Abstract
Quantum technology based on cold-atom interferometers is showing great promise for fields such as inertial sensing and fundamental physics. However, the finite free-fall time of the atoms limits the precision achievable on Earth, while in space interrogation times of many seconds will lead to unprecedented sensitivity. Here we realize simultaneous 87Rb–39K interferometers capable of operating in the weightless environment produced during parabolic flight. Large vibration levels (10−2 g Hz−1/2), variations in acceleration (0–1.8 g) and rotation rates (5° s−1) onboard the aircraft present significant challenges. We demonstrate the capability of our correlated quantum system by measuring the Eötvös parameter with systematic-limited uncertainties of 1.1 × 10−3 and 3.0 × 10−4 during standard- and microgravity, respectively. This constitutes a fundamental test of the equivalence principle using quantum sensors in a free-falling vehicle. Our results are applicable to inertial navigation, and can be extended to the trajectory of a satellite for future space missions.
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Introduction
The field of quantum physics and atom optics is promising major leaps forward in technology for many applications, including communication, computation, memory and storage, positioning and guidance, geodesy, and tests of fundamental physics. Among these developments, the coherent manipulation of atoms with light, which exploits the particle–wave duality of matter, has led to the development of matter-wave interferometers exhibiting ground-breaking precision1,2,3,4—particularly for measuring inertial effects such as rotations5,6,7 and accelerations3,4,8,9. However, the exquisite sensitivity of these quantum inertial sensors often limits their applicability to very quiet and well-controlled laboratory settings—despite recent efforts that have led to major technological simplifications and the emergence of portable devices3,10,11. The precision of these instruments becomes particularly relevant when it comes to fundamental tests of general relativity. For instance, the universality of free fall (UFF), a cornerstone of general relativity, which states that a body will undergo an acceleration in a gravitational field that is independent of its internal structure or composition, can be probed at the quantum scale12,13. Tests of the UFF generally involve measuring the relative acceleration between two different test masses in free fall with the same gravitational field, and are characterized by the Eötvös parameter
where a1 and a2 are the gravitational accelerations of the two masses. Presently, the most precise measurement of
Our experiment, where two matter-wave sensors composed of rubidium-87 and potassium-39 operate simultaneously in the weightless environment produced by parabolic flight (Fig. 1), represents an atom-interferometric test of the UFF in microgravity. We demonstrate measurements of
Results
Operation during steady flight
When the aircraft is in steady flight, each of the matter-wave inertial sensors acts as an atom-based gravimeter3,8,9,24, where counter-propagating light pulses drive Doppler-sensitive single-diffraction Raman transitions between two hyperfine ground states and , where p is the momentum of the atoms resonant with the Raman transition. This creates a superposition of two internal states separated by the two-photon momentum ħ keff, where ħ is the reduced Planck’s constant and keff≃(4
where P0 is the mean probability of finding the atom in one interferometer output port, C is the fringe contrast and
Operation during parabolic flight
To operate in weightlessness, we introduced a new interferometer geometry consisting of two simultaneous single-diffraction Raman transitions in opposite directions, which we refer to as double single diffraction (DSD). In microgravity, the residual Doppler shift is small and the two opposite Raman transitions are degenerate. Thus, we choose a fixed Raman detuning
where 2P0, C≤1/2 since the sample is initially split into two velocity classes by the first
Correlated atomic sensor measurements
Onboard the aircraft the dominant source of interferometer phase noise is caused by vibrations of the reference mirror, which serves as the inertial phase reference for both 87Rb and 39K sensors. Hence, the atomic signal caused by its motion is indistinguishable from motion of the atoms. To make this distinction, we measured the mirror motion with a mechanical accelerometer from which we compute the vibration-induced phase ϕvib and correlate it with the normalized output population of each species. We refer to this process as the fringe reconstruction by accelerometer correlation (FRAC) method10,24,25. Furthermore, since the two pairs of Raman beams follow the same optical pathway and operate simultaneously, the vibration noise is common mode and can be highly suppressed from the differential phase between interference fringes.
