An important, but also difficult, research field in condensed matter physics is that of strongly correlated systems. This thesis considers two topics in this field. The first topic is disorder and frustration in spin models. The introduction of disorder into quantum spin chains creates a complex problem. The ground state of the random-bond spin-1 Heisenberg chain is studied by means of stochastic series expansion quantum Monte Carlo simulation, applying the concept of directed loops. It is found that this system undergoes a phase transition to the random-singlet phase if the bond disorder is strong enough. Further a frustrated spin system is investigated. The frustration is introduced by having spins positioned on a triangular lattice. Performing a quantum Monte Carlo simulation for such a frustrated lattice leads to the occurrence of the infamous sign problem. This problem is investigated and it is shown that it is possible to use a meron cluster approach to reduce its effect for some specific models. The second topic concerns atomic condensates in optical lattices. A system of trapped bosonic atoms in such a lattice is described by a Bose-Hubbard model with an external confining potential. Using quantum Monte Carlo simulations it is demonstrated that the local density approximation that relates the observables of the unconfined and the confined models yields quantitatively correct results in most of the interesting parameter range of the model. Further, the same model with the addition that the atoms carry spin-1 is analyzed using density matrix renormalization group calculations. The anticipated phase diagram, with Mott insulating regions of dimerized spin-1 chains for odd particle density, and on-site singlets for even density is confirmed. Also an ultracold gas of bosonic atoms in an anisotropic two dimensional optical lattice is studied. It is found that if the system is finite in one direction it exhibits a quantum phase transition. The Monte Carlo simulations performed show that the transition is of Kosterlitz-Thouless type. / QC 20100628

A complex system is a system for which the statement "the whole is greater than the sum of its parts" holds. A network can be viewed as a backbone of a complex system. Combining the knowledge about the entities constituting the complex system with the properties of the interaction patterns we can get a better understanding of why the whole is greater than the sum. One of the purposes of network studies, is to relate the particular structural and dynamical properties of the network to the function it is designed to perform. In the present work I am briefly presenting some of the advances that have been achieved in the field of the complex networks together with the contributions which I have been involved in.

Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such systems are likely candidates for quantum computing, and experimentally feasible for instance as superconducting qubits. At quantum critical points the ground state of these systems is very complicated, and the entanglement is usually larger than at non-critical points. This entanglement can be used to identify the critical points through what we denote the entanglement signature, even for very small systems. From another perspective, it seems that the entanglement is an essential tool to find an unknown ground state, since this gives rise to a simple decomposition of the state.

This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.

The terahertz (THz) frequency range. 0.1 - 20 THz, exists between the microwave and infrared ranges and contains abundant information on the dynamics of charge and spin carriers in condensed matter systems. Since its advent two decades ago, THz spectroscopy has been extensively used to study a wide range of solid state materials, including typical semiconductors, conducting polymers, insulators, superconductors, and artificially grown structures such as quantum wells. In these systems, electronic and photonic events tend to occur on the time scale of tens to hundreds of femtoseconds, which results in many important excitations, resonances and dynamical phenomena in the THz frequency range. In this dissertation work, we have developed a typical THz time-domain spectroscopy (TDS) system to investigate the THz dynamics of quantum-confined electrons in two important types of carbon nanomaterial: single-walled carbon nanotubes (SWNTs) and graphene. Polarization dependent THz transmission measurements were conducted on a highly-aligned SWNT film on a sapphire substrate, revealing extremely high anisotropy: virtually no attenuation was observed when the polarization of the THz beam was perpendicular to the nanotube axis, while the THz beam was strongly absorbed when its polarization was parallel to the tube axis. From the measured absorption anisotropy, we calculated the reduced linear dichrosim to be 3, corresponding to a nematic order parameter of 1. These observations are a direct result of the one-dimensional nature of conduction electrons in the nanotubes and at the same time, demonstrate that any misalignment of nanotubes in the film mast have characteristic length scales much smaller than the wavelengths used in these experiments (1.5 mm - 150 μm). Based on this work, an ideal THz linear polarizer built with parallel stacks of such aligned SWNT films was synthesized, exhibiting a degree of polarization of 99.9% throughout the frequency range 0.2 - 2.2 THz and a high extinction ratio of 10 -3 (or 30 dB). The THz complex conductivity of the thin SWNT film was extracted through a proper model directly from the TDS data without Kramers-Kronig analysis. Both real and imaginary parts of the conductivity showed a non-Drude frequency dependence, indicating the presence of plasmon-dipole resonance at higher frequencies. Finally, the optical conductivity of large-area. graphene grown from solid state carbon source was studied in a wide spectral range (7 cm -1 - 9500 cm -1 ) using THz-TDS and Fourier transform infrared spectroscopy. We observed that the Fermi level E f of graphene could be tuned by both electrical gating and thermal annealing. The optical conductivity measured at different carrier concentrations exhibited Drude-like frequency dependence, and different 2 E f onsets in the spectrum were probed as well.

