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Hybridizing matter-wave and classical accelerometers

Hybridizing matter-wave and classical accelerometersJ. Lautier,1 L. Volodimer,1 T. Hardin,1 S.Merlet,1 M. Lours,1 F. Pereira Dos Santos,1 and A. Landragin1, a)

LNE-SYRTE, Observatoire de Paris, CNRS, UPMC, 61 avenue de lObservatoire, 75014 Paris,

France

(Dated: 8 October 2014)

We demonstrate a hybrid accelerometer that benefits from the advantages of both conventional and atomicsensors in terms of bandwidth (DC to 430 Hz) and long term stability. First, the use of a real time correction

of the atom interferometer phase by the signal from the classical accelerometer enables to run it at bestperformances without any isolation platform. Second, a servo-lock of the DC component of the conventionalsensor output signal by the atomic one realizes a hybrid sensor. This method paves the way for applicationsin geophysics and in inertial navigation as it overcomes the main limitation of atomic accelerometers, namelythe dead times between consecutive measurements.

PACS numbers: Valid PACS appear hereKeywords: Atom interferometry, Inertial navigation, Gravimetry

Atom interferometers have demonstrated to be bothvery sensitive and accurate inertial sensors, which openswide area of applications in geophysics and inertial guid-ance. These possibilities are already exploited in absolute

cold atom gravimetry1, where record sensitivities havebeen demonstrated2,3. In the mean time, developmentshave been conducted in order to simplify and reduce thesize of such devices to be compliant with these applica-tions46. One of the main remaining difficulties comesfrom the intrinsic low frequency sampling, in the orderof 1 Hz, of the vibration noise in cold atom devices. Thisis associated to their sequential operation leading to deadtimes between consecutive measurements and aliasing ef-fect of the high frequency vibration noise7. Differentmethods have been developed to overcome these difficul-ties. One consists in using an active or a passive isolationplatform1,2,8,9, in which the cut-off frequency is below the

cycling frequency. However, these set-ups are bulky, andthus ill-suited for operation in noisy or mobile environ-ment because of their low frequency resonances. A sec-ond method consists in increasing the cycling frequency(330 Hz has been demonstrated10) but to the price of adrastic reduction in the sensitivity, which scales quadrat-ically with the interrogation time. A last method is basedon the post-correlations between simultaneous measure-ments from classical and atom accelerometers8. It en-ables reaching the state of the art performance in abso-lute gravimetry11, and operating an atom interferometerin a noisy environment such as a plane12. However, inthe latter, this method leads to a reduction of the effec-tive bandwidth, and does not solve the dead time issue.Hybridizing classical and matter-wave inertial sensors en-ables to overcome these limitations.In this paper, we demonstrate how such a combinationbetween a force balanced accelerometer and an atomicgravimeter enables operating both instruments at maxi-mum performances. The combined signal associates the

a)Electronic mail: arnaud.landragin@obspm.fr

large bandwidth of the mechanical sensor and the longterm stability and the accuracy of the atomic sensor. Weexploit the correlation between the acceleration measure-ments in order to real-time compensate the atomic inter-

ferometer phase fluctuations due to vibrations, and tooperate this instrument at its maximum sensitivity. Fur-thermore, we take the full advantage of these correlationsto correct for the drift of the mechanical accelerometer.In a reciprocal fashion, the specific advantages of one sen-sor are used to overtake the characteristic limitations ofthe other. This results in a hybrid sensor, which combineslarge bandwidth (DC to 430 Hz), and the bias stabilityand the accuracy of the atomic interferometer.We work with a Mach-Zehnder-like/2/2 gravime-ter relying on stimulated Raman transitions13. The sen-sor head of our instrument is described in8. The lasersystem and a typical measurement sequence are pre-

sented in14

. A vertical laser beam and its retro-reflectionon a mirror form the two counter-propagating Ramanbeams. These are used to coherently split, deflect, andrecombine a cloud of cold 87Rb atoms in free-fall in thegravity field. With this geometry, the atomic phase-shift at the output of the interferometer is given by15:

=122+3=keffgT2 where i is the phase dif-ference between the two Raman lasers, at the positionof the center of mass of the wavepacket, at the time of

the i-th Raman pulse. keffis the effective wave-vector,gthe acceleration of the Earth gravity, and T the free-evolution time between two consecutive pulses. Suchatomic accelerometers are thus sensitive to the relative

acceleration between the free-falling atoms and the retro-reflecting mirror, that sets the phase reference for the Ra-man lasers. Residual vibrations of the latter thus inducea phase noise vib. Besides, the free-fall of the atomsinduces a Doppler shift which requires to sweep phase-continuously the frequency difference between the twoRaman lasers to drive the two-photon transitions overthe interrogation time, according to (t)=(0)+t.This adds an additional contributionT2 to the atomicphase shift .

http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2http://arxiv.org/abs/1410.0050v2mailto:arnaud.landragin@obspm.frmailto:arnaud.landragin@obspm.frhttp://arxiv.org/abs/1410.0050v2

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the cycling time is Tc = 500 ms. The red dots representthe calculated phase shifts vib of standard deviationvib = 3.3 rad that the ground vibrations should have in-duced on the atomic phase without any correction. Theblack dots stand for the residual atomic phase fluctua-tions with the RTC (res = 57 mrad). This residue is en-larged on Fig.2(b). The contribution to the interferome-ter phase of the discarded end of the signal was calculated

to remain negligible, of standard deviation on the orderof 2 mrad. Nevertheless, the interferometer phase can inprinciple be corrected from this contribution a posterioriif necessary. Fig.3shows the Allan standard deviation ofthe measurement of gdelivered by our gravimeter withthe RTC technique. The mean atomic phase is modu-lated through the RTC module to measure alternativelyon the right and on the left of the central fringe so as toreject detection fluctuations11. We associate to our mea-surement a short-term sensitivity of 6.5 107 m.s2 atone second measurement time. The sensitivity improvesup to 300 s to reach a level of 3108 m.s2. Comparedto the level of ground vibration noise, we find a rejectionefficiency of about 60. This performance is a factor of 3above the limit arising from detection noise.