Figure 3 displays interferometer fringes for both 87Rb and 39K, recorded during steady flight (1 g) and in weightlessness (0 g) while undergoing parabolic manoeuvres, for interrogation times T=1 and 2 ms. Owing to the large Doppler shift induced by the gravitational acceleration, fringes recorded in 1 g were obtained with the single-diffraction interferometer along the +keff direction. Matter-wave interference in 0 g was realized using the DSD configuration along both ±keff simultaneously, which requires a Doppler shift close to zero. Least-squares fits to these fringes yield the FRAC phases , which are related to the gravitational acceleration of each species. From these fits we measure a maximum signal-to-noise ratio of SNR≃8.9, and infer an acceleration sensitivity of (keffT2 SNR)−1≃1.8 × 10−4 g per shot. The best performance onboard the aircraft was achieved with the Rb interferometer at T=5 ms (SNR≃7.6), which yielded 3.4 × 10−5 g per shot—more than 1,600 times below the level of vibration noise during steady flight (∼0.055 g).
Correlation between the potassium and rubidium interferometers is clearly visible when the same data are presented in parametric form (Fig. 3c,f). We obtain general Lissajous figures when the acceleration sensitivity of the two species are not equal25, as shown in Fig. 3c. These shapes collapse into an ellipse (with an ellipticity determined by the differential phase) only when the interferometer scale factor ratio
Tests of the UFF
Using the sensitivity to gravitational acceleration along the z axis of the aircraft, we made a direct test of the UFF in both standard gravity and in weightlessness. The relative acceleration between potassium and rubidium atoms is measured by correcting the relative FRAC phase shift for systematic effects (see Methods), and isolating the differential phase due to a possible UFF violation
where is the ratio of interferometer scale factors when T is much larger than the Raman pulse durations25. The Eötvös parameter was then obtained from , where aeff is the average projection of the gravitational acceleration vector a along the z axis over the duration of the measurements. This quantity depends strongly on the trajectory of the aircraft. For our experiments, we estimate m s−2 and m s−2 during 1 g and 0 g, respectively, where the uncertainty is the 1
Discussion
Although the systematic uncertainty was dominated by technical issues related to time-varying magnetic fields, the sensitivity of our measurements was primarily limited by two effects related to the motion of the aircraft—vibrational noise on the retro-reflection mirror and rotations of the interferometer beams. These effects inhibited access to large interrogation times due to a loss of interference contrast, and are particularly important for future satellite missions targeting high sensitivities with free-fall times of many seconds.
In addition to phase noise on the interferometer, large levels of mirror vibrations cause a loss of interference contrast due to a Doppler shift of the two-photon resonance. To avoid significant losses, the Doppler shift must be well bounded by the spectral width of the Raman transition
During parabolic manoeuvres, the aircraft’s trajectory is analogous to a Nadir-pointing satellite in an elliptical orbit. The rotation of the experiment during a parabola causes a loss of contrast due to the separation of wave-packet trajectories (Fig. 4c) and the resulting imperfect overlap during the final
We have realized simultaneous dual matter-wave inertial sensors capable of operating onboard a moving vehicle—enabling us to observe correlated quantum interference between two chemical species in a weightless environment, and to demonstrate a UFF test in microgravity at a precision two orders of magnitude below the level of ambient vibration noise. With the upcoming launch of experiments in the International Space Station32,33, and in a sounding rocket34, this work provides another important test bed for future cold-atom experiments in weightlessness. In the Zero-G aircraft, even if the limit set by its motion cannot be overcome, an improvement of more than four orders of magnitude is expected by cooling the samples to ultra-cold temperatures, and actively compensating the vibrations and rotations of the inertial reference mirror. This will approach the desired conditions for next-generation atom interferometry experiments, such as those designed for advanced tests of gravitation35, gradiometry36 or the detection of gravitational waves37.
