Theory of Large-Momentum-Transfer Atom Interferometry in the Quasi-Bragg Regime

Atom interferometers are versatile instruments offering great accuracy and stability, suitable for fundamental science and practical applications. In usual setups, the sensitivity of the sensor to inertial forces including gravitational signals scales with the spatial separation of two atomic wave packets. Consequently, increasing this separation using large momentum transfer (LMT) promises to enhance the performance of today’s devices by orders of magnitude. To date, despite several proof-of-principle experiments, only a handful of Bragg diffraction-based LMT implementations have yielded actual metrological gain. Hence, in this thesis we investigate the current sensitivity limits of Bragg interferometers resulting from the insufficient control of the atom-light interaction in two parts. In the first part we develop an analytical theory for Bragg pulses based on the pivotal insight that the elastic scattering of atoms from time-dependent optical lattices can be accurately described using the adiabatic theorem. We show that efficient Bragg operations can be realized with any smooth pulse shape, suggesting that adiabaticity may be a necessary requirement. Moreover, we find that high-quality Gaussian pulses are exclusively adiabatic. Our model incorporates corrections to the adiabatic evolution due to LandauZener processes, as well as the effects of a finite atomic velocity distribution. We verify its accuracy by comparison with exact numerical descriptions of Gaussian pulses transferring four, six, eight, and ten photon recoils (ℏk). We then extend our formalism to study the rich phenomenology of Bragg interferometers, which is quite different from that of a standard two-mode interferometer. We confirm the accuracy of our analysis through extensive numerical simulations for the example of a Mach-Zehnder interferometer. In particular, we determine the atomic projection noise limit of the interferometer and provide the means to saturate it. Furthermore, we evaluate the systematic errors intrinsic to the Bragg diffraction process, commonly known as the diffraction phase. We demonstrate their suppression by two orders of magnitude down to a few µrad using appropriate pulse parameters. In the second part of this thesis, we present twin-lattice interferometry based on symmetric Bragg diffraction and Bloch oscillations combined with slowly expanding BoseEinstein condensates. This method promises to address many of the constraints of previous LMT implementations enabling unprecedented momentum separations of up to 408 ℏk in the QUANTUS-1 experiment. We model the experimental contrast decay with increasing momentum transfer and conclude that in particular the interaction of the atomic ensemble with a distorted laser beam leads to spatial decoherence and to contrast loss. The results presented in this thesis indicate that technical imperfections currently limit the scalability of the experiment and our theoretical analysis will be highly instrumental in the design of future sensors with momentum separations of up to one thousand photon recoils or more

Large-momentum-transfer atom interferometers with μ\murad-accuracy using Bragg diffraction

Large-momentum-transfer~(LMT) atom interferometers using elastic Bragg scattering on light waves are among the most precise quantum sensors to date. To advance their accuracy from the mrad to the $\mu$rad regime, it is necessary to understand the rich phenomenology of the Bragg interferometer, which differs significantly from that of a standard two-mode interferometer. We develop an analytic model for the interferometer signal and demonstrate its accuracy using comprehensive numerical simulations. Our analytic treatment allows the determination of the atomic projection noise limit of an LMT Bragg interferometer, and provides the means to saturate this limit. It affords accurate knowledge of the systematic phase errors as well as their suppression by two orders of magnitude down to a few $\mu\mathrm{rad}$ using appropriate light pulse parameters.Comment: 7 pages, 5 figures,comments welcome!; Assembled supplemental material together with mansucrip

Universal atom interferometer simulation of elastic scattering processes

In this article, we introduce a universal simulation framework covering all regimes of matter-wave light-pulse elastic scattering. Applied to atom interferometry as a study case, this simulator solves the atom-light diffraction problem in the elastic case, i.e., when the internal state of the atoms remains unchanged. Taking this perspective, the light-pulse beam splitting is interpreted as a space and time-dependent external potential. In a shift from the usual approach based on a system of momentum-space ordinary differential equations, our position-space treatment is flexible and scales favourably for realistic cases where the light fields have an arbitrary complex spatial behaviour rather than being mere plane waves. Moreover, the solver architecture we developed is effortlessly extended to the problem class of trapped and interacting geometries, which has no simple formulation in the usual framework of momentum-space ordinary differential equations. We check the validity of our model by revisiting several case studies relevant to the precision atom interferometry community. We retrieve analytical solutions when they exist and extend the analysis to more complex parameter ranges in a cross-regime fashion. The flexibility of the approach, the insight it gives, its numerical scalability and accuracy make it an exquisite tool to design, understand and quantitatively analyse metrology-oriented matter-wave interferometry experiments. © 2020, The Author(s)

Precision inertial sensing with quantum gases

Quantum sensors based on light-pulse atom interferometers allow for high-precision measurements of inertial and electromagnetic forces such as the accurate determination of fundamental constants as the fine structure constant or testing foundational laws of modern physics as the equivalence principle. These schemes unfold their full performance when large interrogation times and/or large momentum transfer can be implemented. In this article, we demonstrate how precision interferometry can benefit from the use of Bose-Einstein condensed sources when the state of the art is challenged. We contrast systematic and statistical effects induced by Bose-Einstein condensed sources with thermal sources in three exemplary science cases of Earth- and space-based sensors.Comment: 13 page

