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Interferometric studies in the transportable Quantum Gravimeter QG-1

Nina Heine

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Pioneering work on cold atom based quantum sensors introduced new measurement concepts to geosciences, promising independent tests of established methods as well as showing unprecedented stability, in the case of gravimetry. This naturally raises the question, whether unprecedented stability could be paired with unprecedented accuracy. Unfortunately, systematic effects originating from the thermal expansion and horizontal motion of the cold atom source prohibit this intrinsically. However, employing delta-kick collimated Bose-Einstein Condensates (BECs) instead, these leading order uncertainty contributions, i.e. wavefront aberrations and the Coriolis contribution, can be overcome. One of the major challenges here is to minimise the sensor size and power consumption to allow for mobile operation. This thesis elaborates on the development of a transportable BEC gravimeter referred to as the Quantum Gravimeter QG-1. A compact sensor size is realized by using an atom-chip based BEC source. The source performance is optimised at two operation locations producing samples of > 10^5 87Rb atoms after less than 1 s of evaporation time. The evaporation procedure is optimised for minimal residual centre-of-mass oscillation. Subsequently the atoms are released from the magnet trap, delta-kick collimated by a magnetic potential and prepared for interferometry by state transfer and purification. After this procedure up to 10^5 atoms remain in the desired, to first order, magnetically insensitive mF = 0 state, exhibiting an effective temperature of 19.8 nK in the z and 400 pK in the y direction. With this source atom interferometers of high fringe contrast of > 90 % could be operated for pulse separation times of up to 60 ms. The main focus of this work lies on the analysis of the first test of long-term operation. For this purpose the instrument was operated for eight consecutive days. This comprises a new milestone for the interruption-free operability of BEC gravimeters. The acceleration signal’s instability reveals a pressure-dependent long-term drift, which originated from the reference oscillator. Environmental and experimental data is used to correct the acceleration signal. This method reduces the long-term instability to the expected 1/√𝜏 behaviour and reveals correlation of the remaining instability with the sample’s position stability. The acceleration spectral density indicates a limitation of the short-term instability by residual vibrations of the passive isolation platform. The analysis procedure itself is evaluated by comparison of three different approaches of image evaluation. The important role of spatially resolving detection in the analysis of sources of instability, as well as in the characterisation of systematic effects is highlighted by application to setting an upper bound on the uncompensated Coriolis contribution and second order Zeeman shift. Future benefits of image-based detection for characterising systematics, such as wavefront aberrations, as well as its role in the alignment of the interferometer with respect to gravity are pointed out. Strategies for suppressing a phase shift originating from the BEC’s mean-field energy are introduced. These findings are a profound basis for entering the commissioning phase of the device, which includes the establishment of an initial uncertainty budget, the development of standardized measurement and evaluation procedures, the participation in comparisons and the preparation of measurement campaigns.