Methods
Experimental set-up
Experiments were carried out onboard the Novespace A310 Zero-G aircraft, where the interferometers operated during more than 100 parabolic manoeuvres, each consisting of ∼20 s of weightlessness (0 g) and 2–5 min of standard gravity (1 g). Two laser-cooled atomic samples (87Rb at 4
Evaluation of systematic effects
To evaluate the systematic effects on the measurement of
where is the phase due to the relative gravitational acceleration a between the reference mirror and the atoms with scale factor and
where i is an index corresponding to a given systematic effect. In general, these phases can depend on both the magnitude and the sign of . To simplify the analysis, we divide into two separate phases labelled for the direction-independent phase shifts and to denote the direction-dependent shifts (that is, those proportional to the sign of ). We isolate these components by evaluating the sum and the difference between systematics corresponding to each momentum transfer direction
For the specific case of the single-diffraction interferometer used in 1 g along +, the systematic phase shift is given by . In comparison, for the DSD interferometer, only direction-dependent systematic effects can shift the phase of the fringes measured as a function of . In the ideal case, the sum of is the sole contribution to the systematic shift of the DSD fringes, since is direction-independent and thus contributes only to the fringe contrast (Fig. 2). However, in the more general case, these two phases can indirectly affect the phase of the DSD interferometer when the two pairs of Raman beams do not excite the selected velocity classes with the same probability. We denote this contribution , thus the total systematic phase for the interferometers used in 0 g is
Table 1 displays a list of the systematic phase shifts affecting the interferometers operated at T≃2 ms onboard the aircraft (Fig. 3d–f).
Phase corrections and η measurements
The raw interferometer phase for each species is measured directly from fits to the fringes reconstructed using the FRAC method (Fig. 3). We refer to this quantity as the FRAC phase . For the interferometers used in standard gravity, the measured fringes follow equation (2) with total phase . Since the vibration phase is the quantity used to scan , the FRAC phase is related to the sum of all other phase contributions through
where is an integer representing a certain fringe. Assuming that , and provided the total uncertainty from all other phases is much less than
The Eötvös parameter is obtained from
where aeff is the effective gravitational acceleration to which the atom interferometer is sensitive over the duration of a measurement. To estimate aeff, we first compute the gravitational acceleration along the vertical z′ axis, , over a two-dimensional grid of latitude () and longitude (
where 〈⋯〉 denotes an average. Table 2 contains the list of corrections applied to the raw data to obtain
Coriolis phase shift
During steady flight, if the aircraft is tilted by angles
where first term is due to an atomic velocity v0 at the start of the interferometer and the second originates from a constant acceleration a0= g+
where
Table 3 displays the mean value and range of variation of some inertial parameters during each flight configuration. These data imply that the dominant contribution to the Coriolis phase during steady flight is the instability in the roll angle. The corresponding phase shift at T=2 ms is estimated to be ≃0.1(3) mrad for both 87Rb and 39K. In comparison, during a parabolic trajectory the atoms are in free-fall and the acceleration relative to the mirror is close to zero, hence the Coriolis phase shift is much less sensitive to the orientation of the aircraft relative to g. However, during this phase the aircraft can reach rotation rates of |
These simple estimates, although useful to give an intuitive understanding, do not include effects due to finite Raman pulse lengths , time-varying rotation rates
which describes the Coriolis phase shift due to an atomic trajectory undergoing a time-dependent rotation
which contains the interferometer sensitivity function gs(t). In the limit of short pulse lengths, and constant accelerations and rotations, equation (16) reduces to equation (13).
During the flight, we measure the acceleration of the Raman mirror in the rotating frame (Fig. 1) using a three-axis mechanical accelerometer, and the rotation rates
DSD phase shift
The DSD interferometer that we use in microgravity is sensitive to an additional systematic shift that is not present in the single-diffraction interferometer. This phase shift arises from the fact that we cannot distinguish between the atoms that are diffracted upwards and downwards. For instance, if there is an asymmetry in the number of atoms diffracted along these two directions, and the direction-independent phase
For the T≃2 ms fringes shown in Fig. 3e, we estimate ɛ≃0.05 for both rubidium and potassium interferometers. Hence, using the total direction-independent systematics listed in columns 5 and 7 of Table 1, we obtain DSD phase shifts of ≃−39(3) mrad and ≃−29(30) mrad.
