Continuous Cold-atom Inertial Sensor with 1 nrad.s −1 Rotation Stability
I. Dutta, D. Savoie, B. Fang, B. Venon, C.L. Garrido Alzar, R. Geiger, A. Landragin
CContinuous Cold-atom Inertial Sensor with nrad.s − Rotation Stability
I. Dutta, D. Savoie, B. Fang, B. Venon, C.L. Garrido Alzar, R. Geiger, ∗ and A. Landragin † LNE-SYRTE, Observatoire de Paris, PSL Research University,CNRS, Sorbonne Universit´es, UPMC Univ. Paris 06,61 avenue de l’Observatoire, 75014 Paris, France (Dated: August 31, 2018)We report the operation of a cold-atom inertial sensor which continuously captures the rotationsignal. Using a joint interrogation scheme, where we simultaneously prepare a cold-atom source andoperate an atom interferometer (AI) enables us to eliminate the dead times. We show that suchcontinuous operation improves the short-term sensitivity of AIs, and demonstrate a rotation sensi-tivity of 100 nrad.s − / √ Hz in a cold-atom gyroscope of 11 cm Sagnac area. We also demonstrate arotation stability of 1 nrad.s − at 10 s of integration time, which establishes the record for atomicgyroscopes. The continuous operation of cold-atom inertial sensors will enable to benefit from thefull sensitivity potential of large area AIs, determined by the quantum noise limit. PACS numbers: 03.75.Dg, 37.25.+k
Over the past two decades, important progress in cold-atom physics has established atom interferometry as aunique tool for precision measurements of time and fre-quency and of gravito-inertial effects. Atom interferom-etry addresses various applications ranging from preci-sion measurements of fundamental constants [1, 2], toinertial navigation [3–5], to geophysics and geodesy [6–9] and has been proposed for gravitational wave detec-tion [10, 11]. New techniques are being developed to im-prove the potential of atom interferometers (AIs), suchas large momentum transfer beam splitters [12, 13], longinterrogation times in tall vacuum chambers [14], mi-crogravity platforms [4, 15], or operation of AIs withultracold atomic sources [16]. Advanced detection andatom preparation methods have moreover been proposedand demonstrated to go beyond the quantum projectionnoise in AIs [17, 18]. However, benefiting from these newtechniques to fully exploit the potential of AIs requiresto handle the problem of dead times between successivemeasurements occurring in cold-atom sensors.Dead times in AIs originate from the preparation of theatomic source prior to the entrance in the interferometriczone and to the detection of the atoms at the AI output.The inertial information during these preparation and de-tection periods is lost. Dead times, for example, stronglymitigate the possibility to realize inertial measurementunits (IMUs) based on AIs [19]. In addition, the sequen-tial operation of AIs leads to inertial noise aliasing, whichdegrades the AI sensitivity in the presence of dead times.This reduces the performance of AIs of potentially highsensitivities [14]. High data rate interferometers usingrecapture methods have been reported to partially over-come the problem of dead times but at the cost of strongreduction of sensitivity [20]. The inertial noise aliasing inAIs can be alleviated by using auxiliary sensors of largebandwidth [21], but this limits the sensitivity during thedead time period to that of the auxiliary sensor. Con-tinuous operation (i.e. without dead times) is therefore a key point to benefit from the full potential of atominterferometry.In this letter, we report the first continuous operationof a cold-atom inertial sensor. We demonstrate such op-eration in an AI gyroscope which features a Sagnac areaof 11 cm , representing a 27-fold increase with respect toprevious experiments [22]. The continuous operation im-proves the short-term sensitivity of the gyroscope, whichwe illustrate by demonstrating a rotation sensitivity of100 nrad.s − / √ Hz. Moreover, we show that the contin-uous operation does not affect the long-term sensitivitypotential of AIs and report a stability of 1 nrad.s − after10 s of integration time.The principle of the experiment is sketched in Fig. 1.We realize a light-pulse AI using two counter-propagatingRaman beams which couple the | F = 3 , m F = 0 (cid:105) and | F = 4 , m F = 0 (cid:105) clock states of Cesium atoms. Accord-ing to the Sagnac effect [23, 24], the rotation sensitivityof the AI is proportional to the area enclosed by the 2arms. Our AI gyroscope is based on a fountain configura-tion with four Raman pulses to create a folded geometrythanks to gravity [3]. Similar folded geometries can beobtained in trapped atom interferometers [25]. The fourpulse fountain configuration allows us to increase the in-terferometric area up to 11 cm and leads to zero DCsensitivity to acceleration. The rotation induced phaseshift Φ Ω is given byΦ Ω = 12 (cid:126)k eff · (cid:16) (cid:126)g × (cid:126) Ω (cid:17) T , (1)where (cid:126)k eff is the two-photon momentum transfer, (cid:126)g is theacceleration due to gravity, (cid:126) Ω is the rotation rate and T is half the interferometric time. Following atom jugglingmethods initially introduced to measure collisional shiftsin fountain clocks [26], we implement a sequence of jointinterrogation of successive atom clouds as described in[27], see Fig.1(a). Experimentally, the joint operationis obtained by using the same π/ a r X i v : . [ phy s i c s . a t o m - ph ] A p r clouds entering and exiting the AI zone. Thus, the ex-periment cycle time T c equals the AI interrogation time2 T . Accelerometers (b) x time (a) time z g FIG. 1. (Color online) (a) Schematic and operation principleof the continuous cold-atom gyroscope. Continuous measure-ment is performed with a joint interrogation sequence wherethe bottom π/ T toavoid the recombination of parasitic interferometers resultingfrom the imperfect π pulses. The gyroscope measures rota-tion rate along the y direction, i.e. perpendicular to the AIarea. Cesium atoms loaded from a 2D Magneto-Optical Trap(MOT) are trapped and cooled in a 3D-MOT during200 ms. We launch 2 × atoms vertically at a speed of5 . − using moving molasses with a (3D) cloud tem-perature of 1 . µ K. Light pulse interferometry is realizedusing two phase-locked Raman lasers which couple theCesium clock states characterized by an hyperfine split-ting corresponding to 9 .
192 GHz. The Raman lasers aresent to the atoms through two optical windows separatedby 58 cm, yielding an interrogation time 2 T = 800 ms.We use Raman beams with 1 /e diameter equal to 40 mmand 100 mW of total power. After the MOT and priorto the interrogation, 2 × atoms are prepared in the | F = 4 , m F = 0 (cid:105) state. The AI output signal is deter- mined by the probability of transition from the F = 4to the F = 3 state, which is experimentally realized us-ing fluorescence detection of the two levels after the AIlight-pulse sequence.We lift the degeneracy between the two ± ¯ hk eff transi-tions [28] by tilting the Raman beams by an angle of incli-nation θ = 3 . o (Fig. 1(a)). Large area AIs require pre-cise parallelism of the interrogation beams in order for thetwo paths to recombine within the coherence length of thecold atoms at the interferometer output [29]. We imple-ment a generic protocol to meet the required beam align-ment of the Raman beams in the vertical ( z ) and horizon-tal ( y ) directions. For the z direction, we first measurethe two beam angles using Doppler spectroscopy, whichdetermines the parallelism with a precision of 20 µ rad.We then operate two 3-pulse AI accelerometers at thebottom and top Raman beam positions with an interro-gation time of 60 ms to measure the projection of gravityon the beam directions, which allows us to reach a preci-sion of 5 µ rad. To adjust the horizontal ( y ) parallelism,we optimize the contrast of a Ramsey-Bord´e AI using thebottom and top Raman beams as described in Ref. [30],and reach a parallelism precision of 200 µ rad. With thisprotocol, we achieve a contrast of 4 % in the continuousAI at 2 T = 800 ms, mainly limited by inhomogeneities ofthe Rabi frequency over the atom cloud extension. Forthis value of contrast, the AI phase noise due to detectionnoise amounts to 400 mrad / √ Hz and was estimated withthe method described in [4]. The detection noise level islimited by stray light in the fluorescence detection sys-tem and was measured independently without atoms inthe interferometer. The limitations associated with jointoperation (mainly