Transmission Spectra of Rb 87 atoms near an Optical Nanofiber.

We present measurements of the transmission spectra of 87Rb atoms at 780 nm in the vicinity of a nanofiber. A uniform distribution of fixed atoms around a nanofiber should produce a spectrum that is broadened towards the red due to shifts from the van der Waals potential. If the atoms are free, this also produces an attractive force that accelerates them until they collide with the fiber which depletes the steady-state density of near-surface atoms. It is for this reason that measurements of the van der Waals interaction are sparse. We confirm this by measuring the spectrum cold atoms from a magneto-optical trap around the fiber, revealing a symmetric line shape with nearly the natural linewidth of the transition. When we use an auxiliary 750 nm laser we are able to controllably desorb a steady flux of atoms from the fiber that reside near the surface (less than 50 nm) long enough to feel the van der Walls interaction and produce an asymmetric spectrum. We quantify the spectral asymmetry as a function of 750 nm laser power and find a maximum. Our model, which that takes into account the change in the density distribution, qualitatively explains the observations. In the future this can be used as a tool to more comprehensively study atom-surface interactions.

Degenerate mixtures of rubidium and ytterbium for engineering open quantum systems

In the last two decades, experimental progress in controlling cold atoms and ions now allows us to manipulate fragile quantum systems with an unprecedented degree of precision. This has been made possible by the ability to isolate small ensembles of atoms and ions from noisy environments, creating truly closed quantum systems which decouple from dissipative channels. However in recent years, several proposals have considered the possibility of harnessing dissipation in open systems, not only to cool degenerate gases to currently unattainable temperatures, but also to engineer a variety of interesting many-body states. This thesis will describe progress made towards building a degenerate gas apparatus that will soon be capable of realizing these proposals. An ultracold gas of ytterbium atoms, trapped by a species-selective lattice will be immersed into a Bose-Einstein condensate (BEC) of rubidium atoms which will act as a bath. Here we describe the challenges encountered in making a degenerate mixture of rubidium and ytterbium atoms and present two experiments performed on the path to creating a controllable open quantum system. The first experiment will describe the measurement of a tune-out wavelength where the light shift of $\Rb{87}$ vanishes. This wavelength was used to create a species-selective trap for ytterbium atoms. Furthermore, the measurement of this wavelength allowed us to extract the dipole matrix element of the $5s \rightarrow 6p$ transition in $\Rb{87}$ with an extraordinary degree of precision. Our method to extract matrix elements has found use in atomic clocks where precise knowledge of transition strengths is necessary to account for minute blackbody radiation shifts. The second experiment will present the first realization of a degenerate Bose-Fermi mixture of rubidium and ytterbium atoms. Using a three-color optical dipole trap (ODT), we were able to create a highly-tunable, species-selective potential for rubidium and ytterbium atoms which allowed us to use $\Rb{87}$ to sympathetically cool $\Yb{171}$ to degeneracy with minimal loss. This mixture is the first milestone creating the lattice-bath system and will soon be used to implement novel cooling schemes and explore the rich physics of dissipation.

Nonlinear Optics and Carrier Dynamics in Nanostructured and Two-Dimensional Materials

