Controlled Bose-condensed sources for atom interferometry

Abstract

This thesis contributes to the debate over the viability of using Bose-condensed sources to improve the sensitivity of atom interferometers. Specifically, we present theoretical investigations into (1) the effect of source momentum width on large momentum transfer (LMT) atom interferometry with Bragg pulses, and (2) the prospect of stabilising a high flux, narrow linewidth, continuously pumped atom laser via measurement-based feedback control of the BEC that forms the lasing mode of the atom laser. To begin, this thesis considers the effect of the atomic source's momentum width on the phase sensitivity of Bragg pulse atom interferometers in the Mach-Zehnder configuration. We show that an atomic cloud's momentum width places a fundamental upper bound on the maximum transfer efficiency of a Bragg mirror pulse, and furthermore limits the phase sensitivity of a Bragg pulse atom interferometer. We quantify these momentum width effects and precisely compute how mirror efficiencies and interferometer phase sensitivities vary as functions of Bragg order and source type. In particular, we show that narrow momentum width Bose-condensed sources give comparable sensitivities to broad momentum width thermal sources, even after incorporating the lower atom flux of Bose-condensed sources. Coupled with other favourable properties of Bose-condensed sources, such as their high tolerance to classical noise due to optical wavefront aberrations and the Coriolis effect, this suggests that LMT Bragg atom interferometry with Bose-condensed sources should yield improved sensitivities over current inertial sensors. Furthermore, our results and methodology allow for the efficient optimisation of Bragg pulses, which will help in the design of LMT Bragg mirrors and beamsplitters for atom-interferometer-based inertial sensors, irrespective of source type. In the second part of this thesis, we investigate the prospect of measurement-based feedback control of a BEC, with the aim of reducing density fluctuations by cooling the condensate to a stable spatial mode. Firstly, we consider the effects of experimental imperfections on the estimation-based feedback control of a weakly-interacting BEC undergoing continuous position measurement. These limitations violate the assumption that the estimator (i.e., filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We show that the control scheme is robust to detector inefficiency, time delay, technical noise and miscalibrated parameters. These results imply that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback. Secondly, we designed a feedback-control scheme for a trapped condensate, with interatomic interactions of any strength, based on a phase-contrast imaging setup. We derive the filtering equation for the system, and show that it gives a continuous measurement of the condensate's density. A semiclassical analysis of this control scheme shows that feedback-cooling of an interacting BEC is also possible, and that the interatomic interactions actually increase the effectiveness of the control. Therefore, measurement-based feedback control can stabilise the spatial mode of a BEC, which is a requirement for the high flux, narrow linewidth, continuously pumped atom laser sources that could potentially give inertial measurement sensitivities orders of magnitude beyond current state-of-the-art devices. Show more