This thesis compared anionic polyelectrolyte wrapping stabilization with poly(sodium 4-stryene-sulfonate), (PSS), polyelectrolyte and methoxy (polyethylene glycol)-thiol (mPEG (5000) -SH) strategies. From this data the critical gold nanorod (GNR) and cetyl-trimethylammonium bromide (CTAB) concentration ratio needed for GNR stabilization was determined using optical and chemical extraction methods. This was followed by functionalization with a heterobifunctional Polyethylene glycol (PEG) linker, such as a-thio-w-carboxy poly(ethylene glycol) termed t-PEG-c and carbodiimide chemistries for antibody linkage with Immunoglobulin G (IgG), and epidermal growth factor receptor (EGFR) based Human Epidermal growth factor Receptor 2 (Her2), and Cetuximab (C225) antibodies, for in vitro cancer cell targeting. Confocal, two-photon luminescence (TPL), and dark scattering microscopy, and fluorescence, zeta potential, and Nanoparticle Enzyme-linked immunosorbent assay (ELISA) were used to monitor changes to the GNR surface. An untreatable form of bladder cancer was then studied using the t-GNR-PEG-c-Ab bioconjugates with C225 antibody, which housed a glyceraldehyde-3-phosphate (GAPDH), Fluorescein isothiocyanate (FITC) labeled siRNA, termed GAPDH-siRNA-FITC, which was included within a Luciferase based plasmid. A salt based electrostatic heating method was used to trap the GAPDH-siRNA-FITC from the PEG layer by activating the PEG polymer pour point, while a laser based heating system was used for in vitro release inside cancer cells. The down regulation of the GAPDH gene was targeted by the siRNA. as GAPDH has been shown to be up-regulated in many cancers and down-regulated by chemotherapeutic drugs. Cell culture, and subsequent imaging by transmission electron microscopy (TEM), TPL and confocal microscopy were used to view the internalized conjugates, and reverse transcriptase polymerase chain reaction (RT-PCR) were used to determine if the release of the GAPDH-siRNA caused a reduction in the expression of GAPDH-mRNA. Plasmonic gene silencing of the gene by the GAPDH-siRNA was then compared to a lipid based Dharmafect control in terms of transfection ability. RT-PCR results evidenced gene silencing of the plasmonic-GAPDH-siRNA vector when compared to the Dharmafect control. Silencing likely resulted from the zwitterionic charges of the plasmonic vector and the encapsulated GAPDH-siRNA, which yielded near neutral charge tendencies. This differs significantly from the Dharmafect lipid vector, which is cationic in nature. Endosomal release of the plasmonic vector is further enhanced by the laser excitation of the GNR at the longitudinal surface plasmon resonance (LSPR), which allows for the endosomal release of the GAPDH-siRNA through pore formation leading to cytoplasmic transport and subsequent gene silencing. Near neutral charges were welcomed in this plasmonic gene therapy study as they tend to favor endosomal release, pore formation, and transport.

Single-walled carbon nanotubes (SWNTs) are one of the leading candidate materials to realize novel nanoscale photonic devices. In order to assess their performance characteristics as optoelectronic materials, it is crucial to examine their optical properties in highly non-equilibrium situations such as high magnetic fields, low temperatures, and under high photoexcitation. Therefore, we present our latest result on the magnetic susceptibility anisotropy of metallic carbon nanotubes due to the Aharonov-Bohm effect. Here, we performed magnetic linear dichroism on a metallic-enriched HiPco SWNT sample utilizing a 35 T Hybrid Magnet to measure absorption with light polarization both perpendicular and parallel to the magnetic field. By relating these values with the nematic order parameter for alignment, we found that the metallic carbon nanotubes do not follow a strict diameter dependence across the 7 chiralities present in our sample. In addition to the studying the absorption properties exhibited at high magnetic field, we performed temperature-dependent (300 K to 11 K) photoluminescence (PL) on HiPco SWNTs embedded in an ι -carrageenan matrix utilizing intense fs pulses from a wavelength-tunable optical parametric amplifier. We found that for each temperature the PL intensity saturates as a function of pump fluence and the saturation intensity increases from 300 K to a moderate temperature around 100-150 K. Within the framework of diffusion-limited exciton-exciton annihilation (EEA), we successfully estimated the density of 1D excitons in SWNTs as a function of temperature and chirality. These results coupled with our results of magnetic brightening, or an increase in PL intensity as a function of magnetic flux through each SWNT due to the Aharonov-Bohm effect, yield great promise that in the presence of a high magnetic field the density of excitons can be further increased.

