Topological invisibility in chiral mirror lattices

Photonic topological edge states in one-dimensional dimer chains have long been thought to be robust to structural perturbations by mapping the topological Su–Schrieffer–Heeger model of a solid-state system. However, the edge states at the two ends of a finite topological dimer chain will interact as a result of near-field coupling. This leads to deviation from topological protection by the chiral symmetry from the exact zero energy, weakening the robustness of the topological edge state. With the aid of non-Hermitian physics, the splitting frequencies of edge states can be degenerated again, with topological protection recovered by altering the gain or loss strength of the structure. This point of coalescence is known as the exceptional point (EP). The intriguing physical properties of EPs in topological structures give rise to many fascinating and counterintuitive phenomena. In this work, based on a finite non-Hermitian dimer chain composed of ultra-subwavelength resonators, we propose theoretically and verify experimentally that the sensitivity of topological edge states is greatly affected when the system passes through the EP. Using the EP of a non-Hermitian dimer chain, we realize a new sensor that is sensitive to perturbation of on-site frequency at the end of the structure and yet topologically protected from internal perturbation of site-to-site couplings. Our demonstration of a non-Hermitian topological structure with an EP paves the way for the development of novel sensors that are not sensitive to internal manufacturing errors but are highly sensitive to changes in the external environment.

Resonant transmission of light has been observed in symmetric Fibonacci TiO2/SiO2 multilayers, which is characterized by many perfect transmission peaks. The perfect transmission dramatically decreases when the mirror symmetry in the multilayer structure is deliberately disrupted. Actually, the feature of perfect transmission peaks can be considered as general evidence for dielectric multilayers with symmetric internal structure. It opens a unique way to control light propagation.

A comprehensive phase-shift analysis of ${\ensuremath{\pi}}^{+}\ensuremath{-}p$ elastic-scattering data at 310-Mev incident-pion laboratory kinetic energy has been performed. The experimental data utilized include measurements of the differential and total cross sections and of the recoil-proton polarization. The $D$-wave phase shifts were found to be definitely needed in order to attain an adequate fit to the data. A general search for phase-shift solutions was carried out, using $S$-, $P$-, and $D$-wave phase shifts. One solution\char22{}of the Fermi type\char22{}was found that fits the data significantly better than any of the other solutions obtained. The calculated errors in the phase shifts of this set vary from 0.4 to 0.6 deg. Because it was felt that these errors might be deceivingly restrictive, the effects of small nuclear $F$-wave phase shifts on the results of the analysis were investigated and were found to be large: not only are the uncertainties in the original Fermi-type solution increased, but additional sets of phase shifts arise that fit the data well. One of these new solutions is similar to the original Fermi set except that the magnitudes of the phase shifts in this new fit are in general larger than those in the initial solution, and the signs of the $D$-wave phase shifts are reversed. The nuclear phase shifts in the original Fermi solution and their rms errors are (when $F$-wave phase shifts are allowed): ${S}_{3,1}=\ensuremath{-}17.2\ifmmode\pm\else\textpm\fi{}2.6$ deg, ${P}_{3,1}=\ensuremath{-}2.9\ifmmode\pm\else\textpm\fi{}4.0$ deg, ${P}_{3,3}=135.0\ifmmode\pm\else\textpm\fi{}0.6$ deg, ${D}_{3,3}=3.1\ifmmode\pm\else\textpm\fi{}2.6$ deg, ${D}_{3,5}=\ensuremath{-}4.9\ifmmode\pm\else\textpm\fi{}2.1$ deg, ${F}_{3,5}=0.5\ifmmode\pm\else\textpm\fi{}0.6$ deg, ${F}_{3,7}=\ensuremath{-}0.6\ifmmode\pm\else\textpm\fi{}1.4$ deg. Although theory appears to favor this set, further theoretical and experimental evidence is desirable. The values given here for the first five phase shifts approximate the corresponding values obtained when the $F$-wave phase shifts were assumed negligible. However, all except ${P}_{3,3}$ fall outside the limits set by the small original errors. Inelastic-scattering processes were neglected during the phase-shift analysis. Calculations indicate that, if these processes could properly be taken into account, any changes in the quoted values of the phase shifts would probably be well within the corresponding errors given here. Extension of the phase-shift inquiries to include $G$ waves was attempted, but it was observed that the available data and theory do not allow the $G$-wave interaction to be significantly incorporated into the analysis.