Understanding and measuring the interaction of light with sub-wavelength structures and atomically thin materials is of critical importance for the development of next generation photonic devices.  One approach to achieve the desired optical properties in a material is to manipulate its mesoscopic structure or its composition in order to affect the properties of the light-matter interaction.  There has been tremendous recent interest in so called two-dimensional materials, consisting of only a single to a few layers of atoms arranged in a planar sheet.  These materials have demonstrated great promise as a platform for studying unique phenomena arising from the low-dimensionality of the material and for developing new types of devices based on these effects.  A thorough investigation of the optical and electronic properties of these new materials is essential to realizing their potential.  In this work we present studies that explore the nonlinear optical properties and carrier dynamics in nanoporous silicon waveguides, two-dimensional graphite (graphene), and atomically thin black phosphorus. We first present an investigation of the nonlinear response of nanoporous silicon optical waveguides using a novel pump-probe method. A two-frequency heterodyne technique is developed in order to measure the pump-induced transient change in phase and intensity in a single measurement. The experimental data reveal a characteristic material response time and temporally resolved intensity and phase behavior matching a physical model dominated by free-carrier effects that are significantly stronger and faster than those observed in traditional silicon-based waveguides.  These results shed light on the large optical nonlinearity observed in nanoporous silicon and demonstrate a new measurement technique for heterodyne pump-probe spectroscopy. Next we explore the optical properties of low-doped graphene in the terahertz spectral regime, where both intraband and interband effects play a significant role. Probing the graphene at intermediate photon energies enables the investigation of the nonlinear optical properties in the graphene as its electron system is heated by the intense pump pulse. By simultaneously measuring the reflected and transmitted terahertz light, a precise determination of the pump-induced change in absorption can be made. We observe that as the intensity of the terahertz radiation is increased, the optical properties of the graphene change from interband, semiconductor-like absorption, to a more metallic behavior with increased intraband processes. This transition reveals itself in our measurements as an increase in the terahertz transmission through the graphene at low fluence, followed by a decrease in transmission and the onset of a large, photo-induced reflection as fluence is increased.  A hybrid optical-thermodynamic model successfully describes our observations and predicts this transition will persist across mid- and far-infrared frequencies.  This study further demonstrates the important role that reflection plays since the absorption saturation intensity (an important figure of merit for graphene-based saturable absorbers) can be underestimated if only the transmitted light is considered. These findings are expected to contribute to the development of new optoelectronic devices designed to operate in the mid- and far-infrared frequency range.  Lastly we discuss recent work with black phosphorus, a two-dimensional material that has recently attracted interest due to its high mobility and direct, configurable band gap (300 meV to 2eV), depending on the number of atomic layers comprising the sample. In this work we examine the pump-induced change in optical transmission of mechanically exfoliated black phosphorus flakes using a two-color optical pump-probe measurement. The time-resolved data reveal a fast pump-induced transparency accompanied by a slower absorption that we attribute to Pauli blocking and free-carrier absorption, respectively. Polarization studies show that these effects are also highly anisotropic - underscoring the importance of crystal orientation in the design of optical devices based on this material. We conclude our discussion of black phosphorus with a study that employs this material as the active element in a photoconductive detector capable of gigahertz class detection at room temperature for mid-infrared frequencies.

Degenerate Gases of Strontium for Studies of Quantum Magnetism

We describe the construction and characterization of a new apparatus that can produce degenerate quantum gases of strontium. The realization of degenerate gases is an important first step toward future studies of quantum magnetism. Three of the four stable isotopes of strontium have been cooled into the degenerate regime. The experiment can make nearly pure Bose-Einstein condensates containing approximately 1x10^4 atoms, for strontium-86, and approximately 4x10^5 atoms, for strontium-84. We have also created degenerate Fermi gases of strontium-87 with a reduced temperature, T/T_F of approximately 0.2. The apparatus will be able to produce Bose-Einstein condensates of strontium-88 with straightforward modifications. We also report the first experimental and theoretical results from the strontium project. We have developed a technique to accelerate the continuous loading of strontium atoms into a magnetic trap. By applying a laser addressing the 3P1 to 3S1 transition in our magneto-optical trap, the rate at which atoms populate the magnetically-trapped 3P2 state can be increased by up to 65%. Quantum degenerate gases of atoms in the metastable 3P0 and 3P2 states are a promising platform for quantum simulation of systems with long-range interactions. We have performed an initial numerical study of a method to transfer the ground state degenerate gases that we can currently produce into one of the metastable states via a three-photon transition. Numerical simulations of the Optical Bloch equations governing the three-photon transition indicate that >90% of a ground state degenerate gas can be transferred into a metastable state.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.