Quadratic Zeeman effect and magnetic gradient
The primary source of systematic phase shift in this work originated from a time-varying B-field during the interferometer produced by a large aluminium breadboard near the coils used to produce a magnetic bias field for the interferometers. Owing to the relatively large pulsed fields (∼1.5 G) required to sufficiently split the magnetically sensitive transitions in 39K, Eddy currents produced in the aluminium breadboard during the interferometer significantly shift the resonance frequency of the clock transition via the quadratic Zeeman effect. We recorded the field just outside the vacuum system with a flux gate magnetometer (Bartington MAG-03MCTPB500) and used these data, in conjunction with spectroscopic calibrations of the field at the location of the atoms, to compute the associated systematic phase shift for each shot of the experiment.
The second-order (quadratic) Zeeman effect shifts the frequency of the clock transition as , where KRb=575.15 Hz G−2 for 87Rb and KK=8513.75 Hz G−2 for 39K (ref. 41). This effect can shift the phase of the interferometers in three ways: (i) due to a B-field that is non-constant in time ; (ii) from a field that is non-constant in space ; or (iii) via the force on the atoms from a spatial magnetic gradient . The total systematic shift due to magnetic field effects is the sum of these three phases
We model the local magnetic field experienced by the atoms as follows
where
The phase shift due to a temporal variation of the B-field can be computed using40
where is the interferometer sensitivity function25,38 and is the clock shift at the initial position of the atoms. Similarly, the phase due to the clock shift from a spatially non-uniform field can be expressed as
Here is the centre-of-mass trajectory of atom j along the interferometer pathways, and are the initial atomic position and selected velocity, respectively, is the corresponding recoil velocity and a is a constant acceleration along the direction of z. We have ignored the influence of the magnetic gradient force on the atomic trajectory since it is small compared that of gravity. In equation (22), we have used the difference between the field experienced by a falling atom and that of a stationary atom at z= to separate the spatial effect of the field from the temporal one.
To measure |B(z, t)|, we used velocity-insensitive Raman spectroscopy of magnetically sensitive two-photon transitions and we extracted the resonance frequency as a function of the time in free fall in standard gravity—yielding a map of |B(z, t)|. However, this method cannot distinguish between the temporally and spatially varying components of the field. To isolate the spatial gradient
The phase shift arising from the force on the atoms due to the magnetic gradient can be computed by evaluating the state-dependent atomic trajectories and following the formalism of ref. 42. Up to order and =hKj/Mj, this phase can be shown to be
where the ∓ sign convention corresponds to . We emphasize that this phase scales (
Data availability
The authors declare that the primary data supporting the findings of this study are available within the article and its Supplementary Information file. Additional data are available from the corresponding author on request.
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How to cite this article: Barrett, B. et al. Dual matter-wave inertial sensors in weightlessness. Nat. Commun. 7, 13786 doi: 10.1038/ncomms13786 (2016).
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References
Dickerson, S. M., Hogan, J. M., Sugarbaker, A., Johnson, D. M. S. & Kasevich, M. A. Multiaxis inertial sensing with long-time point source atom interferometry. Phys. Rev. Lett. 111, 083001 (2013).
Rosi, G., Sorrentino, F., Cacciapuoti, L., Prevedelli, M. & Tino, G. M. Precision measurement of the Newtonian gravitational constant using cold atoms. Nature 510, 518–521 (2014).
Gillot, P., Francis, O., Landragin, A., Pereira Dos Santos, F. & Merlet, S. Stability comparison of two absolute gravimeters: optical versus atomic interferometers. Metrologia 51, L15 (2014).