We demonstrate a heterogeneous photonic metastructure involving monolayer graphene achieving a substantial Faraday rotation angle and nearly perfect transmittance simultaneously. This breaks the longstanding tradeoff between the Faraday rotation angle and the transmission coefficient in conventional magneto-optical devices. Faraday rotation is enhanced across the interface between two photonic crystals due to the presence of an interface mode, i.e. optical Tamm state, which presents a strong electromagnetic field confinement at the location of the graphene sheet. This interface mode also helps to maintain a nearly perfect optical transmission through the structure thanks to a resonant tunneling mechanism. This exciting result was achieved particularly in the quantum regime with low Fermi level.

In this article, we develop a unified perspective of unidirectional topological edge waves in nonreciprocal media. We focus on the inherent role of photonic spin in nonreciprocal gyroelectric media, i.e. magnetized metals or magnetized insulators. Due to the large body of contradicting literature, we point out at the outset that these Maxwellian spin waves are fundamentally different from well-known topologically trivial surface plasmon polaritons. We first review the concept of a Maxwell Hamiltonian in nonreciprocal media, which immediately reveals that the gyrotropic coefficient behaves as a photon mass in two dimensions. Similar to the Dirac mass, this photonic mass opens bandgaps in the energy dispersion of bulk propagating waves. Within these bulk photonic bandgaps, three distinct classes of Maxwellian edge waves exist – each arising from subtle differences in boundary conditions. On one hand, the edge wave solutions are rigorous photonic analogs of Jackiw-Rebbi electronic edge states. On the other hand, for the exact same system, they can be high frequency photonic counterparts of the integer quantum Hall effect, familiar at zero frequency. Our Hamiltonian approach also predicts the existence of a third distinct class of Maxwellian edge wave exhibiting topological protection. This occurs in an intriguing topological bosonic phase of matter, fundamentally different from any known electronic or photonic medium. The Maxwellian edge state in this unique quantum gyroelectric phase of matter necessarily requires a sign change in gyrotropy arising from nonlocality (spatial dispersion). In a Drude system, this behavior emerges from a spatially dispersive cyclotron frequency that switches sign with momentum. A signature property of these topological electromagnetic edge states is that they are oblivious to the contacting medium, i.e. they occur at the interface of the quantum gyroelectric phase and any medium (even vacuum). This is because the edge state satisfies open boundary conditions – all components of the electromagnetic field vanish at the interface. Furthermore, the Maxwellian spin waves exhibit photonic spin-1 quantization in exact analogy with their supersymmetric spin-1/2 counterparts. The goal of this paper is to discuss these three foundational classes of edge waves in a unified perspective while providing in-depth derivations, taking into account nonlocality and various boundary conditions. Our work sheds light on the important role of photonic spin in condensed matter systems, where this definition of spin is also translatable to topological photonic crystals and metamaterials.

We present detailed calculations of laser action in two-dimensional disordered systems in the localized regime. The systems are made of circular particles imbedded in an active dielectric medium, described by a population of four-level atoms. Without pumping the active medium, the existence of localized modes is studied as a function of the filling fraction and of the radius of the scattering particles. When pumping the active medium above threshold, we find that the localized modes of the passive system act as the regular modes of a conventional cavity. They are not modified by the presence of gain. By introducing local pumping of the atomic system, the spectrum of the laser emission is found to depend on the position of the pump in agreement with recent experimental results. It is shown that local pumping allows a selective excitation of individual localized modes.

