• Continuous Optical Measurement of Cold Atomic Spins

      Jessen, Poul S.; Smith, Gregory A.; Jessen, Poul S.; Anderson, Brian P.; Cronin, Alexander D. (The University of Arizona., 2006)
      Quantum measurement is one of the most important features of quantum theory. Although mathematical predictions have been verified in great detail, practical implementation has lagged behind. Only recently have people begun to take advantage of quantum measurement properties to produce new technologies. This research helps fill that technological gap by experimental examination of a continuous, optical measurement for an ensemble of cold atomic spins. The essential physics reduces to the interaction between an atomic ensemble and a weak optical field, which has many well known results. While this work demonstrates many novel applications of the interaction, it also shows that the whole can be more than the sum of the individual parts. Starting with basic characterization of the measurement system using laser-cooled cæsium atoms, the mean value of a spin component is obtained in real time. In essence, the angular momentum of the atomic spins creates a Faraday-like rotation in the polarization of a laser probe beam. With slight modifications, additional spin components are also observed, and are shown to be in good agreement with predictions. In measuring spin dynamics, it is important to account for effects of the probe on the spin states as well. Capitalizing on this as a resource, the probe-induced ac-Stark shift is used to transform a quasi-classical spin-coherent state into a highly quantum Schrödinger cat type of superposition between two spin states. Finally, this work combines all the previous results to demonstrate how a continuous measurement of the spin with a carefully crafted evolution created in part by the probe, allows for nearly real-time determination of the complete spin density matrix. In a single 1.5 millisecond run, a spin density matrix is determined with fidelities ranging from about 85% to 90% across a wide spectrum of test states.
    • Exactly Solvable Light-Matter Interaction Models for Studying Filamentation Dynamics

      Kolesik, Miroslav; Brown, Jeffrey Michael; Moloney, Jerome V.; Wright, Ewan M.; Kolesik, Miroslav (The University of Arizona., 2016)
      This dissertation demonstrates the usefulness of exactly solvable quantum models in the investigation of light-matter interaction phenomena associated with the propagation of ultrashort laser pulses through gaseous media. This work fits into the larger research effort towards remedying the weaker portions of the standard set of medium modeling equations commonly used in simulations. The ultimate goal is to provide a self-consistent quantum mechanical description that can integrate Maxwell and Schrödinger systems and provide a means to realistically simulate nonlinear optical experiments on relevant scales. The study of exactly solvable models begins with one of the simplest quantum systems available, one with a 1D Dirac-delta function potential plus interaction with the light field. This model contains, in the simplest form, the most important "ingredients" that control optical filamentation, i.e. discrete and continuum electronic states. The importance of both states is emphasized in the optical intensity regime in which filaments form, where both kinds of electronic states simultaneously play a role and may not even be distinguishable. For this model atom, an analytical solution for the time-dependent light-induced atomic response from an arbitrary excitation waveform is obtained. Although this system is well-known and has been studied for decades, this result is probably the most practically useful and general one obtained thus far. Numerical implementation details of the result are also given as the task is far from trivial. Given an efficient implementation, the model is used in light-matter interaction simulations and from these it is apparent that even this toy model can qualitatively reproduce many of the nonlinear phenomena seen in experiments. Not only does this model capture the basic physics of optical filamentation, but it is also well-suited for high harmonic generation simulations. Next, a theoretical framework for using Stark resonant states (or metastable states) to represent the medium's polarization response is presented. Researchers have recognized long ago the utility of Gamow resonant states as a description of various decay processes. Even though a bound electron experiences a similar decay-like process as it transitions into the continuum upon ionization, it was unclear whether field-induced Stark resonant states carry physically relevant information. It is found that they do, and in particular it is possible to use them to capture a medium's polarization response. To this end, two quantum systems with potentials represented by a 1D Dirac-delta function and a 1D square well are solved, and all the necessary quantities for their use as medium models are presented. From these results it is possible to conjecture some general properties that hold for all resonance systems, including systems that reside in higher than one dimensional space. Finally, as a practical application of this theory, the Metastable Electronic State Approach (MESA) is presented as a quantum-based replacement for the standard medium modeling equations.
    • Multidimensional Microscopic Modeling of Nonequilibrium Carrier Dynamics within Vertical External-Cavity Surface-Emitting Lasers

      Moloney, Jerome V.; McLaren, Samuel Ayers; Kolesik, Miroslav; Brio, Moysey (The University of Arizona., 2021)
      Mode-locked vertical external-cavity surface emitting lasers are promising compact sources for high-power, ultrafast pulses with excellent beam quality and the flexibility offered by an external cavity. Typical models of these lasers use macroscopic or quasi-static approaches based on rate or delay differential equations. Although these approaches have shown widespread success, they often require numerous experimentally tuned parameters and do not capture the ultrafast nonequilibrium dynamics present as the field interacts with the quantum well. The Maxwell Semiconductor Bloch Equations has reduced parametrization and captures the carrier dynamics by coupling together a numerical wave propagator to a first principles quantum mechanical description of the induced microscopic polarization within the active semiconductor quantum well. This gives a detailed view into the ultrafast nonequilibrium charge carrier dynamics where carriers are driven far from Fermi distributions and allows the predictive design of future VECSEL devices. Previous work utilizing this model has been restricted to a single longitudinal dimension and linearly oriented cavities. In this thesis, the model is expanded to include transverse effects as well as to model cavities exhibiting non-normal incidence on the semiconductor heterostructures within it. The former is done through the coupling of single-dimensional models using a pseudospectral wave propagator. The latter is done through a reference frame transform in conjunction with an expansion of the Semiconductor Bloch Equations. Optimal cavity conditions for achieving modelocking within a variety of standard, as well as unconventional, VECSEL cavities are explored and characterized as they are driven by the underlying nonequilbrium carrier dynamics.