Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically non-trivial phases of matter with ultracold atoms has become a major focus of cold atom experiments. However, several obvious differences exist between cold atom and solid state systems, for instance the finite size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states which belong to a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.Comment: 12 pages, 10 figures, updated figures and minor text correction

Photonic currents in driven and dissipative resonator lattices

Arrays of coupled photonic cavities driven by external lasers represent a highly controllable setup to explore photonic transport. In this paper we address (quasi)-steady states of this system that exhibit photonic currents introduced by engineering driving and dissipation. We investigate two approaches: in the first one, photonic currents arise as a consequence of a phase difference of applied lasers and in the second one, photons are injected locally and currents develop as they redistribute over the lattice. Effects of interactions are taken into account within a mean-field framework. In the first approach, we find that the current exhibits a resonant behavior with respect to the driving frequency. Weak interactions shift the resonant frequency toward higher values, while in the strongly interacting regime in our mean-field treatment the effect stems from multiphotonic resonances of a single driven cavity. For the second approach, we show that the overall lattice current can be controlled by incorporating few cavities with stronger dissipation rates into the system. These cavities serve as sinks for photonic currents and their effect is maximal at the onset of quantum Zeno dynamics.Comment: 12 pages, 11 figure

Creating exotic condensates via quantum-phase-revival dynamics in engineered lattice potentials

In the field of ultracold atoms in optical lattices a plethora of phenomena governed by the hopping energy $J$ and the interaction energy $U$ have been studied in recent years. However, the trapping potential typically present in these systems sets another energy scale and the effects of the corresponding time scale on the quantum dynamics have rarely been considered. Here we study the quantum collapse and revival of a lattice Bose-Einstein condensate (BEC) in an arbitrary spatial potential, focusing on the special case of harmonic confinement. Analyzing the time evolution of the single-particle density matrix, we show that the physics arising at the (temporally) recurrent quantum phase revivals is essentially captured by an effective single particle theory. This opens the possibility to prepare exotic non-equilibrium condensate states with a large degree of freedom by engineering the underlying spatial lattice potential.Comment: 9 pages, 6 figure

Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi--metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi--metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.Comment: 4+ pages, 4 figures; includes Supplemental Material (5 pages). Published versio

Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.2$. This is in good agreement with recent analytical results.Comment: 14 pages in plain TeX, 6 figures upon reques

Multilayer Mirrors for Attosecond Pulse Shaping between 30 and 200 eV

Attosecond (as) physics has become a wide spreaded and still growing research field over the last decades. It allows for probing and controlling core- and outer shell electron dynamics with never before achieved temporal precision. High harmonic generation in gases in combination with advanced extreme ultraviolet (XUV ) optical components enable the generation of isolated attosecond pulses as required for absolute time measurements. But until recently, single attosecond pulse generation has been restricted to the energy range below 100 eV due to the availability of sources and attosecond optics. Multilayer mirrors are the up to date widest tunable optical components in the XUV and key components in attosecond physics from the outset. In this thesis, the design, fabrication and measurement of periodic and aperiodic XUV multilayer mirrors and their application in the generation and shaping of isolated attosecond pulses is presented. Two- and three material coatings based on a combination of molybdenum, silicon, boron carbide, lanthanum and scandium covering the complete spectral range between 30 and 200 eV are developed and characterized. Excellent agreement between reflectivity simulations and experiments is based on the highly stable ion beam sputter deposition technique. It allows for atomically smooth deposition and the realization of aperiodic multilayer structures with high precision and reproducibility. XUV reflectivity simulation of lanthanum containing multilayer coatings are based on an improved measured set of optical constants, introduced in this thesis. This work enabled the generation of the shortest ever measured isolated light pulses so far, the creation of the first isolated attosecond pulses above 100 eV , the first demonstration of absolute control of the “attochirp” by means of multilayer mirrors and the formation of spectrally cleaned attosecond pulses, in a spectral region which lacks appropriate filter materials, for a never before achieved combination of spectral and temporal resolution at 125 eV . Here presented concepts are in principle not restricted to specific energies or experimental set-ups and may be extended in the near future to enter completely new regimes of ultrashort physics