Improved detection of small atom numbers through image processing

We demonstrate improved detection of small trapped atomic ensembles through advanced post-processing and optimal analysis of absorption images. A fringe removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation and is applied to real experimental data to measure the population differences and intrinsic atom shot-noise between spatially separated ensembles each comprising between 10 and 2000 atoms. The combined techniques improve our signal-to-noise by a factor of 3, to a minimum resolvable population difference of 17 atoms, close to our ultimate detection limit.Comment: 4 pages, 3 figure

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection

We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of estimation phase approaches Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.Comment: 9 pages, 2 figures, 3 table

The Optimal Implementation of On-Line Optimization for Chemical and Refinery Processes.

On-line optimization is an effective approach for process operation and economic improvement and source reduction in chemical and refinery processes. On-line optimization involves three steps of work as: data validation, parameter estimation, and economic optimization. This research evaluated statistical algorithms for gross error detection, data reconciliation, and parameter estimation, and developed an open-form steady state process model for the Monsanto designed sulfuric acid process of IMC Agrico Company. The plant model was used to demonstrate improved economics and reduced emissions from on-line optimization and to test the methodology of on-line optimization. Also, a modified compensation strategy was proposed to improve the misrectification of data reconciliation algorithms and it was compared with measurement test method. In addition, two ways to conduct on-line optimization were studied. One required two separated optimization problems to update parameters, and the other combined data validation and parameter estimation into one optimization problem. Two-step estimation demonstrated a better performance in estimation accuracy than one-step estimation for sulfuric acid process, while one-step estimation required less computation time. The measurement test method, Tjoa-Biegler\u27 contaminated Gaussian distribution method, and robust method were evaluated theoretically and numerically to compare the performance of these methods. Results from these evaluation were used to recommend the best way to conduct on-line optimization. The optimal procedure is to conduct combined gross error detection and data reconciliation to detect and rectify gross errors in plant data from DCS using Tjoa-Biegler\u27s method or robust method. This step generates a set of measurements containing only random errors which is used for simultaneous data reconciliation and parameter estimation using the least squares method (the normal distribution). Updated parameters are used in the plant model for economic optimization that generates optimal set points for DCS. Applying this procedure to the Monsanto sulfuric acid plant had an increased profit of 3% over current operating condition and an emission reduction of 10% which is consistent with other reported applications. Also, this optimal procedure to conduct on-line optimization has been incorporated into an interactive on-line optimization program which used a window interface developed with Visual Basic and GAMS to solve the nonlinear optimization problems. This program is to be available through the EPA Technology Tool Program

Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control

Optical phase estimation is a vital measurement primitive that is used to perform accurate measurements of various physical quantities like length, velocity and displacements. The precision of such measurements can be largely enhanced by the use of entangled or squeezed states of light as demonstrated in a variety of different optical systems. Most of these accounts however deal with the measurement of a very small shift of an already known phase, which is in stark contrast to ab-initio phase estimation where the initial phase is unknown. Here we report on the realization of a quantum enhanced and fully deterministic phase estimation protocol based on real-time feedback control. Using robust squeezed states of light combined with a real-time Bayesian estimation feedback algorithm, we demonstrate deterministic phase estimation with a precision beyond the quantum shot noise limit. The demonstrated protocol opens up new opportunities for quantum microscopy, quantum metrology and quantum information processing.Comment: 5 figure