Sven Abend, Martina Gebbe, Matthias Gersemann, Henning Ahlers, Hauke Müntinga, Enno Giese, Naceur Gaaloul, Christian Schubert, Cláus Lämmerzahl, Wolfgang A. Ertmer, W. P. Schleich, Ernst Maria Rasel
We demonstrate a quantum gravimeter by combining the advantages of an atom chip for the generation, delta-kick collimation, and coherent manipulation of freely falling Bose-Einstein condensates (BECs) with an innovative launch mechanism based on Bloch oscillations and double Bragg diffraction. Our high-contrast BEC interferometer realizes tens of milliseconds of free fall in a volume as little as a one centimeter cube and paves the way for measurements with sub-μGal accuracies in miniaturized, robust devices.
We demonstrate a quantum gravimeter by combining the advantages of an atom chip for the generation, delta-kick collimation, and coherent manipulation of freely falling Bose-Einstein condensates (BECs) with an innovative launch mechanism based on Bloch oscillations and double Bragg diffraction. Our high-contrast BEC interferometer realizes tens of milliseconds of free fall in a volume as little as a one centimeter cube and paves the way for measurements with sub-μGal accuracies in miniaturized, robust devices.
The quantum gravimeter QG-1 is designed to perform local gravity measurements in field with residual uncertainties surpassing state-of-the-art absolute gravimeters. It will use delta-kick collimated Bose-Einstein condensates (BEC) of 87 Rb atoms as the source for matter-wave interferometry and aims for an uncertainty level below 3 nm/s 2 with a repetition rate of 0.5 Hz. In the frame of this thesis, the atom-chip source has been set up and characterized. In order to meet the requirements for transportability, the apparatus needs to be compact and robust. Additionally, a high BEC flux is desired for the targeted statistical uncertainty. To meet these requirements a double magneto-optical trap (MOT) configuration based on a 3-layer atom chip has been implemented. Furthermore, a compact high power fiber-based laser system has been developed to provide the light for atomic manipulation. To power and control this laser system and generate the magnetic fields necessary to trap atoms, a miniaturized electronic system with low power consumption has been utilized and characterized. The steps towards trapping the atoms inside a magnetic trap on which the evaporation will be implemented have been realized and optimized. A two-dimensional MOT has been employed and an optimized atomic beam flux of 2.2 × 10 9 atoms/s with a mean longitudinal velocity of 17.2 m/s and a narrow longitudinal velocity distribution of 2.2 m/s has been used to load a 3D-chip MOT. The resulting 3D-MOT has been characterized and a loading rate of 8.1×10 8 atoms/s has been attained. After loading for 300 ms, 2.4×10 8 atoms are trapped in the 3D-MOT. Applying a subsequent compressed MOT stage, the cloud density has been increased by a factor of 10. This denser atomic ensemble with 2.9 × 10 10 atoms/cm 3 has been further cooled in a polarization gradient cooling (PGC) stage to 5.6 μK in order to increase the mode match with the subsequent magnetic trap. In the initial large volume magnetic trap generated by the wire structures on the mesoscopic and the base layers of the atom-chip assembly, 3.6 × 10 7 atoms have been captured. This trap features a temperature of 44.3 μK, a trapping frequency of 9.1 Hz in its weak confining axis and a phase-space density of 4.5 × 10 −7 . The process of transferring the atoms into the final magnetic trap with higher trapping frequency for an efficient BEC evaporation, which is formed by the wire structures on the base and science chip has been tested. With this, all the necessary functionalities of a high-flux BEC source setup have been demonstrated.
Inertial sensors based on matter-wave interferometry are currently approaching the precision and accuracy of state-of-the-art classical sensors. While these devices are often realised with ultracold but not Bose-condensed atoms as matter waves, employing Bose-Einstein Condensates (BEC) promises to overcome certain limitations, especially those related to the ensemble's expansion. The point-source like character of BECs also enables utilising spatial interference patterns to measure e.g. rotation rates in single-shot experiments. Matter wave-based inertial sensors are considered for experiments ranging from Gravitational Wave detection to tests of the Universality of Free Fall (UFF) to gain insight into the joint between Quantum Mechanics and General Relativity. In the scope of this thesis, matter-wave interferometry with BECs was demonstrated for the first time in a microgravity environment with the QUANTUS-1 apparatus. The same instrument was then employed as a quantum tiltmeter utilising a novel beam-splitting mechanism known as Bragg Double Diffraction. To this end, the QUANTUS-1 apparatus designed as a BEC instrument to be operated in the drop tower at ZARM at University of Bremen was equipped with optics and laser systems required for performing matter-wave interferometry based on Bragg Diffraction. The apparatus employs an atom chip to create BECs of around 10000 Rubidium 87 atoms within 15 s. With a Mach-Zehnder like interferometer scheme, spatial interference fringes were observed after a free evolution time in the interferometer of up to 677 ms. To achieve these long time scales, a method known as Delta-Kick Collimation (DKC) was adapted to slow the expansion of the BEC to a kinetic energy equivalent below 1 nK, and the atoms were transferred to a non-magnetic Zeeman state via an adiabatic rapid passage (ARP). A similar interferometer scheme with a newly developed beam-splitter mechanism known as Bragg Double Diffraction was used to measure the tilt of the instrument on ground with a precision of up to 4.4 AA rad. This thesis presents an overview of the apparatus including ground-based characterisations of all required experimental steps. Results from over 400 free fall experiments are evaluated for expansion studies of the BEC and matter-wave interferometry in microgravity. The time-evolution of first and second order Bragg Double Diffraction beam splitters is studied, and an interferometer sensitive to the tilt of the instrument is implemented. Based on this work, a gravimeter with a new launch mechanism comprising Bragg beam splitters and Bloch oscillations to enable atomic fountains in atom-chip based devices was developed. The microgravity experiments were adapted for the MAIUS-1 sounding-rocket instrument to create the first man-made BEC in outer space and study the feasibility of operating matter-wave interferometers on space-borne platforms. The results of this thesis lay the groundwork for future space-borne missions using matter-wave interferometry for precision measurements of inertial forces.
