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# Compact cold atom gravimeter for field applications

Authors:
• CNAM and The French Aeropace Lab ONERA

## Abstract and Figures

We present a cold atom gravimeter dedicated to field applications. Despite the compactness of our gravimeter, we obtain performances (sensitivity 42 microGal/Hz^0.5, accuracy 25 microGal) close to the bestgravimeters. 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.
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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 Charriere,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 =
108m/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-
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,
atiment 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/2π25.1MHz/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=PmC
2cos (keﬀ gα)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 αkeﬀ 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
ni
4|keﬀ|1
|keﬀ|T2arcsin 3
X
i=0
(1)niPni
2C!
α0
n+1 =α0
nG(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).
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Using light as a probe to detect a mechanical motion is one of the most successful experimental approaches in physics. The history of mechanical sensing based on the reflection, refraction and scattering of light dates back to the 16th century, where in the Cavendish experiment, the angle of rotation induced by the gravitational force is measured by the deflection of a light beam reflected from a mirror attached to the suspension. In modern science, mechano-optical transducers are such devices that could detect, measure and convert a force or displacement signal to an optical one, and are widely used for force detection. Especially, ultraweak force sensor with ultrahigh spatial resolution is highly demanded for detecting force anomaly in surface science, biomolecule imaging, and atomtronics. Here we show a novel scheme using a single trapped ion as a mechano-optical transduction. This method utilizes the force-induced micromotion, converting the micromotion to a time-resolved fluorescence signal, in which the ion's excess micromotion coupled to the Doppler shift of the scattered photons. We demonstrate the measurement sensitivity about 600 $\textrm{zN}/\sqrt{\textrm{Hz}}$ (1 $\textrm{zN} =10^{-21}$N). By alternating the detection laser beam in all three dimensions, the amplitude and the direction of a vector force can be precisely determined, constituting a 3D force sensor. This mechano-optical transducer provides high sensitivity with spatial resolution in single-atom level, enabling the applications in material industry and the search for possible exotic spin-dependent interactions that beyond the standard model.
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We have built an atom interferometer that can measure g, the local acceleration due to gravity, with a resolution of Δg/g = 2 × 10−8 after a single 1.3 s measurement cycle, 3 × 10−9 after 1 min and 1 × 10−10 after two days of integration time. The difference between our value for g and one obtained by a falling corner-cube optical interferometer is (7 ± 7) × 10−9 g. The atom interferometer uses velocity-selective stimulated Raman transitions and laser-cooled caesium atoms in an atomic fountain. We extend previous methods of analysing the interferometer to include the effects of a gravitational gradient. We also present detailed experimental and theoretical studies of potential systematic errors and noise sources.
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This publication is an introductory text describing the developing field of environmental geophysics. It contains case histories with examples from Australia, North America, Antarctica, Europe and China. Also included are chapters on detailed survey design, ground penetrating radar, electro-magnetic methods in environmental applications, electrical sub-surface imaging, spectral induced polarisation, and high resolution engineering reflection seismology. In this publication the greatest emphasis is given to the use of geophysics in civil engineering and in environmental and groundwater investigations.
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