Detection of a weak magnetic field via cavity enhanced Faraday rotation

We study the sensitive detection of a weak static magnetic field via Faraday rotation induced by an ensemble of spins in a bimodal degenerate microwave cavity. We determine the limit of the resolution for the sensitivity of the magnetometry achieved using either single-photon or multiphoton inputs. For the case of a microwave cavity containing an ensemble of Nitrogen-vacancy defects in diamond, we obtain a magnetometry sensitivity exceeding 0.5~\text{\nano\tesla}/\sqrt{\text{\hertz}}, utilizing a single photon probe field, while for a multiphoton input we achieve a sensitivity about 1 \text{\femto\tesla}/\sqrt{\text{\hertz}}, using a coherent probe microwave field with power of P_\text{in}=1~\text{\nano\watt}.Comment: 8 pages, 7 figure

Essays on the Bayesian estimation of stochastic cost frontier

This dissertation consists of three essays that focus on a Bayesian estimation of stochastic cost frontiers for electric generation plants. This research gives insight into the changing development of the electric generation market and could serve to inform both private investment and public policy decisions. The main contributions to the growing literature on stochastic cost frontier analysis are to 1. Empirically estimate the possible efficiency gain of power plants due to deregulation. 2. Estimate the cost of electric power generating plants using coal as a fuel taking into account both regularity restrictions and sulfur dioxide emissions. 3. Compare costs of plants using coal to those who use natural gas. 4. Apply the Bayesian stochastic frontier model to estimate a single cost frontier and allow firm type to vary across regulated and deregulated plants. The average group efficiency for two different types of plants is estimated. 5. Use a fixed effects and random effects model on an unbalanced panel to estimated group efficiency for regulated and deregulated plants. The first essay focuses on the possible efficiency gain of 136 U.S. electric power generation coal-fired plants in 1996. Results favor the constrained model over the unconstrained model. SO2 is also included in the model to provide more accurate estimates of plant efficiency and returns to scale. The second essay focuses on the predicted costs and returns to scale of coal generation to natural gas generation at plants where the cost of both fuels could be obtained. It is found that, for power plants switching fuel from natural gas to coal in 1996, on average, the expected fuel cost would fall and returns to scale would increase. The third essay first uses pooled unbalanced panel data to analyze the differences in plant efficiency across plant types – regulated and deregulated. The application of a Bayesian stochastic frontier model enables us to apply different mean plant inefficiency terms by plant type on a single stochastic frontier. The fixed effect panel estimation technique is then applied to the same unbalanced panel data. The results provide evidence that deregulated power plants are more costefficient than regulated plants