In this dissertation I present results for lattice boson systems based on quantum Monte Carlo simulations by the Worm algorithm. Lattice bosons can be realized by ultracold gases in optical lattices and, under certain conditions, they are described by the Bose-Hubbard model. I will discuss the ground state, i.e. the phase diagram and properties of elementary excitations, as well as finite temperature thermodynamic properties of the two- and three-dimensional systems. These results provide bench-marks and guidance for experimentalists. I will also discuss the phase diagram of the one-dimensional hard-core Bose-Hubbard model with three-body interactions. The model is realized by cold polar molecules in optical lattices. The ground state presents a novel solid phase at unconventional filling, characterized by coexisting charge density wave and bond orders. Such phase has not been predicted by the preexisting mean field theory.

This thesis presents an extensive study of wrinkling of thin polystyrene films, tens of nanometers in thickness, floating on the surface of water or water modified with surfactant. First, we study the wrinkling of floating thin polystyrene films under a capillary force exerted by a drop of water placed on its surface. The wrinkling pattern is characterized by the number and length of wrinkles. A metrology for measuring the elasticity and thickness of ultrathin films is constructed by combining the scaling relations that are developed for the length of the wrinkles with those for the number of wrinkles. This metrology is validated on polymer films modified by plasticizer. While the polystyrene films are modified with a large mass fraction of plasticizer, the relaxation of the wrinkles is observed and characterized, which affords a simple method to study the viscoelastic response of ultrathin films. Casting air bubbles beneath the films instead of placing water drops on the films, we observe the film inside the contact line is slightly deformed out of plane and there are hierarchical wrinkling patterns around both sides of the contact line. Second, we construct a metrology to measure the strength of the interaction between two localized wrinkle patterns induced by placing two drops of water on a floating thin polymer film. Third, we study the wrinkling of a floating thin polymer film due to a point force exerted on its surface. Wrinkling occurs in the film only when the pushing depth reaches a critical value. The threshold is measured and is consistent with theoretical prediction. Finally, we study the behavior of incompressible, rectangular films floating on liquid and pushed inwards along two opposite edges. Far from the uncompressed edges the membranes buckle along the force direction, developing a periodic pattern of wrinkles. Approaching the uncompressed edges, the coarse pattern in the bulk is matched to fine structures by a smooth evolution to higher wave numbers. We show how the observed multi-scale morphology is controlled by a dimensionless parameter that quantifies the relative strength of the edge forces and the rigidity of the bulk patterns.

This thesis reports experimental study of surface plasmon excitations--localized surface plasmons (SPs) and propagating surface plasmon polaritons (SPPs)--and their interactions with dipole emitters CdSe/ZnS (core/shell) nanocrystals. This study will contribute to potential applications of SP-enhanced fluorescent sensors and fast SPP-waveguided electronics. Our angle-dependent, polarization-related extinction spectra show that SPs in 2D nanodisk arrays are not only related to the intrinsic properties of individual nanoparticles, but also dependent on the dipole-dipole interactions among them. SP resonance peaks are red-shifted with increasing incidence angle. As the nanodisk center-to-center distance decreases within sub-wavelengths, coupling to waveguide modes and diffracted evanescent wave modifies the transmission. The out-of-disk-plane dipole surface plasmon resonance is used to couple to nanocrystals and to test the conventional assumption that dipole emission rates are homogeneous in time-resolved photoluminescence (PL) measurements of ensemble samples. Our new finding is that the spontaneous emission rate of dipole emitters deposited on a 2D gold nanodisk array depends on the detection angle and polarization. At the band-edge emission wavelength of nanocrystals, the out-of-incidence-plane, s-polarized PL measurements are detection angle-independent, and the in-plane-of-incidence, p-polarized PL measurements show an additional decay caused by SP-enhanced emission. In planar gold films we perform reflectivity measurements in the Kretschmann-Raether (KR) configuration and determine the frequency- and momentum-dependent SPP resonance. In hybrid samples of planar gold films and semiconductor nanocrystals, the coupling between the dipole emitters and SPPs can generate SPP emission through an inverted KR hemisphere prism. For the first time we observed a decay rate increase of SPP emission as a function of nanocrystals emission wavelength in gold films with silica separation layers, as compared to free-space dipole emission detected in the front of the metal surface. Simulations based on the theory of Ford and Weber show that this increase is primarily due to energy transfer of perpendicular dipoles into lossy surface waves. Our results of polarization-selective and angle-dependent SP-enhanced emission can be used to optimize and tune the performance of light sources or fluorescent sensors. The study of SPP emission will lead to efficient energy transfer in fast plasmonic device applications. Keywords: Au, CdSe/ZnS nanocrystals, SP, SPP emission, nanodisk arrays, time-resolved single photon counting.

