGal)

Raman laser generated by modulation -18 8

Light shift second order 43 2

Coriolis eﬀect 0 19

Wavefront curvature 0 12

Verticality 0 2

Laser wavelength 0 5

Total 25 25

TABLE I. Main systematic eﬀects on the gravity measure-

ments.

-10 010 20 30 40

980894

980896

980898

980900

980902

980904

980906

980908

980910

Gravity acceleration (mGal)

Height (m)

-10 010 20 30 40

-0.4

-0.3

-0.2

-0.1

0.0

fit residu (mGal)

Height (m)

FIG. 3. Gravity measurements versus height in an elevator.

The points are the experimental measurements. The lines are

a linear ﬁt of the measurements overground and underground.

The inset in the up right corner is the diﬀerence between the

measurements and the overground linear ﬁt and shows clearly

the two slopes which correspond to the gravity gradient over-

ground and underground.

set thanks to an inclinometer. Between each gravity mea-

surement at a given level, a gravity measurement at the

level -2 was done in order to check for the repeatability of

gravity measurements. The gravity measurements at the

level -2 have a standard deviation of 11 µGal. The grav-

ity measurements at each level are plotted on the Fig. 3.

One can see that the gravity gradient is diﬀerent above

the ﬂoor and under the ﬂoor. Overground, a linear ﬁt

of the data gives a gravity gradient equal to 3086 ±4 E.

This value agrees with the mean gravity gradient on the

Earth (free-air anomaly) given in the literature [17]. Un-

derground, a linear ﬁt of the data gives a gravity gradient

equal to 2626 ±16 E. The lower underground gravity gra-

dient is due to the mass of the soil above the measurement

point which gives a correction equal to 4πρ G where ρis

the density of the soil.

In order to demonstrate the possibility to measure

gravity in a boat or a plane with an atom gravimeter,

we measured gravity while the elevator was moving. To

perform this measurement, our vibration isolation table

which can not work while the elevator is moving was

4

010 20 30 40 50 60

976000

978000

980000

982000

984000

986000

Measurement of the atom gravimeter (mGal)

Time (s)

Start

height=38.8m

level = 11

Stop

height= -7 m

level = -2

1/2 fringe

= π/keffT2

<g> = 980 927 ± 68 mGal

FIG. 4. Gravity measurements in a moving elevator. The red

line corresponds to the averaged value of the gravity measured

during the stabilized part of the descent of the elevator.

blocked. Thus, the time of the interferometer Twas re-

duced from 48 ms to 1 ms in order to have variations of

acceleration smaller than one fringe. The measurements

of the gravimeter acquired when the elevator was mov-

ing from the level 11 to the level -2 are shown on Fig.

4. By assuming that the mean acceleration of the ele-

vator is null during the stabilized part of the descent of

the elevator (10 s - 43 s), the measurements in dynamic

give a measurement of gr avity equal to 980927 ±68 mGal

which agrees with the static measurements. The statis-

tical uncertainty of 68 mGal comes from the acceleration

variations of the elevator and the vibrations.

In conclusion, we demonstrated the possibility to

perform quantitative gravity measurements in a non-

laboratory environment with an atom gravimeter. This

demonstration was possible with the development of a

compact and robust atom gravimeter. Despite the fact

that we chose a small falling distance in order to have a

compact apparatus, we obtain performances (sensitivity

42 µGal/Hz1/2and accuracy 25 µGal) close to the best

gravimeters. Quantitative gravity measurements with a

repeatability of 11 µGal were performed in an elevator

wherein the apparatus is subject to shocks, vibrations

and ﬂuctuations of temperature. These measurements

led us to the determination of the gravity gradient with

a precision of 4 E. We also demonstrated the ability of an

atom gravimeter to be used in a mobile platform by mea-

suring gravity in a moving elevator. Finally, we point out

that technological developments concerning the vibration

isolation system or the association with a classical ac-

celerometer [8, 18] have still to be made in order to have

quantitative gravity measurements in mobile platforms.

We thank the SHOM for their gravity measurements in

our laboratory. This work was supported by the French

Defence Agency (DGA).

[1] A. Peters, K.Y. Chung and S. Chu, Metrologia 38, 25-61

(2001).

[2] H. M¨uller, S. W. Chiow, S. Herrmann, S. Chu and K. Y.

Chung, Phys. Rev Lett. 100, 031101 (2008).

[3] A. Louchet-Chauvet, T. Farah, Q. Bodart, A. Clairon,

A. Landragin, S. Merlet and F. Pereira Dos Santos, New

Journal of Physics 13, 065025 (2011).

[4] T M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt and

F. Klopping, Metrologia 32, 159-180 (1995).

[5] H. J. McGuinness, A. V. Rakholia, and G. W. Bieder-

mann, Appl. Phys. Lett. 100, 011106 (2012).

[6] J. M. Reynolds, An Introduction to Applied and Environ-

mental Geophysics (Wiley-Blackwell, 2011).

[7] C. Jeleki, Navigation 52, 1-14 (2005).

[8] R. Geiger, V. M´enoret, G. Stern, N. Zahzam , P. Cheinet ,

B. Battelier, A. Villing , F. Moron, M. Lours, Y. Bidel, A.

Bresson, A. Landragin and P. Bouyer, Nature Commun.

2, 474 (2011).

[9] X. Wu, Gravity Gradient Survey with a Mobile

Atom Interferometer, Ph.D. thesis, Stanford University,

http://atom.stanford.edu/WuThesis.pdf (2009).

[10] H.J. Metcalf, P. van der Straten, Laser Cooling and Trap-

ping (Springer, New York, 1999).

[11] O. Carraz, F. Lienhart, R. Charri`ere, M. Cadoret, N.

Zahzam, Y. Bidel and A. Bresson, Appl. Phys. B 97,

405-411 (2009).

[12] Y. Tamura, Bulletin d’Information des Mar´ees Terrestres

99, 68136855 (1987).

[13] J. Le Gou¨et, P. Cheinet, J. Kimb, D. Holleville, A. Cla-

iron, A. Landragin, and F. Pereira Dos Santos, Eur. Phys.

J. D 44, 419425 (2007).

[14] O. Carraz, R. Charri`ere, M. Cadoret, N. Zahzam, Y.

Bidel, and A. Bresson, Phys. Rev. A 86, 033605 (2012).

[15] P. Clad´e, E. de Mirandes, M. Cadoret, S. Guellati-

Kh´elifa, C. Schwob, F. Nez, L. Julien, and F. Biraben,

Phys. Rev. A 74, 052109 (2006).

[16] A. Gauguet, T. E. Mehlst¨aubler, T. L´ev`eque, J. Le

Gou¨et, W. Chaibi, B. Canuel, A. Clairon, F. Pereira

Dos Santos, and A. Landragin, Phys. Rev. A 78, 043615

(2008).

[17] W. Torge, Gravimetry, (de Gruyter, Berlin; New York,

1989).

[18] S. Merlet, J. Le Gou¨et, Q. Bodart, A. Clairon, A. Landra-

gin, F. Pereira Dos Santos and P. Rouchon, Metrologia

46, 8794 (2009).