The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Enhanced light emission in active silicon-on-insulator photonic crystal slabs and slot waveguides

We present experimental measurements on Silicon-on-insulator (SOI) photonic crystal slabs with an active layer containing Er3+ ions-doped Silicon nanoclusters (Si-nc), showing strong enhancement of 1.54 μm emission at room temperature. We provide a systematic theoretical analysis to interpret such results. In order to get further insight, we discuss experimental data on the guided luminescence of unpatterned SOI planar slot waveguides, which show enhanced light emission in transverse-magnetic (TM) modes over transverse-electric (TE) ones. ©2007 IEEE.

Ultracompact triplexer by coupling and decoupling of multiple photonic crystal waveguides

We investigate numerically the self-imaging effect in a system of multiple coupled photonic crystal waveguides (M-CPCWs) with asymmetric coupling. Then two couplers of 2-CPCWs and 3-CPCWs are cascaded to form an ultracompact triplexer by employing coupling and decoupling of M-CPCWs. The wavelength of 1310 nm propagates along the input direction because the M-CPCWs are decoupled at the same decoupling frequency. The other two wavelengths (1490 and 1550 nm) are separated by combining multimode interference and the dual mode coupling effect. Only by introducing a single defect near the crossing point between two output photonic crystal waveguides (PCWs) are the high extinction ratios for the three wavelengths achieved simultaneously.

A new way of uniform splitting of the optical power by directional coupling between the photonic crystal waveguides

Directional coupler can be constructed by putting multiple photonic crystal waveguides together. The propagation of the optical field entering this system symmetrically was analysed numerically according to self-imaging principle. On the basis of this structure, ultracompact multiway beam splitter was designed and the ones with three and four output channels were discussed in details as examples. By simply tuning the effective refractive index of two dielectric rods in the coupler symmetrically to induce the redistribution of the power of the optical field, uniform or free splitting can be achieved. Compared with the reported results, this way is simpler, more feasible and more efficient and has extensive practical value in future photonic integrated circuits.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

Structure tuning of line-defect waveguides based on silicon-on-insulator photonic crystal slabs

We present fabrication and experimental measurement of a series of photonic crystal waveguides. The complete devices consist of an injector taper down from 3 mu m into a triangular-lattice air-hole single-line-defect waveguide with lattice constant from 410nm to 470nm and normalized radius 0.31. We fabricate these devices on a siliconon-insulator substrate and characterize them using a tunable laser source over a wavelength range from 1510nm to 1640nm. A sharp attenuation at photonic crystal waveguide mode edge is observed for most structures. The edge of guided band is shifted about 30nm with the 10nm increase of the lattice constant. We obtain high-efficiency light propagation and broad flat spectrum response of the photonic crystal waveguides.

Active planar waveguides based on sol-gel Er3+-doped SiO2-ZrO2 for photonic applications: Morphological, structural and optical properties

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

PbO-GeO2 rib waveguides for photonic applications

This work presents for the first time to our knowledge the fabrication and characterization of rib waveguides produced with PbO-GeO2 (PGO) thin films. The target was manufactured using pure oxides ( 60 PbO-40 GeO2, in wt%) and amorphous thin films were produced with the RF sputtering technique. PGO thin films present small absorption in the visible and in the near infrared and refractive index of similar to 2.0. The definition of the rib waveguide structure was made using conventional optical lithography followed by plasma etching, performed in a Reactive Ion Etching (RIE) reactor. Light propagation mode in the waveguide structure was analyzed using integrated optic simulation software. Optical loss measurements were performed to determine the propagation loss at 633 nm, for ribs with height of 70 nm and width of 3-5 mu m; experimental values around 2 dB/cm were found for the propagation loss and confirmed the theoretical calculations. The results obtained demonstrate that PGO thin films are potential candidates for application in integrated optics. Published by Elsevier B.V.