OBJECTIVE: Develop robust, versatile and computationally efficient models for an as yet not designed gyroscope based on a four level N-scheme atomic system and a bidirectional ring resonator. DESCRIPTION: It has long been known since the pioneering work of Sagnac that light can be a utilized to perform interferometrically sensitive measurements of rotation. If one considers a ring cavity rotating about an axis perpendicular to the cavity plane, light traveling in one direction experiences a different cavity length than a light beam traveling through the cavity in the opposite direction. Assuming a dispersionless medium, the speed of light is constant, which means that the transit time of the light in the cavity in one direction is different than the transit time of the light in the other direction. This difference in path lengths directly translates to a phase shift. On the other hand, the field of"slow light"is still in its infancy. It has only been since 1999 that researchers have been able to slow the group velocity of light from 300,000 km/s to 100"s of m/s. Through the use of a specially prepared medium consisting of two lasers (a"pump"and a"probe") and an atomic gas, an extremely narrow resonance can be generated in the absorption spectrum of the probe. Using the Kramers-Kroneig relation, this implies a sharp feature in the mediums"index of refraction. Since the group velocity of the probe light is inversely proportional to the derivative of the index of refraction, a sharp feature in the index of refraction directly translates to a decrease in the group velocity of light. For this work, it is noteworthy that if the medium consists of one excited state and two ground states (the configuration that yields the largest amount of light slowing) the two beams of light need to be co-propagating for this effect to take place: a beam that is counter-propagating relative to another will not experience any significant light slowing, due to the Doppler shift. Thus, one can envision the possibility of one pump beam circulating in one direction around a ring cavity and two probe beams, one co-propagating with the pump and the other counter-propagating with the pump. Because of the light slowing effect, one beam will have a dramatically increased cavity transit time as compared to the other. Ultimately, this leads to an increased sensitivity for a gyroscope over a conventional gyroscope. Since the change in the group velocity is on the order of one million, this same factor is the anticipated increase in sensitivity. Slow light gyroscopes have been the focus of some in-house research. The novelty of the scheme currently being investigated is the inclusion of a third field (the"control") that allows optical control over the group velocity. In this four level scheme, the group velocity is a function of the control field intensity in a manner that is fundamentally different than the dependence of the group velocity on the pump laser in a three level scheme. Here, the group velocity can be made arbitrarily small or large (up to c) and can even be made negative. This control over the group velocity translates into the ability to control the dynamic range of the gyroscope. During periods of slow rotation rates, the gyroscope can be operated in"high sensitivity"mode by selecting the correct control intensity for slowest group velocity. During periods of large rotation rates, the group velocity can be changed so as to"degrade"the sensitivity to current fiber-optic gyroscope performance. A full initial model has been developed that includes all laser fields with arbitrary strength and frequency detuning with respect to atomic transitions, all atomic levels with associated decay rates and dynamics, and propagation of all fields. However, the current model is cumbersome to implement, difficult to adapt to changing configurations and computationally intensive. This program seeks to develop robust, versatile and computationally efficient models to help guide experiments and assist in the designing of a gyroscope based on a four-level slow light atomic system. PHASE I: Develop equations necessary to model the full four-level three laser field system, including all atomic parameters, laser parameters and resonator parameters. Develop a methodology that will enable the development of a full scale numerical program in Phase II. A successful Phase I will demonstrate a methodology that is computationally efficient and adaptable to changing configurations. PHASE II: Develop an algorithm and full numerical model based on the methodology developed in Phase I. Initial model and algorithm validation can be performed in collaboration with experiments being performed at Pax River or an outside laboratory. Develop a laboratory proto-type design based on the modeling results. Fabricate and evaluate the prototype for use in operational areas such as long-term GPs denied areas or areas with high rotation rates. PHASE III: Finalize and validate design. Transition the developed technology to appropriate platforms. PRIVATE SECTOR COMMERCIAL POTENTIAL/DUAL-USE APPLICATIONS: Any commercial application that requires a sensitive and stable gyroscope that may also be subject to large and sudden rotations will be able to use this technology. This can include, but is not limited to air navigation and underwater navigation. REFERENCES: 1. Harris, S.E., Yamamoto, Y. (1998). Photon Switching by Quantum Interference."Physical Review Letters,"81(17), 3611-3614. 2. Abi-Salloum, T., Meiselman, S., Davis, J.P., & Narducci, F.A. (2009). Four Level''N-scheme''in bare and quasi-dressed states pictures."Journal of Modern Optics", 56(18 & 19), 1926-1932. 3. Abi-Salloum, T.Y., Henry, B., Davis, J.P., & Narducci, F.A. (2010). Resonances and Excitation Pathways in Four-Level'N-Scheme''Atomic Systems."Physical Review A", 82(1), 013834(1-6).