Experimental Measurement of the Berry Curvature from Anomalous Transport

Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can be related to global topological invariants such as those classifying quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a wave packet. Here, we experimentally demonstrate for the first time that wave packet dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time-evolution of a wave packet in a 1D geometrical "charge" pump, where the Berry curvature leads to an anomalous displacement of the wave packet under pumping. This is both the first direct observation of Berry curvature effects in an optical system, and, more generally, the proof-of-principle demonstration that semi-classical dynamics can serve as a high-resolution tool for mapping out geometrical properties

Optical mesh lattices with PT-symmetry

We investigate a new class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response is studied in both the passive and parity-time (PT) symmetric regime. The possibility of band merging and the emergence of exceptional points along with the associated optical dynamics are considered in detail both above and below the PT-symmetry breaking point. Finally unidirectional invisibility in PT-synthetic mesh lattices is also examined along with possible superluminal light transport dynamics.Comment: 14 pages, 17 figures, published in Physical Review

Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green's operators is again a generalized Green's operator for the product of the corresponding differential operators and which boundary problem it solves. Moreover, we show that---provided a factorization of the underlying differential operator---a generalized boundary problem can be factored into lower order problems corresponding to a factorization of the respective Green's operators. We illustrate our results by examples using the Maple package IntDiffOp, where the presented algorithms are implemented.Comment: 19 page

An improved method for high-throughput quantification of autophagy in mammalian cells

Autophagy is a cellular homeostatic pathway with functions ranging from cytoplasmic protein turnover to immune defense. Therapeutic modulation of autophagy has been demonstrated to positively impact the outcome of autophagy-dysregulated diseases such as cancer or microbial infections. However, currently available agents lack specificity, and new candidates for drug development or potential cellular targets need to be identified. Here, we present an improved method to robustly detect changes in autophagy in a high-throughput manner on a single cell level, allowing effective screening. This method quantifies eGFP-LC3B positive vesicles to accurately monitor autophagy. We have significantly streamlined the protocol and optimized it for rapid quantification of large numbers of cells in little time, while retaining accuracy and sensitivity. Z scores up to 0.91 without a loss of sensitivity demonstrate the robustness and aptness of this approach. Three exemplary applications outline the value of our protocols and cell lines: (I) Examining autophagy modulating compounds on four different cell types. (II) Monitoring of autophagy upon infection with e.g. measles or influenza A virus. (III) CRISPR/Cas9 screening for autophagy modulating factors in T cells. In summary, we offer ready-to-use protocols to generate sensitive autophagy reporter cells and quantify autophagy in high-throughput assays

Spawning rings of exceptional points out of Dirac cones

The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformations of the Dirac cone often reveal intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain

Optical Properties of Highly Conductive SrMoO₃ Oxide Thin Films in the THz Band and Beyond

Strontium molybdate (SrMoO₃) thin films are grown epitaxially by pulsed laser deposition onto gadolinium scandate (GdScO₃) substrates and characterized in the terahertz (THz) and visible part of the electromagnetic spectrum. X-ray diffraction measurements prove a high crystallinity and phase-pure growth of the thin films. The high-quality SrMoO₃ thin films feature a room temperature DC conductivity of around 3 1/μΩm. SrMoO₃ is characterized in the THz frequency range by time domain spectroscopy. The resulting AC conductivity is in excellent agreement with the DC value. A Lorentz-Drude oscillator approach models the THz and visible conductivity of SrMoO₃ very well. We compare the results of the SrMoO₃ thin films to a standard, sputtered gold film, with a resulting THz conductivity of 8 1/μΩm. The comparison demonstrates that oxide thin film–based devices can play an important role in future THz technology

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

International audienceWe consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay