Paper detail

Continuous Measurement and Stochastic Methods in Quantum Optical Systems

This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the quantum measurement statistics of a quasi-monochromatic laser probe. We identify the shortest timescale that successive measurements approximately commute. Our model predicts that for a probe in the near infrared, noncommuting measurement effects are apparent for subpicosecond times. The second dissertation topic attempts to find an approximation to a conditional master equation, which maps identical product states to identical product states. Through a technique known as projection filtering, we find such a equation for an ensemble of qubits experiencing a diffusive measurement of a collective angular momentum projection, and global rotations. We then test the quality of the approximation through numerical simulations. In the presence of strong randomized rotations, the approximation reproduces the exact expectation values to within 95%. The final topic applies the projection filter to the problem of state reconstruction. We find an initial state estimate based on a single continuous measurement of an identically prepared atomic ensemble. Given the ability to make a continuous collective measurement and simultaneously applying time varying controls, it is possible to find an accurate estimate given based upon a single measurement realization. Here we explore the fundamental limits of this protocol by studying an idealized model for pure qubits, which is limited only by measurement backaction. Using the exact dynamics to produce simulated measurements, we then numerically search for a maximum likelihood estimate based on the approximate expression. Our estimation technique nearly achieves an average fidelity bound set by an optimum POVM.