<p> It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, &ndash;&gamma;, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction, we extract a finite topological term, &ndash;&gamma; , in the region of bond-strength parameter space corresponding to high geometrical frustration. Thus, we provide strong evidence for the existence of an exotic topologically ordered state and shed light on the nature of this model's strongly frustrated, and long controversial, intermediate phase.</p>

<p> To determine the mechanical and optical response of diamond crystals at high stresses and to evaluate anisotropy effects, single crystals (Type IIa) were shock compressed along the [100], [110], and [111] orientations to ~120 GPa peak elastic stresses. Particle velocity histories and shock velocities, measured using laser interferometry, were used to examine nonlinear elasticity, refractive indices, and Hugoniot elastic limits of shocked diamond. Time-resolved Raman spectroscopy was used to measure the shock compression induced frequency shifts of the triply degenerate 1332.5 cm^-1 Raman line. </p><p> Longitudinal stress-density states for elastic compression along different orientations were determined from the measured particle velocity histories and elastic shock wave velocities. The complete set of third-order elastic constants was determined from the stress-density states and published acoustic data. Several of these constants differed significantly from those calculated using theoretical models. </p><p> The refractive index of diamond shocked along [100] and [111] was determined from changes in the optical path length along the direction of uniaxial strain. Linear photoelasticity theory predicted the measured refractive index along [111]. In contrast, the refractive index along [100] was nonlinear. The refractive indices for [110] compression were not determined, but the data showed evidence of birefringence. </p><p> The splitting and frequency shifts of the diamond Raman line were measured for shock compression along [111] and were in good agreement with predictions from prior shock work. Frequency shifts were also measured along [100] and [110] up to ~60 GPa, extending previous measurements. The anharmonic force constants determined from all shock compression measurements agree with the previous shock compression determinations. </p><p> Hugoniot elastic limits for diamond shock compressed along different orientations were determined from the measured wave profiles. The elastic limits for the three orientations were highest at ~90 GPa peak elastic stress, but decreased at the higher peak elastic stress. Shear strengths were determined from the measured elastic limits: shocked diamond was strongest for compression along [110] and weakest for compression along [111]. The shear strength dependence on shock propagation direction was correlated with the stress magnitude normal to the slip plane, which appeared to inhibit the onset of inelastic deformation. </p>

<p> Gyromagnetic phenomena have been of interest since the dawn of modern electromagnetic theory. While rotation-induced magnetization in electronic systems has been known for over 100 years, the phenomenon remains largely unexplored in nuclear degrees of freedom. This thesis explores the influence of external angular momentum on nuclear polarization, utilizing optical fields endowed with orbital angular momentum (OAM). To that end, I employ novel holographic methods to project light fields with programmable OAM content into fluid samples. To quantify the OAM in such fields, I introduce new techniques of holographic video microscopy to characterize optical forces. These optical manipulation and detection schemes are combined with standard NMR spectroscopy to reveal the effects of optical forces on the nuclear hyperpolatization of both absorbing and non-absorbing samples. These experiments provide evidence of a non-resonant coupling between the orbital angular momentum of light and nuclear spins.</p>

<p> This thesis investigates the fundamental nanoscale near-field light matter interaction between a probe tip and plasmonic antenna nanostructures. The thesis is focused on polarization control of metallic plasmon modes using scattering-type scanning near-field optical microscopy (s-SNOM). Part of the thesis is dedicated to spectroscopic near-field comparison of coated and bare single plasmonic particles in the infrared wavelength range (&lambda;= 9&ndash;11 &micro;m) using s-SNOM. By tuning the wavelength of the incident light, we have acquired information on the spectral polarization dependence plasmon modes and plasmon/phonon&ndash;polariton resonant near-field interactions. The enhanced near-field coupling between the probe tip and high index Au nanostructures and Au-core thin silica coating (thickness &ap;10 nm) is described and quantified. </p>

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1018. Adviser: Richard L. Weaver. Includes bibliographical references (leaves ) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--Lehigh University, 2007.

Thesis (Ph.D.)--Lehigh University, 2008.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. / Source: Dissertation Abstracts International, Volume: 69-11, Section: B, page: 6871. Adviser: Eduardo Fradkin. Includes bibliographical references (leaves 180-191) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1058. Includes bibliographical references (leaves 78-81) Available on microfilm from Pro Quest Information and Learning.

<p> I discuss the design and operation of a system for levitating a charged, &mu;m-scale, multilayer graphene nanoplatelet in a quadrupole electric field trap in high vacuum. Levitation decouples the platelet from its environment and enables sensitive mechanical and magnetic measurements. </p><p> First, I describe a method of generating and trapping the nanoplatelets. The platelets are generated via liquid exfoliation of graphite pellets and charged via electrospray ionization. Individual platelets are trapped at a pressure of several hundred mTorr and transferred to a trap in a second chamber, which is pumped to UHV pressures for further study. All measurements of the trapped platelet's motion are performed via optical scattering. </p><p> Second, I present a method of gyroscopically stabilizing the levitated platelet. The rotation frequency of the platelet is locked to an applied radio frequency (rf) electric field <i><b>E</b></i>_rf. Over time, frequency-locking stabilizes the platelet so that its axis of rotation is normal to the platelet and perpendicular to <i><b>E</b></i>_rf. </p><p> Finally, I present optical data on the interaction of a multilayer graphene platelet with an applied magnetic field. The stabilized nanoplatelet is extremely sensitive to external torques, and its low-frequency dynamics are determined by an applied magnetic field. Two mechanisms of interaction are observed: a diamagnetic polarizability and a magnetic moment proportional to the frequency of rotation. A model is constructed to describe this data, and experimental values are compared to theory.</p><p>