DOI
10.15488/21038

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Research in Optical Sciences•Jan 1, 2012•0 citations
Pioneering work on cold atom based quantum sensors introduced new measurement concepts to geosciences, promising independent tests of established methods as well as showing unprecedented stability, in the case of gravimetry. This naturally raises the question, whether unprecedented stability could be paired with unprecedented accuracy. Unfortunately, systematic effects originating from the thermal expansion and horizontal motion of the cold atom source prohibit this intrinsically. However, employing delta-kick collimated Bose-Einstein Condensates (BECs) instead, these leading order uncertainty contributions, i.e. wavefront aberrations and the Coriolis contribution, can be overcome. One of the major challenges here is to minimise the sensor size and power consumption to allow for mobile operation. This thesis elaborates on the development of a transportable BEC gravimeter referred to as the Quantum Gravimeter QG-1. A compact sensor size is realized by using an atom-chip based BEC source. The source performance is optimised at two operation locations producing samples of > 10^5 87Rb atoms after less than 1 s of evaporation time. The evaporation procedure is optimised for minimal residual centre-of-mass oscillation. Subsequently the atoms are released from the magnet trap, delta-kick collimated by a magnetic potential and prepared for interferometry by state transfer and purification. After this procedure up to 10^5 atoms remain in the desired, to first order, magnetically insensitive mF = 0 state, exhibiting an effective temperature of 19.8 nK in the z and 400 pK in the y direction. With this source atom interferometers of high fringe contrast of > 90 % could be operated for pulse separation times of up to 60 ms. The main focus of this work lies on the analysis of the first test of long-term operation. For this purpose the instrument was operated for eight consecutive days. This comprises a new milestone for the interruption-free operability of BEC gravimeters. The acceleration signal’s instability reveals a pressure-dependent long-term drift, which originated from the reference oscillator. Environmental and experimental data is used to correct the acceleration signal. This method reduces the long-term instability to the expected 1/√𝜏 behaviour and reveals correlation of the remaining instability with the sample’s position stability. The acceleration spectral density indicates a limitation of the short-term instability by residual vibrations of the passive isolation platform. The analysis procedure itself is evaluated by comparison of three different approaches of image evaluation. The important role of spatially resolving detection in the analysis of sources of instability, as well as in the characterisation of systematic effects is highlighted by application to setting an upper bound on the uncompensated Coriolis contribution and second order Zeeman shift. Future benefits of image-based detection for characterising systematics, such as wavefront aberrations, as well as its role in the alignment of the interferometer with respect to gravity are pointed out. Strategies for suppressing a phase shift originating from the BEC’s mean-field energy are introduced. These findings are a profound basis for entering the commissioning phase of the device, which includes the establishment of an initial uncertainty budget, the development of standardized measurement and evaluation procedures, the participation in comparisons and the preparation of measurement campaigns.
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
In the past century, the development of gravimeters with low uncertainty and long-term stability has led to new fields of research in geodesy and geoscience. Decreasing the instrumental measurement uncertainty further will enable observations of previously inaccessible phenomena, for instance, mass transport in hydrology and volcanology. During the last decades, quantum sensors based on the interference of cold atoms have been developed. Using a cold atomic gas as test mass, the accuracy of these sensors is not limited by mechanical properties but by effects caused by the thermal expansion of the atomic ensemble. The application of ultra-cold atomic ensembles with lower expansion rates in atom interferometer gravimeters is projected to reduce the leading order uncertainties by more than an order of magnitude. At the same time, atom chip technology makes it possible to prepare ultra-cold atomic ensembles at a high repetition rate and to miniaturise the sensor size. These advancements promise the realisation of an absolute gravimeter with unprecedented accuracy. This thesis describes the design considerations and the assembly of the transportable Quantum Gravimeter (QG-1) based on light-pulse atom interferometry of Bose-Einstein condensates (BEC) prepared on an atom chip. It is estimated, that the two leading order uncertainties of systematic biases governing the instrumental measurement uncertainty of current generation cold atom gravimeters are reduced to less than 1 nm/s² in the QG-1 apparatus. The established design of an atom-chip-based BEC source pioneered in the Quantus collaboration is modified to meet the requirements of QG-1. A free optical aperture of 18 mm for the interferometry laser beam is realised by changing the orientation of the atom-chip-based BEC source. Therefore, a new layout of the mesoscopic wire structure of the atom chip is required. The design described in this thesis enables atom interferometry with a free falling test mass with a baseline of 330 mm. The retro-reflection mirror is placed inside the vacuum chamber to eliminate optical elements in the atom interferometer beam path. It is mounted on a custom designed tip/tilt-stage with compact size and a large dynamic range of up to a hundredfold of the Earth's rotation rate for characterisation. Furthermore, a compact, robust and transportable fibre based laser system with modular electronics and a computer control system are set up. The key result of this thesis is the reliable operation of the ultra-cold atomic source on the atom chip. After optimisation of the trap loading procedure for a high atom number and low excitation of oscillations, it was shown that the necessary design change of the atom chip allows for efficient operation. The compressed magnetic trap has a geometrically averaged trap frequency of 2π · 256 Hz and the trapped ensemble has a lifetime of 3.2 s. The evaporative cooling procedure starts with 3.3 · 10⁷ atoms at a temperature of 166 μK. Within 1.3 s, or 2.3 s for the complete sequence, 3000 atoms are prepared at a temperature of 160 nK close to the critical temperature for Bose-Einstein condensation.
A precision inertial sensor based on the interference of matter waves has been designed and implemented. The apparatus is capable of producing both cold thermal and ultracold Bose-Einstein condensate (BEC) atomic ensembles as the inertial test mass. BECs of up to 5x10^6 Rubidium 87 atoms with an effective temperature of 50nK are produced every 13 seconds using a combination of two and three dimensional magneto-optical traps (2D and 3D MOT) and evaporative cooling in a hybrid magnetic-quadrupole and crossed optical dipole trap. The atomic cloud is then propagated through a vertically oriented Mach-Zehnder interferometer utilizing Bragg diffraction beam splitters. An 2.6m drop tube allows for up to 750ms of free fall and interferometer times of up to 250ms. The drop has four regions of imaging corresponding to 0, 25, 220, 530, and 750ms of expansion. Standard absorption imaging is used for the upper two imaging regions and frequency modulation imaging (FMI) is used for the lower regions. FMI exhibits near atom-shot noise limited signal-to-noise of 948 on a 1x10^6 atom cloud. The inertial reference is provided by the Bragg beam retro-reflector which is suspended via a geometric anti-spring passive vibration isolation system providing 65 dB of isolation at 70 Hz. Prior to the first interferometer pulse the ensemble is placed into a spin superposition of the |F=1> ground state manifold using horizontal co-propagating Raman beams. The three internal spin states remain orthogonal throughout the interferometer sequence resulting in three simultaneous interferometer with separable magnetic gradient and gravitational acceleration signals. The effects of meanfield energy on the interferometric phase uncertainty is explored under current trap conditions. It is found that 30 ms of free expansion prior to the first beam splitter decreases the internal energy such that the expected meanfield phase noise is below 1mrad. No significant decrease in the interferometer contrast is observed for all available T, whereas a thermal test mass interferometer of equivalent longitudinal temperature produces no interference at interferometer times > 100ms. A direct comparison of test mass spatial coherence length in an optically transversely confined interferometer is investigated. The visibility and contrast of a BEC and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100%, nearly independent of p pulse efficiency, while thermal sources have fringe visibilities limited to the p pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond that of the thermal source. A BEC test mass is used for the simultaneous precision measurement of gravity and magnetic field gradients. An 8 hour data run of a 130ms interferometer shows good agreement between the interferometer output and a theoretical model of the solid earth tides. The residual of the theoretical model and the experimental data show a 1000 run precision of dg/g = 1.45x10^9 corresponding to a phase noise of 3.8mrad. The integrated phase noise of the apparatus shows a sensitivity to magnetic field gradients of 120pT/m. By varying the central spatial position of a 40ms interferometer the magnetic field gradient along a portion of the drop tube is measured.
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.
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.