Extended free fall enables experiments with quantum gases unbiased by gravity. Apart from a 10m-fountain, we have access to various platforms comprising the Bremen drop- and gravi-tower, the Einstein Elevator, sounding rockets as well as NASA‘s cold atom laboratory (CAL) in orbit, all offering experiments with different durations and repetition rates. Atom chips turned out to successfully create Rubidium Bose-Einstein condensates on these platforms. Recently we have lowered the expansion energies of Bose-Einstein condensates to an unprecedented level corresponding to 38pK which makes them an excellent resource for interferometry. We exploit the latter to study delta-kick collimation as well to extend interferometry times in free fall. Atom chips also allow to investigate quantum mixtures in absence of bouyancy. For this purpose, we have been creating potassium 41 BECs by sympathetic cooling with rubidium. These experiments were continued to space by sounding rocket missions and the CAL. In future, the recently inaugurated Einstein elevator as well as gravitower will be important platforms to increase the experimental cycles to study quantum gas mixtures and high-precision interferometry as well as to test fundamental physics such as Einstein’s principle of equivalence and the nature of dark energy on ground in free fall.
Matter-wave interferometers show great a potential for improving inertial sensing. The absence of drifts recommends them for a variety of applications in geodesy, navigation, or fundamental physics. Here, ultracold atomic ensembles, featuring a velocity distribution well below the photon recoil velocity, open up new perspectives. In contrast to standard laser cooling methods, they allow to reach better beam-splitting efficiencies and, hence, a higher contrast as well as to reduce systematic uncertainties and biases. Presently, Bose-Einstein condensates (BECs) provide the means to achieve the lowest expansion energies of few picokelvin. Indeed, the momentum distribution of a BEC can be further narrowed after reaching the regime of ballistic expansion, where all mean field energy is converted to kinetic energy, by the application of the delta-kick collimation technique. With such ensembles, Bragg processes can be driven with an efficiency of above 95% as well as Bloch oscillations performed without large atomic losses or dephasing. Both enable efficient large momentum transfer in interferometers to enhance their sensitivity for inertial effects. In a so-called twin-lattice atom interferometers more than thousand photon recoils are used to form compact but sensitive atom interferometers. These methods not only bring in reach extremely accurate gravimeters and accelerometers but also gyroscopes. Like the Sagnac effect in ring laser or fiber gyroscopes, the sensitivity of atom interferometers to rotations increases with the space-time area enclosed by the interferometer. In the case of light interferometers, the latter can be enlarged by forming multiple fiber loops. However, the equivalent for matter-wave interferometers remains an experimental challenge. An atom interferometer with scalable area may be formed in a twin lattice combined with a relaunch mechanism to obtain multi loops as well. Due to this scalability, it offers the perspective of reaching unprecedented sensitivities for rotations in comparably compact sensor head setups. Moreover, atom-chip technologies offer the possibility to generate a BEC and perform delta-kick collimation in a fast and reliable away, paving the way for field-deployable miniaturized atomic devices. Last but not least, the extremely low expansion energies of BECs open up to extend the time atoms spend in the interferometer to tens of seconds. This brings in reach unprecedented sensitivities in space-borne applications such as satellite geodesy.
Abstract Gravimetry with low uncertainty and long-term stability opens up new fields of research in geodesy, especially in hydrology and volcanology. The main limitations in the accuracy of current generation cold atom gravimeters stem from the expansion rate and the residual centre-of-mass motion of their atomic test masses. Our transportable quantum gravimeter QG-1 aims at overcoming these limitations by performing atom interferometry with delta-kick collimated Bose–Einstein condensates generated by an atom chip. With our approach we anticipate to measure the local gravitational acceleration at geodetic campaigns with an uncertainty less than 1 nm/s2 surpassing the state-of-the-art classic and quantum based systems. In this paper, we discuss the design and performance assessment of QG-1. Graphical abstract
Cold atom free-fall interferometers now realize state-of-the-art precision inertial sensors, opening perspectives towards embedded devices for applications and fundamental physics tests on earth and in space. The acceleration of gravity can be measured in a stimulated Raman transition interferometer where the acceleration under gravity of a cloud of freely falling atoms is sensed by three Raman pulses allowing to split, reflect and interfere atomic wave packets [1]. The gravimeter developped at SYRTE allows to measure the acceleration of gravity at state-of-the-art performances compared to the best classical absolute gravimeters, with a sensitivity of 2×10−8g over 1s and an exactitude of 5×10−9 g [2]. This exactitude is currently limited by wavefront aberrations of the lasers, sampled by residual transverse trajectories of the molasse-cooled cloud over the free fall. Unbalanced transverse trajectories will also bias the measurement due to Coriolis effect [3]. We will investigate the use of a colder atom source to reduce these systematic effects, by implementing Bose-Einstein condensation of the initial cloud, allowing both better position control and better focusing of our source.