No description available.

Emergent phenomena that occur at length scales smaller than approximately half the wavelength of light cannot be resolved by conventional optical techniques due to the Abbe diffraction limit. Scattering-type scanning near-field infrared microscopy (S-SNIM) can circumvent this diffraction limit allowing infrared spectroscopy at nano-scale dimensions independent of the wavelength. Additionally, there is enhanced surface sensitivity resulting from this nanoconfinement of infrared light. S-SNIM is uniquely suitable to study a diverse range of material properties inaccessible by far-field optics in the infrared such as the optical properties of ultrathin films as well as hybrid light matter surface waves called polaritons. Initially, this work describes a broadband infrared plasma light source that has been developed and implemented in our S-SNIM setup to realize broadband S-SNIM in the far- and mid-infrared. This system is then utilized to investigate propagating surface phonon polaritons (SPhPs) in bulk strontium titanate (STO). STO is a perovskite polar dielectric that has a uniquely broad range of the far-infrared in which it can support SPhPs while already having a diverse range of technologically advantageous properties. This work opens the door to envisage STO as a platform for perovskite-based broadband far-infrared and terahertz nano-photonics.Finally, the insulator to metal transition (IMT) in ultrathin vanadium dioxide (VO2) films is investigated. An IMT is an emergent characteristic of quantum materials. When the IMT occurs in materials with interacting electronic and lattice degrees of freedom, it is often difficult to determine if the energy gap in the insulating state is formed by Mott electron-electron correlations or by Peierls charge-density wave (CDW) ordering. To solve this problem, we investigate a representative material, VO2, which exhibits strong electron-electron interactions as well as CDW (Peierls) ordering. Ultrathin VO2 films on rutile (001) TiO2 substrates have been fabricated. These VO2 films undergo the IMT without the CDW (Peierls) ordering. Infrared and optical measurements discover the Mott-Hubbard semiconductor gap of 0.6 eV in the rutile phase below Tc ≈ 306 K. Above Tc, a Drude feature along with an increase in the optical conductivity due to a Mott IMT is observed. These results establish the route to a purely electronic IMT with profound implications for fundamental and applied studies of this phenomenon. Near-field infrared nano-imaging on this VO2 film exhibits a percolative phase transition in the vicinity of Tc, a uniform fully metallic phase above Tc, and a uniformly insulating phase below Tc. Near-field infrared spectroscopy demonstrates an SPhP feature stemming primarily from the TiO2 substrate. This SPhP feature is sensitive to the IMT in the ultrathin VO2 film.