Hardman, K. S. et al. Simultaneous precision gravimetry and magnetic gradiometry with a Bose-Einstein condensate: a high precision, quantum sensor. Phys. Rev. Lett. 117, 138501 (2016).
Gustavson, T. L., Bouyer, P. & Kasevich, M. A. Precision rotation measurements with an atom interferometer gyroscope. Phys. Rev. Lett. 78, 2046–2049 (1997).
Barrett, B. et al. The Sagnac effect: 20 years of development in matter-wave interferometry. C. R. Physique 15, 875–883 (2014).
Dutta, I. et al. Continuous cold-atom inertial sensor with 1 nrad/s rotation stability. Phys. Rev. Lett. 116, 183003 (2016).
Peters, A., Chung, K. Y. & Chu, S. Measurement of gravitational acceleration by dropping atoms. Nature 400, 849–852 (1999).
Hu, Z.-K. et al. Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter. Phys. Rev. A 88, 043610 (2013).
Geiger, R. et al. Detecting inertial effects with airborne matter-wave interferometry. Nat. Commun. 2, 474 (2011).
Freier, C. et al. Mobile quantum gravity sensor with unprecedented stability. J Phys.: Conf. Ser. 723, 012050 (2016).
Hohensee, M. A., Müller, H. & Wiringa, R. B. Equivalence principle and bound kinetic energy. Phys. Rev. Lett. 111, 151102 (2013).
Schlippert, D. et al. Quantum test of the universality of free fall. Phys. Rev. Lett. 112, 203002 (2014).
Zhou, L. et al. Test of equivalence principle at 10−8 level by a dual-species double-diffraction Raman atom interferometer. Phys. Rev. Lett. 115, 013004 (2015).
Williams, J. G., Turyshev, S. G. & Boggs, D. H. Progress in lunar laser ranging tests of relativistic gravity. Phys. Rev. Lett. 93, 261101 (2004).
Schlamminger, S., Choi, K.-Y., Wagner, T. A., Gundlach, J. H. & Adelberger, E. G. Test of the equivalence principle using a rotating torsion balance. Phys. Rev. Lett. 100, 041101 (2008).
Kovachy, T. et al. Quantum superposition at the half-metre scale. Nature 528, 530–533 (2015).
Hartwig, J. et al. Testing the universality of free fall with rubidium and ytterbium in a very large baseline atom interferometer. New J. Phys. 17, 035011 (2015).
Müntinga, H. et al. Interferometry with Bose-Einstein condensates in microgravity. Phys. Rev. Lett. 110, 093602 (2013).
Aguilera, D. et al. STE-QUEST-test of the universality of free fall using cold atom interferometry. Class. Quantum Grav. 31, 115010 (2014).
Williams, J., Chiow, S.-W., Yu, N. & Müller, H. Quantum test of the equivalence principle and space-time aboard the international space station. New J. Phys. 18, 025018 (2016).
Jekeli, C. Navigation error analysis of atom interferometer inertial sensor. J. Inst. Navig. 52, 1–14 (2005).
Groves, P. D. Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems 2nd edn Artech House (2013).
Le Gouët, J. et al. Limits to the sensitivity of a low noise compact atomic gravimeter. Appl. Phys. B 92, 133 (2008).
Barrett, B. et al. Correlative methods for dual-species quantum tests of the weak equivalence principle. New. J. Phys. 17, 085010 (2015).
Preumont, A. et al. A six-axis single-stage active vibration isolator based on Stewart platform. J. Sound Vib. 300, 644 (2007).
Lautier, J. et al. Hybridizing matter-wave and classical accelerometers. Appl. Phys. Lett. 105, 144102 (2014).
Lan, S.-Y., Kuan, P.-C., Estey, B., Haslinger, P. & Müller, H. Influence of the coriolis force in atom interferometry. Phys. Rev. Lett. 108, 090402 (2012).
