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.
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.
Atom chips are an excellent tool for studying ultracold degenerate quantum gases, due to the high degree of controllability afforded by the precise potentials generated from the current-carrying microfabricated wires on the chip surface. The geometries of the trapping potentials are inherently capable of realising extreme aspect ratios, and therefore creating model systems with effectively reduced dimensionality, particularly the theoretically-tractable one-dimensional Bose gas. In addition, the temporal tunability makes it possible to impart non-adiabatic changes on the trapping potentials, allowing experimental investigation of samples which have been brought out of equilibrium - a situation which is not fully theoretically understood. This thesis describes the implementation, development and characterisation of an experimental system for producing the first Bose-Einstein condensates of atomic rubidium 87 gas trapped on the surface of an atom chip in Nottingham. Such an apparatus is very complex and requires careful characterisation in order to run in a stable and reliable way. Details of the experimental setup are thoroughly outlined, including the vacuum system, lasers, electronics, computer control and timing, and the optical imaging system. A newly installed compact two-dimensional magneto-optical trap provides an loading rate of 5e7 atoms per second for loading a three-dimensional mirror-magneto-optical trap with 1.5e8 atoms, at a temperature of 300uK within 10s. The cloud is then sub-Doppler cooled to 50uK, and spin-polarised with 96% purity into the |F=2,mF=+2> ground state within 5ms, in preparation for loading a purely magnetic trap. A millimeter sized copper Z-shaped conductor located beneath the atom chip surface creates a Ioffe-Pritchard magnetic trap, into which the laser cooled cloud is loaded with 70% efficiency, and can be held with a vacuum-limited lifetime of 40s. Evaporative cooling then pre-cools the sample to below 20uK within 10s, to allow the subsequent loading into potentials created by the atom chip with 100% efficiency. A final evaporation stage then cools the cloud below the phase transition temperature of 800nK, resulting finally in pure BECs with 105 atoms confined using the atom chip. Key measurements of various properties of the trapped condensates are presented, which are important in order to characterise the system fully, and to compare with theoretical expectations. In particular, included are the variation of condensate fraction with temperature, the BEC expansion dynamics, and the condensate lifetime in the trap, for example. Finally, it is demonstrated how BECs can be produced on the atom chip without the use of external macroscopic coils, achieved by using novel, integrated sheet structures located beneath the chip surface - unique to this experimental system - to create the necessary bias fields.
Abstract The precision measurement of acceleration due to gravity (g) for potential scientific and industrial applications requires the use of absolute quantum gravimeters (AQGs) as quantum sensors. In this study, the development of magneto-optical trap (MOT) for the Rubidium-87 ( 87 Rb) atoms for integration into an atomic gravimeter has been discussed. The MOT serves as a critical component for the cooling and trapping of neutral atoms, providing a high flux, low temperature atomic ensemble for subsequent measurements in cold atomic physics, such as inertial navigation, exploration, and gravity mapping. Our setup emphasizes compactness without compromising atom number or temperature performance using the single 780 nm extended cavity diode laser. We have presented the optimized optical layout for efficient atom cooling, trapping, and detection. The obtained results show atom loading rate of ∼6.02 × 10 8 atoms within 221 ms that provides fast data acquisition for the entire cycle of AQG. The fluorescence signal from free falling MOT is also obtained, which provides time-of-flight of 211 ms and temperature of 57 μK. The system is robust against environmental perturbation and offers valuable insights into the advancement of atomic ensemble for the realization of high precision quantum sensors for geophysical and navigation applications.