In this work we discuss three problems connected to the damping of oscillations in quantum systems: dynamics and decay in a random matrix model with conserved quantities, energy redistribution and decay of the amplitude mode in a superconductor, and the decay of the gapped mode in a molecular condensate, a bosonic analog to the superconductor. These problems highlight different aspects of damping and energy redistribution in quantum dynamics, while being simple enough that analytic control is possible. The first system captures the idea of a "partially conserved" quantity: in ergodic quantum systems, physical observables have a non-relaxing component if they overlap with a conserved quantity, but how to isolate the non-relaxing component is in general unclear. We compute exact dynamical correlators governed by a Hamiltonian composed of two large interacting random matrices, H=A+B, and we analytically obtain the late-time value of ⟨A(t) A(0)⟩, which quantifies the non-relaxing part of the observable A. We show that the relaxation to this value is governed by a power-law determined by the spectrum of the Hamiltonian H, independent of the observable A, while the long--time value and the amplitude of the oscillations depend on the trace--overlap between the operator and the Hamiltonian. For Gaussian matrices, we further compute out-of-time-ordered-correlators (OTOCs) and find that the existence of a non-relaxing part of A leads to modifications of the late time values and exponents. Our results follow from exact resummation of a diagrammatic expansion and hyperoperator techniques. The above problem deals with energy redistribution in a system with a complex internal structure, but without any spatial dependence nor many--body effects. In the second part of this work we discuss energy relaxation in a system with both: a BCS superconductor. In particular, we study the excitation of the collective Higgs oscillations of the order parameter by incoherent short pulses of light with frequency much larger than the superconducting gap. We find that the excitation amplitude of the Higgs mode is controlled by a single parameter, determined by the total number of quasiparticles excited by the pulse, which we trace back to the universality of the shape of the light-induced quasiparticle cascade at energy below the Debye frequency and above the gap. Our analysis is primarily based on the Keldysh technique for non--equilibrium field theory and the Boltzmann kinetic equation. Finally, we study the damping of the gapped mode in a molecular Bose--Einstein condensate, the Bosonic analogue of a BCS superconductor. This system has the advantage of giving the experimentalist fine control over the interatomic interactions using Feshbach resonances, and is the object of renewed interest as the molecular superfluid phase has only very recently been realized in the lab. We discuss damping in the nontrivial thermodynamic phases: in the molecular superfluid phase the gapped excitation is protected by parity, and is damped only above a threshold momentum --as in the Cherenkov effect--, while in the atomic superfluid phase the gapped mode is damped at all momentum scales. We propose a class of experiments where our results are measurable: transmission (and reflection) of an atom beam through a molecular condensate cloud.

Infrared phenomena at the micro and nanoscales can elucidate fundamental physics of highly correlated and complex systems. However, accessing these length scales require high resolution microscopic instrumentation and novel analysis methods to extract meaningful information. Initially this work describes the implementation of a far-field microscope and subsequent study of single strands of spider silk and temperature dependent behavior of Li2RuO3. Little is known about the internal structure of protein fibrils, the basic building blocks of spider silk. Polarized Fourier-transform infrared micro transmittance on single strands of native spider silk was performed to determine the concentrations and orientations of seven protein secondary structures. Through decomposition of these secondary structures a high crystallinity was observed and corroborated by Raman and XRD analysis. The totality of results will help researchers develop structure-property relationships for the production of artificial silks. Next, the temperature dependent phonon and electronic properties of Li2RuO3(LRO) are presented. LRO forms a valence bond crystal at room temperature and undergoes a high temperature phase transition that involves structural, magnetic, and electronic changes. The orbital degrees of freedom are thought to be fundamental to the evolution of LRO properties across the phase transition. Above the transition temperature (Tc ≈ 500 K), an orbital selective metallic state emerges, which to our knowledge has not been previously reported in LRO. Visible polarized microscopy and scattering-type near-field infrared microscopy(S-SNIM) reveals the existence of domain in LRO. S-SNIM can circumvent the diffraction limit and access the nanoscale through the interaction between an illuminated atomic force microscope tip and sample of interest. Backscattered fields provide information about the local interaction between the tip apex (~20 nm) and sample. Fully unpacking the complicated backscattered fields to unravel the local optical properties is a difficult task though. A numerical model of scattering type near-field infrared microscopy (S-SNIM) was developed and is presented. Numerically modeling the tip-sample interaction allows a universal modeling methodology which is free of tunable phenomeno-logical parameters. Application of this model to describe numerous experimental systems is presented including polaritonic resonant materials, nanostructures, ultrathin, multilayered structures and anisotropic materials. Lastly the developed model is used to describe the observed contrast in LRO.

