Over the last several years considerable efforts have been made to develop Bose-Einstein condensate (BEC) based devices for a number of applications including fundamental research, precision measurements, and navgation systems. These devices, capable of complex functionality, can be built from simpler components which is currently done in both optics and microelectronics. These components include cold atom equivalents of beamsplitters, mirrors, waveguides, diodes, and transistors. The operation of the individual components must be fully understood before they can be assembled into a more complex device. The primary goal of this dissertation is to present a theoretical analysis of these components. It begins with a theoretical analysis of several different types of cold-atom beamsplitters in the context of BEC interferometry. Next, the dynamics of an interferometer that uses optical pulses to control the dynamics of the BEC will be presented. Finally, a proposal for a BEC based component that has behavior that is similar to an electronic transistor is introduced.
Over the last several years considerable efforts have been made to develop Bose-Einstein condensate (BEC) based devices for a number of applications including fundamental research, precision measurements, and navgation systems. These devices, capable of complex functionality, can be built from simpler components which is currently done in both optics and microelectronics. These components include cold atom equivalents of beamsplitters, mirrors, waveguides, diodes, and transistors. The operation of the individual components must be fully understood before they can be assembled into a more complex device. The primary goal of this dissertation is to present a theoretical analysis of these components. It begins with a theoretical analysis of several different types of cold-atom beamsplitters in the context of BEC interferometry. Next, the dynamics of an interferometer that uses optical pulses to control the dynamics of the BEC will be presented. Finally, a proposal for a BEC based component that has behavior that is similar to an electronic transistor is introduced.
Atom interferometers and gyroscopes are highly sensitive atom-optical devices which are capable to measure inertial, gravitational, electric, and magnetic fields and to sense rotations. Theoretically, the signal-to-noise ratio of atomic gyroscopes is about a hundred billion times more than that of their optical counterparts for the same particle flux and the enclosed area. Ultra cold atoms from a Bose-Einstein condensate (BEC) can easily be controlled and coherently manipulated on small chips by laser pulses. Atom-optical devices will therefore play a significant role in fundamental research, precision measurements, and navigation systems. In BEC-based atom interferometers, a BEC in a trap is split by using laser pulses, the split clouds are allowed to evolve, they are reflected, and then recombined by laser pulses to observe interference. The split clouds accumulate spatial phase because of the trap and the nonlinearity caused by atom-atom interactions. A velocity mismatch due to reflection laser pulses also introduces a phase gradient across each cloud. These factors contribute to spatial relative phase between the clouds at recombination, causing the loss of contrast of the interference fringes. The main objective of this dissertation is to study the dynamics of a split condensate in atom Michelson interferometers, investigate the effect of trap frequencies, nonlinearity, and the velocity mismatch on the contrast, and to obtain the best theoretical limit of performance in terms of the experimental parameters: trap frequencies, number of atoms, and the velocity imparted to the clouds by the splitting laser pulses.
Abstract : Theoretical work established a quantum framework in which to address atom analogs of electronic devices and circuits. Initial focus was on isolated elements, particularly atom diodes and atom transistors. Two theoretical approaches addressed different device strategies, one based on double and triple potential wells, the other based on periodic structures that are analogous to semiconductor materials. The first approach is suited to implementations using ultracold atom chip technology, whereas the second is amenable to optical lattice experiments. Both approaches established the presence of atom flux gain in a simple transistor configuration. Further theoretical work developed an open quantum systems approach to simple yet complete circuits. This work provides the analytical tools for treating more complex atomtronic circuits. Corresponding experimental work focused on building an atom chip based Bose-Einstein Condensation (BEC) system for carrying out atom transistor experiments. Chip development demonstrated technology for fabricating structures having nanowires suspended across a substrate groove to avoid the deleterious impact of Van der Waals forces. This work established the foundation of atomtronics and the possibility of experimentally demonstrating such circuits in the near future.
This thesis presents experimental and theoretical work investigating the application of Bose-condensed atomic sources to atom interferometer-based inertial sensors. In particular, we focus on gravity sensors, which have applications in fundamental physics, Earth sciences, mineral exploration, and navigation. We develop atomic sources, design and implement several different atomic beamsplitters and mirrors, and build atom interferometers utilising Bose-condensed atomic sources. Theoretical work supports all of these experiments. Coupled with the detailed theoretical analyses, these proof-of-principle experiments show that Bose-condensed sources will be critical in the next generation inertial sensors based on atomic interference. - provided by Candidate.
The subject of this thesis is the use of BECs for atom interferometry. The standard way atom interferometry is today performed is by interrogating free falling samples of atoms. The employed samples are cold (but not condensed) to have high coherence, and dilute, not to interact significantly with each other. This technique represents nowadays an almost mature field of research in which the achievable interferometric sensitivity is bounded by the atomic shot noise. Until a few years ago the employment of BECs in such devices was strongly limited by the effect of the interactions between the condensed atoms. This obstacle is today removable exploiting interaction tuning techniques. The use of BECs would be advantageous for atom interferometry inasmuch they represents the matter analogue of the optical laser providing the maximum coherence allowed by quantum mechanics. Moreover, non-linear dynamic can be exploited in order to prepare entangled states of the system. The realization of entangled samples can lead to sub-shot noise sensitivity of the interferometers. At today very nice proof-of-principle experiments have been realized in this direction but a competitive device is still missing. This thesis work is inserted in a long term project whose goal is the realization of such a device. The basic operational idea of the project starts with the preparation of a BEC in a double well potential. By the effect of strong interactions the atomic system can be driven into an entangled state. Once the entangled state is prepared, interactions can be †switched off†and the interferometric sequence performed. This thesis begins with the description of the apparatus for the production of tunable BECs to be used in the interferometer. We chose to work with 39K atoms because this atomic species presents many convenient Feshabch resonances at easily accessible magnetic field values. The cooling of this particular atomic species presents many difficulties, both for the laser and evaporative cooling processes. For this reason, this was the last alkaline atom to be condensed. Its condensation up to now was only possible by employing sympathetic cooling with another species. In this thesis our solutions to the various cooling issues is reported. In particular we realized sub-Doppler cooling for the first time for this species and we achieved condensation via evaporation in an optical dipole trap taking advantage of a Feshbach resonance. In the last part of this work, are presented original calculations for the effects of thermal fluctuations on the coherence of a BEC in a double well, discussing the interplay between thermal fluctuations and interactions in this system. Estimations and feasibility studies regarding the double well trap to be realized are also reported.
Abstract : During 2005, a new basic research effort was begun to better understand confined cold atom systems and determine if atom interferometry for the detection of rotation was possible utilizing spatially and temporally modulated magnetic fields generated using currents running through traces on microchips. During the next seven years, significant progress has been made in evaluating the constraints posed by both theory and practical experimental considerations. This report encompasses three of these studies: collisional decoherence in trapped interferometers, adjustable microchip ring-traps, and atom chips on direct bonded copper substrates. The first of these describes an analytical model developed to describe the effects of collisions between atoms in a harmonic magnetically confined atom interferometer. The second describes a method to create an agile circular magnetic waveguide for deBroglie waves on a microchip, while the third presents the use of direct bonded copper (DBC) for the straightforward fabrication of high power atom chips. Each of these efforts has incrementally added to our cold atom interferometry knowledge base and has enabled the future construction of a working atom chip based interferometer for the ultrasensitive detection of rotation.
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.