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.

As specialized materials are developed for various applications, it becomes desirable to test them under adverse conditions, such as at elevated temperatures and in harsh environments. It is increasingly important that sensors be developed to meet the growing needs of research and industry. The ability of sapphire to withstand elevated temperatures and many chemically harsh environments has long been recognized. However, currently available sapphire fiber possesses poor optical quality and is not available with a cladding. It has found use in a variety of temperature sensors, but the investigation of sapphire-based strain and displacement sensors has been limited. The primary development of a white-light Michelson interferometer that utilizes a sapphire fiber sensing head is presented in this thesis. Development includes efforts to combat the poor optical quality of the sapphire fiber, minimize polarization mode fading, and preferentially excite the fundamental mode of the sapphire fiber. This thesis demonstrates the feasibility of fabricating a Michelson white-light interferometer capable of measuring displacements in environments ranging from room temperature to 800 degrees Celsius. The sensor developed in this work is capable of measuring displacements exceeding 6.4 millimeters at room temperature, and exceeding 1 millimeter at 800 degrees Celsius. This thesis also presents the application of this sensor to the alignment of a sapphire-fiber based Fabry-Perot sensor. This technique allows the Fabry-Perot sensor to be aligned so that usable fringes are always obtained. Alignment of the sapphire-fiber based Fabry-Perot sensors has been considered prohibitively difficult. / Master of Science

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