This work describes several experiments which examine the properties of $\sp4$He adsorbed on the porous substrate Nuclepore. Adsorption isotherm measurements are made with a capacitive technique on four sizes of Nuclepore filter. These measurements are compared to theories for adsorption, and yield pore sizes for the Nuclepore. Capillary condensation, which occurs in the pores of the Nuclepore at high coverages, is studied using both the capacitive adsorption technique and measurements of the third sound velocity on Nuclepore. These measurements are analyzed using two different theories and also yield pore sizes for the Nuclepore. Third sound attenuation is studied using a third sound resonator. The Kosterlitz-Thouless superfluid transition of $\sp4$He films adsorbed in a cylindrical geometry is examined with third sound propagation on Nuclepore. Pulsed third sound and third sound resonance techniques are employed; the third sound resonator enables frequency effects in the superfluid transition to be examined and compared to theoretical predictions for $\sp4$He films adsorbed in a single cylinder. The experiment gives an upper bound on the ratio of the pore size of the Nuclepore to the size of a vortex in the $\sp4$He film.

The results of electrical transport and AC susceptibility measurements performed with the goal of studying the superconducting and normal state electrical properties of polycrystalline samples of $\rm YBa\sb2Cu\sb3O\sb{7-\delta}$ and $\rm Ag/YBa\sb2Cu\sb3O\sb{7-\delta}$ are reported. I-V characteristics and AC susceptibility for $\approx$2 mm diameter sintered polycrystalline $\rm YBa\sb2Cu\sb3O\sb{7-\delta}$ pellets are studied at selected magnetic fields $0.1\le H\le 80.9$ G and for $80\le T\le 92$ K. Temperature dependent changes in I-V isotherms near the superconducting transition are consistent with predictions of critical scaling associated with a superconducting phase transition. AC susceptibility measurements reveal a variety of interesting phenomena, and in particular provide evidence that these materials are gauge glass granular superconductors. Magnetic field and temperature dependent changes in the I-V characteristics of $\approx$15 $\mu$m diameter $\rm Ag/YBa\sb2Cu\sb3O\sb{7-\delta}$ fibers are studied for $4\le T\le 86$ K, for $0.5\le H\le 9000$ G, and for $1\le J\le 10\sp4$ A/cm$\sp2.$ These measurements reveal a variety of quite different regions of superconducting behavior that are all consistent with a system of weakly coupled superconducting grains.

Stable Frank-Kasper spherical packing phases have been observed in a wide variety of soft-condensed matter systems, but the universality of these phases is not well understood. Recently, it was shown that the Frank-Kasper $\sigma$ and A15 phases are stable in the well-known Landau-Brazovskii (LB) model. In this work we consider the $\sigma$ and A15 phases, as well as the Laves C14 and C15 phases, and show that none of these is stable in the Ohta-Kawasaki (OK) model, which is another widely studied Ginzburg-Landau theory. The LB and OK models differ only in their quadratic coefficients. We conduct a thorough investigation of the role that this coefficient plays in stabilizing the complex phases. We uncover generic principles linking the functional form of the coefficient in reciprocal space with the stability of the complex phases. A Ginzburg-Landau theory for a for diblock copolymer system with a conformational asymmetry parameter is derived, but the complex phases are not found to be stable in this model. We also consider a Ginzburg-Landau theory for a system of hard spheres interacting via a pairwise short-range attractive, long-range repulsive (SALR) potential, and use our framework to demonstrate how the parameters in the potential influence the stability of the Frank-Kasper phases. Taken together, these results provide insight into the universal mechanisms that underlie the formation of the complex spherical packing phases in soft condensed matter. / Thesis / Doctor of Philosophy (PhD) / Soft condensed matter physics is the study of soft, deformable materials, such as soap bubbles, foams, and plastics. Many different soft matter systems undergo a fascinating phenomenon known as self-assembly, wherein the constituent particles spontaneously arrange themselves to form various ordered structures. In particular, the spherical packing phases appear when the particles first cluster into spherical aggregates, which then pack into larger arrangements. This sort of self-assembly is interesting because many different spherical arrangements are observed, including the complex spherical packing phases (also known as the Frank-Kasper phases). The fact that these complex phases appear in many different types of materials is not well understood. In this thesis we use a model known as the Ginzburg-Landau theory to ask which of these arrangements will form in a given system, and why. We uncover generic features of the Ginzburg-Landau theory that control which spherical packing phases appear, and we connect these features to several specific systems. These results provide insight into the mechanisms behind the formation of the complex spherical packing phases in a diverse range of systems.