FIG. 3. (color online) Allan standard deviation of the accel-eration sensitivity of the gravimeter with the real-time com-pensation technique (RTC) without isolation plaform. The

1/2 slope represents the averaging of a white noise.

To take full benefit of the correlation, we perform acomplete hybridation of the two sensors by tying theDC component of the accelerometer signal to the grav-ity changes measured by the atom gravimeter. Indeed,the DC component for most conventional accelerometerssuffers from drift and temperature dependence which de-grades the long term stability of the acceleration mea-surement. We use the measurement protocol describedabove to detect fluctuations of the mean atomic phasecaused by drifts of the conventional sensor. From thesuccessive values ofP, we derive voltage corrections thatwe add to the signal of the auxiliary sensor output sig-

FIG. 4. Allan standard deviation of acceleration signals: fromthe conventional accelerometer alone (blue line) and from thehybrid accelerometer without (red line) and with correctionfrom Earths tides (black line).

nal. This realizes an integrator loop that servo locks itsDC component onto a value that corresponds to the mea-surement made with the atom interferometer. This hy-bridizes the matter-wave and classical sensors, supplyinga continuous measurement of the acceleration being reg-ularly calibrated by the absolute acceleration providedby the atom interferometer.

Fig.4shows the Allan standard deviation of the hybridacceleration signal, acquired by a separate acquisitionunit. For this demonstration, the sensor is placed on apassive isolation platform. We compare the free-running

evolution of the accelerometer signal in an open-loop con-figuration (in blue), with the hybrid signal (in red), even-tually corrected from the Earths tides (in black). Thetime constant of the integrator loop has been chosen tobe about 10 s, where the sensitivities of both sensorsare similar under our specific experimental conditions.For short integration time, the stability of the acceler-ation measurement improves in 1 as we average thehigh frequency vibrations without dead time. At longintegration time, the stability improves in 1/2 with asensitivity corresponding to the one of the atomic sensorwhen corrected from vibrations. The small bump in thestability of the hybrid sensor at 10 s is due to the servo-lock time constant. The resulting hybrid sensor features

strong analogies with atomic clocks. A macroscopic de-vice based on a classical technology is used to probe anabsolute atomic reference. Then, the absolute measure-ment is used to servo the output signal of the local sensor,providing a continuous accurate and stable signal. Theshort-term stability of the hybrid sensor is determined bythe self-noise of the conventional sensor. The long-termstability is set by the measurement of the atomic meanphase provided by the interferometer.

Even if we use conventional analog electronics sub-

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ject to temperature fluctuations, the servo-lock on thegravimeter response makes the hybrid sensor signal off-set follow the temporal variations ofgdue to luni-solartides. Fig.5 shows the monitoring of the mean hybridacceleration over 6 days. We demonstrate a good agree-ment of the hybrid signal with the results given by thetidal model.

FIG. 5. (color online) Long-term variations of the hybridacceleration signal. A grey point represents 1-min averagingof the hybrid acceleration signal. The red curve is a 50-pointadjacent averaging of the grey data and the thin black line isthe tidal model.

In conclusion, we have demonstrated the interest ofhybridizing a conventional and an atomic sensor. By us-ing the signal of a classical accelerometer to compensatein real time the phase shift of the atom interferometer,

we demonstrate that the atomic accelerometer runs atbest performances without any isolation platform. In asecond step, the signal of the atomic sensor is used toservo-lock the output of the conventional sensor in orderto suppress its drifts and to follow gravity changes, whichenables to exploit a classical accelerometer in a fluctuat-ing thermal environment. This hybrid sensor combinesthe advantages of both sensors, providing a continuousand broadband (DC to 430 Hz) signal that benefits fromthe long term stability and accuracy of the atomic sensor.

These features, which make it appealing for geoscience(sismology and gravimetry), are especially of major rele-vance in inertial navigation. Indeed, the high frequencyvariation of the acceleration is the signal of interest forthe calculation of the trajectory of the carrier. The lossof information from dead times is then a major limita-tion, which we overcome with our method. We deter-mine that the residual bias corresponding to the accu-racy of our atomic gravimeter is then the most signifi-cant contribution to the uncertainty in position. A biasof 5 108 m.s2 leads to an error of 5 m after 4h ofnavigation. After a calibration stage to remove the ac-celeration offset, our hybrid accelerometer would allow toreach an error of less than 1 m after 4 h of navigation.

In addition, these methods can be extended to largerange of acceleration by adjusting in real time not onlythe phase but also the difference of frequencies of theRaman lasers for a compensation of the doppler effect.Moreover, following the work presented in16, the servo-lock of the scaling factor of the conventional sensor canalso be realized. Finally, the method developed here isgeneral and can be extended to other type of sensors such

as gyroscopes19,20

or gradiometers21,22

.

ACKNOWLEDGMENTS

The authors would like to thank the Institut Francilienpour la Recherche sur les Atomes Froids (IFRAF), theAgence Nationale pour la Recherche (ANR contract ANR- 09 - BLAN - 0026 - 01) in the frame of the MiniAtom col-laboration, GRAM and CNES for funding this work. J.L.would like to thank UPMC and College des Ingenieurs,in the frame of the program Science and Managementfor supporting his work.

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