light shifts and contrast reduction dueto scattered light by the MOT) have been described in[27], together with mitigation strategies.The AI output signal P is determined by the Earthrotation rate, the vibration noise and the non-inertialnoise. We write it as P = P + A cos (Φ Ω + δ Φ vib + δ Φ ) , (2)where P is the offset of the interferometric signal, A is the fringe amplitude, Φ Ω is the rotation phase, δ Φ vib the vibration phase noise and δ Φ the non-inertial phasenoise (e.g. Raman laser phase, light shift). Increasingthe AI area necessarily comes at the expense of moresensitivity to the vibration noise, δ Φ vib , which has to bereduced to extract the rotation signal, Φ Ω . The exper-iment is mounted on a vibration isolation platform toreduce the effect of vibration noise above ∼ . δ Φ calc using thefour-pulse AI transfer function. Fig. 2 shows the corre-lation between the AI output signal, P , and the phase δ Φ calc calculated from the weighted average of the twoaccelerometers. As the correlation function is non-linear,we use the method described in [31] to extract the rota-tion rate sensitivity of the interferometer. We divide thetotal data set in packets of 20 data points and fit a si-nusoid to extract the offset phase and hence the rotationrate Ω. This procedure yields a short-term sensitivityof 450 mrad / √ Hz, equivalent to rejecting the vibrationnoise by a factor 5. The rejection efficiency is limitedby the detection noise level which currently bounds theshort-term sensitivity of the AI.
Calculated Vibration Phase, / ) calc (rad) -2 : - : : : T r an s i t i on P r obab ili t y FIG. 2. Correlation between the AI signal and the vibrationphase calculated from the signal of auxiliary accelerometers.The AI interrogation time is 2 T = 800 ms. Figure 3(a) shows an uninterrupted operation of thecontinuous cold-atom gyroscope over more than 20000 s.The Allan deviation of the rotation rate sensitivity isshown in Fig. 3(b). We achieve a short-term sensitivityof 100 nrad.s − / √ Hz, which establishes the best perfor-mance to date for cold-atom gyroscopes [22], and rep-resents an improvement of more than 30 compared toprevious 4-pulse gyroscopes [3, 5]. We compared the op-eration of the gyroscope in normal and continuous modesand observed a sensitivity improvement of (cid:39) .
4. Thisis consistent with the expected value of [ T ( n ) c / T ] − / where T ( n ) c = 2 T + T D is the cycle time in normal modewith a dead time T D (cid:39) . τ − / and reaches 1 nrad.s − at 10000 s ofintegration time. This represents the state of the art foratomic gyroscopes [32] (see [24] for a recent review) anda more than 10-fold improvement compared to previouscold-atom gyroscopes [22, 33]. The long-term stability of our gyroscope is a direct consequence of the large Sagnacarea: the AI scale factor in our folded four-pulse geom-etry scales as T when the instabilities linked to fluctu-ations of the atom cloud trajectories and identified aslimits in previous experiments [22, 33] scale as T . Theirimpact is thus reduced in our long- T interferometer. Wefurther eliminate the effect of drifts in one-photon lightshift originating from drifts of the power ratio of the Ra-man lasers. This is accomplished by alternating measure-ments with ± k eff momentum transfer and combining thefitted phase values obtained from the 20-points correla-tion data sets.To avoid the interference of parasitic interferometersoriginating from the imperfect π/ π pulses, weintroduce a time asymmetry of ∆ T = 300 µ s in theRaman pulse sequence [5], see Fig 1(b). The asymme-try introduces a sensitivity to DC acceleration given byΦ DC = 2 k eff T ∆ T g sin θ . Fluctuations of the angle ofinclination of the Raman beams by δθ would result influctuations of the AI phase Φ DC . To minimize thesefluctuations, we stabilize the vibration isolation platformby measuring the tilt of the experiment and using itssignal to compensate the tilt variation via a current-controlled magnetic actuator. We stabilize δθ at the levelof 3 × − rad, ensuring long-term stabilization of Φ DC below 0 . − after 2000 s of integration. Moreover,we alternated measurements with ± ∆ T and did not ob-serve any effect on the rotation signal, as