This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton’s Universal Gravitation constant also known as “Big G”. This tool set is especially applicable to Bose–Einstein– condensed systems present in NASA’s Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrodinger or Gross–Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of the optical density into a format suitable for visualization with sterographic (3D) movies played back through a virtual–reality headset.
This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton’s Universal Gravitation constant also known as “Big G”. This tool set is especially applicable to Bose–Einstein– condensed systems present in NASA’s Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrodinger or Gross–Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of the optical density into a format suitable for visualization with sterographic (3D) movies played back through a virtual–reality headset.
We present a variational model suitable for rapid preliminary design of atom interferometers in a microgravity environment. The model approximates the solution of the three-dimensional rotating-frame Gross-Pitaevskii equation as the sum of Nc Gaussian clouds. Each Gaussian cloud is assumed to have time-dependent center positions, widths, and linear and quadratic phase parameters. We applied the Lagrangian variational method (LVM) with this trial wave function to derive equations of motion for these parameters that can be adapted to any external potential. We also present a one-dimensional (1D) version of this variational model. As an example we apply the model to a 1D atom interferometry scheme for measuring Newton's gravitational constant, G, in a microgravity environment. We show how the LVM model can (1) constrain the experimental parameter space size, (2) show how the value of G can be obtained from the experimental conditions and interference pattern characteristics, and (3) show how to improve the sensitivity of the measurement and construct a preliminary error budget.
A variational technique is applied to solve the time-dependent nonlinear Schr\"odinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schr\"odinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.
Quantum-optical experiments situated in a gravitationally bound experimental setup are fundamentally limited in numerous ways, such as the gravitational sag experienced by the trapped atoms or the limited free-evolution times of an atomic interferometer.These constraints can be overcome by deploying the experiment in a microgravity platform, such as the International Space Station (ISS).The Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL), a collaboration between NASA and DLR and successor to NASA's CAL mission, aims to achieve just that.Planned as a multi-user experimental facility, it will enable numerous quantum-optical experiments with ultracold atomic clouds of different isotopes of rubidium and potassium in the microgravity environment of the ISS.The optical capabilities of this experiment will be manifold: Atoms can be cooled and trapped using a 2D-and 3D-magneto optical trap (MOT).They can then be loaded into a red-detuned crossed optical dipole trap.Using blue-detuned light, arbitrary painted optical potentials can be applied.Atom interferometry along two separate interferometry axes is also possible.Fluorescence and absorption detection are available for imaging of the atomic ensemble.In this paper, we present a compact and robust optical distribution system which is required to enable this functionality.To this end, we use a combination of fiber-to-fiber coupled optical benches, and fiber-based components.This distribution system needs to withstand the vibrational loads during launch to the ISS, and needs to retain a good fiber-to-fiber coupling efficiency under varying environmental conditions, such as temperature fluctuations, without maintenance, through the multi-year mission time.We have designed a total of ten optical benches, eight for light distribution and two as spectroscopic units.The optical benches make use of our micro-optical bench toolkit based on the glass-ceramic Zerodur, which has mechanical properties akin to aluminium and a negligible coefficient of thermal expansion.The toolkit has been
We present theoretical tools for predicting and reducing the effects of atomic interactions in Bose-Einstein condensate (BEC) interferometry experiments. To address mean-field shifts during free propagation, we derive a robust scaling solution that reduces the three-dimensional Gross-Pitaevskii equation to a set of three simple differential equations valid for any interaction strength. To model the other common components of a BEC interferometer---condensate splitting, manipulation, and recombination---we generalize the slowly varying envelope reduction, providing both analytic handles and dramatically improved simulations. Applying these tools to a BEC interferometer to measure the fine structure constant, $\ensuremath{\alpha}$ [S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, Phys. Rev. Lett. 89, 140401 (2002)], we find agreement with the results of the original experiment and demonstrate that atomic interactions do not preclude measurement to better than part-per-billion accuracy, even for atomic species with relatively large scattering lengths. These tools help make BEC interferometry a viable choice for a broad class of precision measurements.
With the recent production of Bose-Einstein condensates using NASA's Cold Atom Laboratory (CAL) aboard the International Space Station, research is underway focusing on the extent to which quantum mechanics can be studied in a microgravity environment. These condensates have the potential to be the coldest ever studied in experiment and in free-fall their place in orbit allows us to observe them in long time-of-flights. This thesis reports fitting analyses and trap frequency characterization of imaging data from condensates in conventional magnetic potentials. This information will be used for the calibration and design of future experiments with CAL, regarding both conventional and radio-frequency dressed traps. Of particular interest to further study are ellipsoidal shell condensates and the quasi-two-dimensional condensate that exists on its surface in the limit of low shell thickness.
The Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL) is a DLR-NASA collaboration targeting the operation of a multi-user facility aboard the International Space Station (ISS). BECCAL will be a pathfinder mission to test concepts of future quantum sensors with applications in e.g. gravity missions for earth observation and search for a violation of the universality of free fall. It will feature various capabilities for quantum-optical, atom-optical, and atom-interferometric manipulation methods of laser-cooled atoms and notably Bose-Einstein condensates. The persistent microgravity condition aboard the ISS opens the opportunity for enhanced free-fall times, overlapping multi-species trap configurations impossible on earth thanks to the lack of gravitational sag, and repeatability for detailed statistical analysis. In this contribution the design implementation of these capabilities will be presented and derived performance estimates will be discussed. The BECCAL payload is designed and constructed by the BECCAL Collaboration comprising the DLR Institute of Quantum Technology, the DLR Institute for Satellite Geodesy and Inertial Sensing, the DLR Institute for Software Technology, the Leibniz Universität Hannover, the Humboldt-Universität zu Berlin, the Johannes Gutenberg-Universität Mainz, the Ferdinand Braun Institut für Höchstfrequenztechnik, the Universität Bremen, the Universtität Hamburg, the Universität Ulm, and OHB System AG, with funding support by the DLR Space Agency.