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
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
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.
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.
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.
Interferometers based on ultracold atoms enable an absolute measurement of inertial forces with unprecedented precision. However, their resolution is fundamentally restricted by quantum fluctuations. Improved resolutions with entangled or squeezed atoms were demonstrated in internal-state measurements for thermal and quantum-degenerate atoms and, recently, for momentum-state interferometers with laser-cooled atoms. Here, we present a gravimeter based on Bose-Einstein condensates with a sensitivity of − 1.7 − 0.5 + 0.4 dB beyond the standard quantum limit. Interferometry with Bose-Einstein condensates combined with delta-kick collimation minimizes atom loss in and improves scalability of the interferometer to very-long-baseline atom interferometers.
Atomic gravimetry measures the gravitional acceleration of an ensemble of identical neutral atoms through the atom interferometry based on Raman two-photon transition, where the Raman lasers are used as “optical ruler" and the identical neutral atoms play the role of test mass and quantum storage of gravity field information. As the novel gravimetry system suffers no mechanical wear and works at a higher repetition rate, atom gravimetry can reach a much better short-term sensitivity than the classical falling-corner-cube counterpart, and the accuracy is reasonably well. Since the very first in-laboratory device built over 30 years ago, atomic gravimetry has matured to a versatile tool that offers both precise and accurate absolute gravity measurement to fundamental research and metrology, such as testing the weak equivalence principle or linking the mass and weight of the test mass in Watt (Kibble) balance. As the current rapid development of compact cold-atom gravimeters, atomic gravimetry is moving out of the laboratory to be used as a quantum enhancement of classical devices in dynamical measurement, such as geophysics survey, inertial navigation and space mission. We review the roadmap for the development of cold-atom absolute gravimetry, highlight recent advances in the dynamical measurement using compact cold atom gravimeters and discuss the associated technological challenges. In the future, with the maturity of its application in dynamical measurement or civil engineering and the innovation in atom interferometry theory, atomic gravimetry could play a more and more important role in our life.
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.