Twin-lattice atom interferometry

Inertial sensors based on cold atoms have great potential for navigation, geodesy, or fundamental physics. Similar to the Sagnac effect, their sensitivity increases with the space-time area enclosed by the interferometer. Here, we introduce twin-lattice atom interferometry exploiting Bose-Einstein condensates. Our method provides symmetric momentum transfer and large areas in palm-sized sensor heads with a performance similar to present meter-scale Sagnac devices

Twin-lattice atom interferometry

Inertial sensors based on cold atoms have great potential for navigation, geodesy, or fundamental physics. Similar to the Sagnac effect, their sensitivity increases with the space-time area enclosed by the interferometer. Here, we introduce twin-lattice atom interferometry exploiting Bose-Einstein condensates of rubidium-87. Our method provides symmetric momentum transfer and large areas offering a perspective for future palm-sized sensor heads with sensitivities on par with present meter-scale Sagnac devices. Our theoretical model of the impact of beam splitters on the spatial coherence is highly instrumental for designing future sensors

ELGAR—a European Laboratory for Gravitation and Atom-interferometric Research

Gravitational waves (GWs) were observed for the first time in 2015, one century after Einstein predicted their existence. There is now growing interest to extend the detection bandwidth to low frequency. The scientific potential of multi-frequency GW astronomy is enormous as it would enable to obtain a more complete picture of cosmic events and mechanisms. This is a unique and entirely new opportunity for the future of astronomy, the success of which depends upon the decisions being made on existing and new infrastructures. The prospect of combining observations from the future space-based instrument LISA together with third generation ground based detectors will open the way toward multi-band GW astronomy, but will leave the infrasound (0.1–10 Hz) band uncovered. GW detectors based on matter wave interferometry promise to fill such a sensitivity gap. We propose the European Laboratory for Gravitation and Atom-interferometric Research (ELGAR), an underground infrastructure based on the latest progress in atomic physics, to study space–time and gravitation with the primary goal of detecting GWs in the infrasound band. ELGAR will directly inherit from large research facilities now being built in Europe for the study of large scale atom interferometry and will drive new pan-European synergies from top research centers developing quantum sensors. ELGAR will measure GW radiation in the infrasound band with a peak strain sensitivity of $3.3{\times}1{0}^{-22}/\sqrt{\text{Hz}}$ at 1.7 Hz. The antenna will have an impact on diverse fundamental and applied research fields beyond GW astronomy, including gravitation, general relativity, and geology.AB acknowledges support from the ANR (project EOSBECMR), IdEx Bordeaux—LAPHIA (project OE-TWR), theQuantERA ERA-NET (project TAIOL) and the Aquitaine Region (projets IASIG3D and USOFF).XZ thanks the China Scholarships Council (No. 201806010364) program for financial support. JJ thanks ‘AssociationNationale de la Recherche et de la Technologie’ for financial support (No. 2018/1565).SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grants No. DLR∼50WM1641 (PRIMUS-III), 50WM1952 (QUANTUS-V-Fallturm), and 50WP1700 (BECCAL), 50WM1861 (CAL), 50WM2060 (CARIOQA) as well as 50RK1957 (QGYRO)SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by ‘Niedersächsisches Vorab’ through the ‘Quantum- and Nano-Metrology (QUANOMET)’ initiative within the project QT3, and through ‘Förderung von Wissenschaft und Technik in Forschung und Lehre’ for the initial funding of research in the new DLR-SI Institute, the CRC 1227 DQ-mat within the projects A05 and B07DS gratefully acknowledges funding by the Federal Ministry of Education and Research (BMBF) through the funding program Photonics Research Germany under contract number 13N14875.RG acknowledges Ville de Paris (Emergence programme HSENS-MWGRAV), ANR (project PIMAI) and the Fundamental Physics and Gravitational Waves (PhyFOG) programme of Observatoire de Paris for support. We also acknowledge networking support by the COST actions GWverse CA16104 and AtomQT CA16221 (Horizon 2020 Framework Programme of the European Union).The work was also supported by the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grant Nos.∼50WM1556, 50WM1956 and 50WP1706 as well as through the DLR Institutes DLR-SI and DLR-QT.PA-S, MN, and CFS acknowledge support from contracts ESP2015-67234-P and ESP2017-90084-P from the Ministry of Economy and Business of Spain (MINECO), and from contract 2017-SGR-1469 from AGAUR (Catalan government).SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967 (B2) andCRC1227 ‘DQ-mat’ within projects A05, B07 and B09.LAS thanks Sorbonne Universités (Emergence project LORINVACC) and Conseil Scientifique de l'Observatoire de Paris for funding.This work was realized with the financial support of the French State through the ‘Agence Nationale de la Recherche’ (ANR) in the frame of the ‘MRSEI’ program (Pre-ELGAR ANR-17-MRS5-0004-01) and the ‘Investissement d'Avenir’ program (Equipex MIGA: ANR-11-EQPX-0028, IdEx Bordeaux—LAPHIA: ANR-10-IDEX-03-02).Peer Reviewe

Diffractive focusing of a uniform Bose-Einstein condensate

We propose a straightforward implementation of the phenomenon of diffractive focusing with uniform atomic Bose-Einstein condensates. Both, analytical as well as numerical methods not only illustrate the influence of the atom-atom interaction on the focusing factor and the focus time, but also allow us to derive the optimal conditions for observing focusing of this type in the case of interacting matter waves.Comment: 26 pages, 7 figure