expected. Thetilt in the y direction was measured to drift by less than10 µ rad, yielding a negligible phase drift due to a differ-ent projection of the rotation vector on the interferometerarea.Our results represent record inertial sensitivities in aSagnac AI. We emphasize that such performances wereobtained, for the first time, without loss of informationon the inertial signal thanks to the joint operation ofthe interferometer. In our setup, the sensitivity is cur-rently limited by the detection noise, yielding a τ − / scaling of the rotation stability. Improving the contrastof our AI (e.g. with more powerful and larger Ramanbeams) and reducing the stray light in our current de-tection system would result in a lower detection noiselimit. In that case, the continuous operation would offerthe possibility to efficiently average the vibration noise as τ − as a result of noise correlations between successivemeasurements. Such scaling of the sensitivity has beendemonstrated in clock configurations to average the localoscillator noise [27, 34]. The continuous operation whichwe demonstrated here will then enable to quickly reachthe quantum projection noise (or Heisenberg) limit inlarge area AIs. Assuming a vibration noise averaging as τ − , a quantum projection noise limited detection with10 atoms and a 20% interferometer contrast, a rotationsensitivity below 1 × − rad.s − in few 100 s is thusaccessible with our setup.If we assume negligible detection noise, observing the (a)(b) ..... FIG. 3. (a) Temporal variation of the rotation rate aroundits mean value. Each point is obtained from the combinationof the two phase measurements extracted from correlationfringes (as shown in Fig. 2) involving 20 data points for eachof the two opposite Raman wavevectors + k eff and − k eff . (b)Allan deviation of the gyroscope sensitivity. The dashed lineis a guide to the eye illustrating the τ − / scaling. The errorbars represent the 68% confidence intervals. τ − scaling would require to operate the AI in its linearregion, i.e. around mid-fringe. Otherwise, the loss ofinertial sensitivity, which occurs when approaching thetop and bottom of the fringe, prevents from observing the τ − scaling (see Fig. S1 in the Supplemental Material fora simulation). Mid-fringe operation can, for example, beachieved by a real time compensation of vibrations witha feedback to the Raman laser phase [21].The sensitivity reached by our instrument allows us toforesee applications in geodesy and geophysics. High ro-tation rate sensitivity combined with the large bandwidthobtained by continuous operation and the multiple-jointtechnique [27] would allow, for instance, the detection ofthe rotational signatures of seismic signals that cover awide range of rotation rates from 10 − rad/s to 1 rad/swith typical signal frequencies in the range of few mHzto tens of Hz [35]. Moreover, signals due to Earth tides,polar motion and ocean loading could be accessible withour device.The continuous operation which we demonstrated herepaves the way to inertial navigation based on AIs, byfully exploiting the sensitivity and long-term stabilityof atomic sensors without loss of information [19]. Fi-nally, the continuous operation will benefit to funda-mental physics experiments with AIs, in particular whenlooking for time varying signals such as in gravitational wave detection [10, 11].We acknowledge the financial support fromD´el´egation G´en´erale de l’Armement (DGA contractNo. 2010.34.0005), Centre National d’Etudes Saptiales(CNES), Institut Francilien de Recherche sur les AtomesFroids (IFRAF), the Action Sp´ecifique du CNRS Grav-itation, R´ef´erences, Astronomie et M´etrologie (GRAM)and Ville de Paris (project HSENS-MWGRAV). I.D.was supported by CNES and FIRST-TF (ANR-10-LABX-48-01), D.S. by DGA and B.F. by FIRST-TF.We thank M. Meunier, T. L´ev`eque and D. Holleville forcontributions to the experimental setup, and F. PereiraDos Santos for careful reading of the manuscript. ∗ [email protected] † [email protected][1] R. Bouchendira, P. Clad´e, S. Guellati-Kh´elifa, F. Nez,and F. Biraben, Phys. Rev. Lett. , 080801 (2011).[2] G. Rosi, F. Sorrentino, L. Cacciapuoti, M. 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