Electrical conduction at the single molecule scale has been studied extensively with molecular nanojunctions. Measurements have revealed a wealth of interesting physics. I3owever; our understanding is hindered by a lack of methods for simultaneous local imaging or spectroscopy to determine the conformation and local environment of the molecule of interest. Optical molecular spectroscopies have made significant progress in recent years, with single molecule sensitivity achieved through the use of surface-enhanced spectroscopies. In particular surface-enhanced Raman spectroscopy (SERS) has been demonstrated to have single molecule sensitivity for specific plasmonic structures. Many unanswered quest ions remain about the SERS process, particularly the role of chemical enhancements of the Raman signal. The primary goal of the research presented here is to combine both electrical and optical characterization techniques to obtain a more complete picture of electrical conduction at the single or few molecule level. We have successfully demonstrated that nanojunctions are excellent SERS substrates with the ability to achieve single molecule sensitivity. This is a major accomplishment with practical applications in optical sensor design. We present a method for mass producing nanojunctions with SERS sensitivity optimized through computer modeling. We have demonstrated simultaneous optical and electrical measurements of molecular junctions with single molecule electrical and SERS sensitivity. Measurements show strong correlations between electrical conductance and changes to the SERS response of nanojunctions. These results allow for one of the most conclusive demonstrations of single molecule SERS to date. This measurement technique provides the framework for three additional studies discussed here as well as opening up the possibilities for numerous other experiments. One measurement examines heating in nanowires rather than nanojunctions. We observe that, the electromigration process used to turn Pt nanowires into nanojunctions heats the wires to temperatures in excess of 1000 K, indicating that thermal decomposition of molecules on the nanowire is a major problem. Another measurement studies optically driven currents in nanojunctions. The photocurrent is a result of rectification of the enhanced optical electric field in the nanogap. From low frequency electrical measurements we are able to infer the magnitude of the enhanced electric field, with inferred enhancements exceeding 1000. This work is significant to the field of plasmonics and shows the need for more complete quantum treatments of plasmonic structures. Finally we investigate electrical and optical heating in molecular nanojunctions. Our measurements show that molecular vibrations and conduction electrons in nano-junctions under electrical bias or laser illumination can be driven from equilibrium to temperatures greater than 600 K. We observe that individual vibrations are also not in thermal equilibrium with one another. Significant heating in the conduction electrons in the metal electrodes was observed which is not expected in the ballistic tunneling model for electrons in nanojunctions this indicates a need for a more completely energy dissipation theory for nanojunctions.

Silicon oxide (SiO x 1 ∠ x [∠, double =]2) has long been used and considered as a passive and insulating component in the construction of electronic devices. In contrast, here the active role of SiO x in constructing a type of resistive switching memory is studied. From electrode-independent electrical behaviors to the visualization of the conducting filament inside the SiO x matrix, the intrinsic switching picture in SiO x is gradually revealed. The thesis starts with the introduction of some similar phenomenological switching behaviors in different electronic structures (Chapter 1), and then generalizes the electrode-material-independent electrical behaviors on SiO x substrates, providing indirect evidence to the intrinsic SiO x switching (Chapter 2). From planar nanogap systems to vertical sandwiched structures, Chapter 3 further discusses the switching behaviors and properties in SiO x . By localization of the switching site, the conducting filament in SiO x is visualized under transmission electron microscope using both static and in situ imaging methods (Chapter 4). With the intrinsic conduction and switching in SiO x largely revealed, Chapter 5 discusses its impact and implications to the molecular electronics and nanoelectronics where SiO x is constantly used. As comparison, another type of memory effect in semiconductors (carbon nanotubes) based on charge trapping at the semiconductor/SiO x interface is discussed (Chapter 6).

The electronic structure and optical properties of metallic nanoparticles are theoretically investigated front first principles. An efficient implementation of time-dependent density functional theory allows a fully quantum mechanical description of systems large enough to display collective electron oscillations and surface plasmon modes. The results are compared with traditional classical electrodynamical approaches. Different regimes of interest are identified, both where classical electrodynamical models yield accurate descriptions, and where quantum effects are indispensable for understanding plasmonic properties in nanostructures. The limits of validity of classical electrodynamics are clearly established for the study of a variety of relevant geometries.