Strong atom-light interactions along nanostructures: Transition from free-space to nanophotonic interfaces

An exciting frontier in quantum information science is the integration of otherwise "simple'' quantum elements into complex quantum networks. The laboratory realization of even small quantum networks enables the exploration of physical systems that have not heretofore existed in the natural world. Within this context, there is active research to achieve nanoscale quantum optical circuits, for which atoms are trapped near nano-scopic dielectric structures and "wired'' together by photons propagating through the circuit elements. Single atoms and atomic ensembles endow quantum functionality for otherwise linear optical circuits and thereby enable the capability of building quantum networks component by component. Toward these goals, we have experimentally investigated three different systems, from conventional to rather exotic systems : free-space atomic ensembles, optical nano fibers, and photonics crystal waveguides. First, we demonstrate measurement-induced quadripartite entanglement among four quantum memories. Next, following the landmark realization of a nanofiber trap, we demonstrate the implementation of a state-insensitive, compensated nanofiber trap. Finally, we reach more exotic systems based on photonics crystal devices. Beyond conventional topologies of resonators and waveguides, new opportunities emerge from the powerful capabilities of dispersion and modal engineering in photonic crystal waveguides. We have implemented an integrated optical circuit with a photonics crystal waveguide capable of both trapping and interfacing atoms with guided photons, and have observed the collective effect, superradiance, mediated by the guided photons. These advances provide an important capability for engineered light-matter interactions, enabling explorations of novel quantum transport and quantum many-body phenomena.

Multilayer Active Shell Mirrors

This thesis presents a novel active mirror technology based on carbon fiber composites and replication manufacturing processes. Multiple additional layers are implemented into the structure in order to provide the reflective layer, actuation capabilities and electrode routing. The mirror is thin, lightweight, and has large actuation capabilities. These features, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Structural redundancy in the form of added material or support structures is replaced by thin, unsupported lightweight substrates with large actuation capabilities.

Several studies motivated by the desire to improve as-manufactured figure quality are performed. Firstly, imperfections in thin CFRP laminates and their effect on post-cure shape errors are studied. Numerical models are developed and compared to experimental measurements on flat laminates. Techniques to mitigate figure errors for thicker laminates are also identified. A method of properly integrating the reflective facesheet onto the front surface of the CFRP substrate is also presented. Finally, the effect of bonding multiple initially flat active plates to the backside of a curved CFRP substrate is studied. Figure deformations along with local surface defects are predicted and characterized experimentally. By understanding the mechanics behind these processes, significant improvements to the overall figure quality have been made.

Studies related to the actuation response of the mirror are also performed. The active properties of two materials are characterized and compared. Optimal active layer thicknesses for thin surface-parallel schemes are determined. Finite element simulations are used to make predictions on shape correction capabilities, demonstrating high correctabiliity and stroke over low-order modes. The effect of actuator saturation is studied and shown to significantly degrade shape correction performance.

The initial figure as well as actuation capabilities of a fully-integrated active mirror prototype are characterized experimentally using a Projected Hartmann test. A description of the test apparatus is presented along with two verification measurements. The apparatus is shown to accurately capture both high-amplitude low spatial-frequency figure errors as well as those at lower amplitudes but higher spatial frequencies. A closed-loop figure correction is performed, reducing figure errors by 94%.

Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Localization of sources of human evoked responses

The evoked response, a signal present in the electro-encephalogram when specific sense modalities are stimulated with brief sensory inputs, has not yet revealed as much about brain function as it apparently promised when first recorded in the late 1940's. One of the problems has been to record the responses at a large number of points on the surface of the head; thus in order to achieve greater spatial resolution than previously attained, a 50-channel recording system was designed to monitor experiments with human visually evoked responses.

Conventional voltage versus time plots of the responses were found inadequate as a means of making qualitative studies of such a large data space. This problem was solved by creating a graphical display of the responses in the form of equipotential maps of the activity at successive instants during the complete response. In order to ascertain the necessary complexity of any models of the responses, factor analytic procedures were used to show that models characterized by only five or six independent parameters could adequately represent the variability in all recording channels.

One type of equivalent source for the responses which meets these specifications is the electrostatic dipole. Two different dipole models were studied: the dipole in a homogeneous sphere and the dipole in a sphere comprised of two spherical shells (of different conductivities) concentric with and enclosing a homogeneous sphere of a third conductivity. These models were used to determine nonlinear least squares fits of dipole parameters to a given potential distribution on the surface of a spherical approximation to the head. Numerous tests of the procedures were conducted with problems having known solutions. After these theoretical studies demonstrated the applicability of the technique, the models were used to determine inverse solutions for the evoked response potentials at various times throughout the responses. It was found that reliable estimates of the location and strength of cortical activity were obtained, and that the two models differed only slightly in their inverse solutions. These techniques enabled information flow in the brain, as indicated by locations and strengths of active sites, to be followed throughout the evoked response.