Atom optics has been a highly active field of research with many scientific breakthroughs over the past two decades, largely due to successful advances in laser technology, microfabrication techniques, and the development of laser cooling and trapping of neutral atoms. This dissertation details several atom optics experiments with the motivation to develop tools and techniques for precision atom wave interferometry. It provides background information about atom optics and the fundamentals behind laser cooling and trapping, including basic techniques for cold gas thermometry and absorptive detection of atoms. A brief overview of magnetic trapping and guiding in tight wire-based traps is also provided before the experimental details are presented. ❧ We developed a novel laser source of 780 nm light using frequency-doubled 1560 nm fiber amplifier. This laser system provided up to a Watt of tunable frequency stabilized light for two Rb laser cooling and trapping experiments. One system generates Bose-Einstein condensates in an optical trap while the second is based on atom chip magnetic traps. The atom chip system, detailed in this thesis, was designed and built to develop the tools necessary for transport and loading large numbers of cold atoms and explore the potential for guided atom interferometry. Techniques and results from this experiment are presented, including an efficient magnetic transport and loading method to deliver cold atom to atom chip traps. We also developed a modeling tool for the magnetic fields formed by coiled wire geometries, as well as planar wire patterns. These models helped us design traps and determine adiabatic transportation of cold atoms between macro-scale traps and micro-traps formed on atom chips. Having achieved near unity transfer efficiency, we demonstrated that this approach promises to be a consistent method for loading large numbers of atoms into micro-traps. Furthermore, we discuss an in situ imaging technique to investigate magnetic field contours of the traps and the dynamics of atoms within those confining potentials. We also controlled the propagation along the atom chip guides by accelerating atoms with longitudinal magnetic gradients, and investigated an atom focusing scheme. ❧ While the atom chip wire guides perform a role analogous to optical fibers guiding light waves, ""free space"" cold atoms offer great opportunity for precision interferometry. We describe a second on-going atom optics experiment that measures gravity gradients using a pair of atom fountain interferometers separated by one meter. We have demonstrated Gravity Gradiometer resolution down to 4x10⁻⁹ g/m using a 40 kg test mass. The atomic physics subsystem is described in detail, including the vacuum, cold atom source, optics, magnetic coils and shields, and vibration isolation and compensation. The system is designed to be a compact, robust, transportable instrument, taking strides towards future gravity gradient measurements in the field. In the realm of space applications, there has been interest for micro-gravity science experiments aboard the International Space Station, along with instrument development for gravity mapping of Earth and planetary bodies with satellite-based instruments. Furthermore, there are ground-based applications for gravity imaging of local density distributions, precision measurement of gravity, as well as proposals for redefining the kilogram, detecting gravitational waves and determining the Gravitational constant.
Ultra-cold atoms have become indispensable in quantum sensing, quantum computing, and quantum communication applications, as well as in fundamental sciences. In quantum sensing, they enable precision measurements with outstanding sensitivities that can be of great benefit in navigation, geodesy, and fundamental physics applications. The sensitivity of the atom interferometers used herefore typically scales with the square of the interrogation time. Therefore, in atom interferometric measurements, one seeks ensembles that feature a particularly low internal kinetic energy and can thus be detected after a long time-of-flight. The lowest values are achieved using Bose-Einstein condensates in conjunction with delta-kick collimation, a technique for the collimation of the atomic wave function. Bose-Einstein condensation can be achieved using a multi-stage laser cooling scheme, followed by evaporative cooling, which finally brings the temperature down to the critical temperature, typically in the nanokelvin regime. In addition to the low thermal spread, microgravity enables particularly long observation times, as it avoids limitations of the interrogation time due to vacuum chamber constraints, which are present when falling freely under the influence of gravity. Additionally, microgravity enables measurements that are not possible under normal gravity conditions, such as buoyancy-free miscibility studies, truly uniform potentials, and advanced cold atom quantum memories, which are projected to feature unprecedented time-bandwidth products. For the preparation of a Bose-Einstein condensate, two techniques are widely used in science, namely magnetic traps and optical dipole traps. For microgravity missions, magnetic traps on atom chips have been used in nearly all setups so far due to their particularly low SWAP budget and high cold atom flux. In contrast, ground-based experiments often prefer optical traps due to their higher versatility, full optical access, and the absence of surfaces in proximity to the atoms, which is fundamental for precision measurements. Additionally, optical traps enable the manipulation of intra- and inter-species scattering lengths using Feshbach resonances. Compared to atom chip traps, they also feature an intrinsically better symmetry of the trapping potential, in theory leading to fewer aberrations in matter-wave optics. The latter could enable the generation of ensembles in the yet unreached femtokelvin regime using delta-kick collimation with fewer perturbations. This thesis is about the realization of a 1064nm optical dipole trap set up for the microgravity environment of the Bremen Drop Tower. It aims to highlight the advantages of optical traps in conjunction with microgravity and prepare optical trapping technology for use in future microgravity and space missions. The thesis describes the experimental setup, the direct loading process, the characterization of the optical potential, and the optimization and investigation of the evaporative cooling in the optical dipole trap. For the evaporation process, the influence of gravity is comprehensively investigated through analytical calculations and microgravity tests. Bose-Einstein condensation is demonstrated, proving the achievement of condensation through absorption imaging of the spatial distribution, tests on the free evolution of the ensemble, and investigation of the phase-space densities achieved. Up to (74 ± 4)% condensation of an ensemble featuring (30 000 ± 13 000) atoms at a kinetic temperature of (37 ± 3) nK is demonstrated. The evaporation shows high efficiency down to a 3 s evaporation time, while a critical phase-space density can be achieved within (1.29 ± 0.07) s using an even faster evaporation ramp. This opens the door to fundamental physics experiments on Bose-Einstein condensates in microgravity, as well as applications pursuing atomic ensembles with exceptionally low expansion velocities.
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.