We show that a Bose-Einstein condensate (BEC) interferometer on an atom chip is capable of making an absolute force measurement. We demonstrate this by making an absolute measurement of the gravitational acceleration g. We implement two interferometer arms by splitting a BEC into two symmetric wells using radio-frequency (rf) adiabatic potentials. The independent control of the rf currents running through the chip surface allows us to change the polarisation of the rf field and hence the orientation of the double well potential. Tilting of the system with respect to the horizontal introduces an energy difference Δ V and the relative phase between the BECs starts to evolve. After moving the atoms back to their initial position and overlapping the clouds in free fall we measure the resulting phase from the interference pattern. In order to derive a number for g from experimental results a detailed analysis and understanding of the interferometer scheme is essential. For this type of interferometer we have identified two main limitations to the accuracy of the measurement: a systematic error due to rf field gradients, and a statistical error due to phase spreading from atom-atom interactions. Taking all errors into account we expect a value for g to within 16%. The statistical uncertainty of the measurement is 5%. We have a strategy for reducing all systematic errors to less than 1%. In order to reduce the rate of phase spreading we want to squeeze the relative number of atoms between the wells in future experiments.
We show that a Bose-Einstein condensate (BEC) interferometer on an atom chip is capable of making an absolute force measurement. We demonstrate this by making an absolute measurement of the gravitational acceleration g. We implement two interferometer arms by splitting a BEC into two symmetric wells using radio-frequency (rf) adiabatic potentials. The independent control of the rf currents running through the chip surface allows us to change the polarisation of the rf field and hence the orientation of the double well potential. Tilting of the system with respect to the horizontal introduces an energy difference Δ V and the relative phase between the BECs starts to evolve. After moving the atoms back to their initial position and overlapping the clouds in free fall we measure the resulting phase from the interference pattern. In order to derive a number for g from experimental results a detailed analysis and understanding of the interferometer scheme is essential. For this type of interferometer we have identified two main limitations to the accuracy of the measurement: a systematic error due to rf field gradients, and a statistical error due to phase spreading from atom-atom interactions. Taking all errors into account we expect a value for g to within 16%. The statistical uncertainty of the measurement is 5%. We have a strategy for reducing all systematic errors to less than 1%. In order to reduce the rate of phase spreading we want to squeeze the relative number of atoms between the wells in future experiments.
We investigate the use of a Bose-Einstein condensate trapped on an atom chip for making interferometric measurements of small energy differences. We measure and explain the noise in the energy difference of the split condensates, which derives from statistical noise in the number difference. We also consider systematic errors. A leading effect is the variation of the rf magnetic field in the trap with distance from the wires on the chip surface. This can produce energy differences that are comparable with those due to gravity.
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.
An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.
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 sensitivity of atom interferometers is usually limited by the observation time of a free falling cloud of atoms in Earth's gravitational field. Considerable efforts are currently made to increase this observation time, e.g. in fountain experiments, drop towers and in space. In this article, we experimentally study and discuss the use of magnetic levitation for interferometric precision measurements. We employ a Bose-Einstein condensate of cesium atoms with tuneable interaction and a Michelson-interferometer scheme for the detection of micro-g acceleration. In addition, we demonstrate observation times of 1s, which are comparable to current drop-tower experiments, we study the curvature of our force field, and we observe the effects of a phase-shifting element in the interferometer paths.