Roura, A., Zeller, W. & Schleich, W. P. Overcoming loss of contrast in atom interferometry due to gravity gradients. New J. Phys. 16, 123012 (2014).
Rakholia, A. V., McGuinness, H. J. & Biedermann, G. W. Dual-axis, high data-rate atom interferometer via cold ensemble exchange. Phys. Rev. Appl. 2, 8 (2014).
Hoth, G. W., Pelle, B., Riedl, S., Kitching, J. & Donley, E. A. Point source atom interferometry with a cloud of finite size. Appl. Phys. Lett. 109, 071113 (2016).
Soriano, M. et al. in Aerospace Conference 2014 IEEE1–11 (2014).
Lévèque, T. et al. PHARAO laser source flight model: design and performances. Rev. Sci. Instrum. 86, 033104 (2015).
Seidel, S. T., Gaaloul, N. & Rasel, E. M. in Proceedings of 63rd International Astronautical Congress 3, 801 (2012).
Hamilton, P. et al. Atom-interferometry constraints on dark energy. Science 349, 849–851 (2015).
Carraz, O., Siemes, C., Massotti, L., Haagmans, R. & Silvestrin, P. A Space-borne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field. Microgravity Sci. Technol. 26, 139 (2014).
Hogan, J. M. et al. An atomic gravitational wave interferometric sensor in low earth orbit (AGIS-LEO). Gen. Relativ. Gravitation 43, 1953 (2011).
Cheinet, P. et al. Measurement of the sensitivity function in a time-domain atomic interferometer. IEEE Trans. Instrum. Meas. 57, 1141–1148 (2008).
Pavlis, N. K., Holmes, S. A., Kenyon, S. C. & Factor, J. K. Development and evaluation of the earth gravitational model 2008 (EGM2008). J. Geophys. Res. Solid Earth 118, 2633 (2013).
Canuel, B. Étude d’un gyromètre à atomes froids, PhD thesis, Univ. Paris XI https://tel.archives-ouvertes.fr/tel-00193288/document (2007).
Steck, D. A. Rubidium 87 D Line Data. Available at http://steck.us/alkalidata revision 2.1.5 (Accessed on May 2016, 2015).
Bongs, K., Launay, R. & Kasevich, M. A. High-order inertial phase shifts for time-domain atom interferometers. Appl. Phys. B 84, 599–602 (2006).
Lévèque, T., Gauguet, A., Michaud, F., Pereira Dos Santos, F. & Landragin, A. Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique. Phys. Rev. Lett. 103, 080405 (2009).
Acknowledgements
This work is supported by the French national agencies CNES, ANR, DGA, IFRAF, action spécifique GRAM, RTRA ‘Triangle de la Physique’ and the European Space Agency. B. Barrett and L. Antoni-Micollier thank CNES and IOGS for financial support. P. Bouyer thanks Conseil Régional d’Aquitaine for the Excellence Chair. Finally, the ICE team thank A. Bertoldi of IOGS for his assistance during the Zero-G flight campaign in May 2015; V. Ménoret of MuQuans for helpful discussions; D. Holleville, B. Venon, F. Cornu of SYRTE and J.-P. Aoustin of the laboratory GEPI for their technical assistance building vacuum and optical components; and the staff of Novespace.
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P.B. and A.L. conceived the experiment and directed research progress; B. Battelier contributed to construction of the first-generation apparatus, helped to direct research progress and provided technical support; B. Barrett led upgrades to the second generation apparatus, performed experiments, carried out the data analysis and wrote the article; L.A.-M. and L.C. helped upgrade the potassium interferometer and carried out experiments; T.L. provided technical support during flight campaigns. All authors provided comments and feedback during the writing of this manuscript.
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Barrett, B., Antoni-Micollier, L., Chichet, L. et al. Dual matter-wave inertial sensors in weightlessness. Nat Commun 7, 13786 (2016). https://doi.org/10.1038/ncomms13786
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DOI: https://doi.org/10.1038/ncomms13786
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