We report long-lived, highly spatially localized plasmon states on the surface of nanoporous gold nanoparticles—nanosponges—with high excitation efficiency. It is well known that disorder on the nanometer scale, particularly in two-dimensional systems, can lead to plasmon localization and large field enhancements, which can, in turn, be used to enhance nonlinear optical effects and to study and exploit quantum optical processes. Here, we introduce promising, three-dimensional model systems for light capture and plasmon localization as gold nanosponges that are formed by the dewetting of gold/silver bilayers and dealloying. We study light-induced electron emission from single nanosponges, a nonlinear process with exponents of n≈5...7, using ultrashort laser pulse excitation to achieve femtosecond time resolution. The long-lived electron emission process proves, in combination with optical extinction measurements and finite-difference time-domain calculations, the existence of localized modes with lifetimes of more than 20 fs. These electrons couple efficiently to the dipole antenna mode of each individual nanosponge, which in turn couples to the far-field. Thus, individual gold nanosponges are cheap and robust disordered nanoantennas with strong local resonances, and an ensemble of nanosponges constitutes a meta material with a strong polarization independent, nonlinear response over a wide frequency range.

We investigate numerically, within the rotating wave approximation, the existence of stationary anharmonic localized modes in diatomic lattices, where the atoms are ordered according to the Thue-Morse sequence and the Fibonacci sequence, respectively. A symmetric potential with harmonic and quartic terms is used, and both the case of hard and soft anharmonicity is investigated. We find the existence of localized modes for frequencies not allowed in the harmonic approximation, both when we consider hard and soft anharmonicity in the potential. Above the top of the allowed frequency values, there turn out to be only modes with a hard anharmonicity. In contrast to the periodic chains previously investigated, we find for the Thue-Morse lattice even modes which seem to be stable in molecular-dynamics simulations.

The homogeneous and transport properties of a set of metallic fibers were studied. The existence of a plasma frequency was deduced and a precise formula for it was derived. A homogenized system for finite length ohmic wires was derived. Some numerical simulations were made to study the influence of disorder. The persistence of a low-frequency band gap was demonstrated numerically even in the case of a strong disorder. The existence of localized modes was explained in terms of the statistical properties of the medium.

Stability of Majorana bound states in the presence of spin-flip scattering

A topological insulator is realized via band inversions driven by the spin-orbit interaction. In the case of Z2 topological phases, the number of band inversions is odd and time-reversal invariance is a further unalterable ingredient. For topological crystalline insulators, the number of band inversions may be even but mirror symmetry is required. Here, we prove that the chalcogenide Bi2Te3 is a dual topological insulator: it is simultaneously in a Z2 topological phase with Z2 invariants (ν0;ν1ν2ν3) = (1;0 0 0) and in a topological crystalline phase with mirror Chern number -1. In our theoretical investigation we show in addition that the Z2 phase can be broken by magnetism while keeping the topological crystalline phase. As a consequence, the Dirac state at the (111) surface is shifted off the time-reversal invariant momentum Γ; being protected by mirror symmetry, there is no band gap opening. Our observations provide theoretical groundwork for opening the research on magnetic control of topological phases in quantum devices.

Current algebra calculation of ( ππ) s- wave phase shifts

Previously determined experimental drift velocities Vdr and ratios of lateral diffusion coefficient to mobility DT/µ have been refitted directly with a three parameter modified effective range theory (MER T) representation of the S wave phase shift, a one parameter fit to the P wave phase shift and fixed higher partial wave phase shifts. The MERT representation now extends to 1·0 eV, a threefold extension of the energy range of the MERT fit reported by Milloy et al. (1977). The total cross section derived from the phase shifts is also reported, together with the differential cross section at 1·0 eV which is compared with a previous experimental determination.

Using the $\frac{N}{D}$ technique, $T=\frac{1}{2}, \frac{3}{2}$ $P$- and $S$-wave phase shifts are calculated. The $T=\frac{1}{2}$ $P$- and $S$-wave phase shifts are also calculated in the Khuri-Regge representation. For the purpose of comparison with experiments, we use our phase shifts to calculate the angular distributions in the reaction ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}p{\ensuremath{\pi}}^{\ensuremath{-}}$.

Squeezed light is a critical resource in quantum sensing and information processing. Due to the inherently weak optical nonlinearity and limited interaction volume, considerable pump power is typically needed to obtain efficient interactions to generate squeezed light in bulk crystals. Integrated photonics offers an elegant way to increase the nonlinearity by confining light strictly inside the waveguide. For the construction of large-scale quantum systems performing many-photon operations, it is essential to integrate various functional modules on a chip. However, fabrication imperfections and transmission cross talk may add unwanted diffraction and coupling to other photonic elements, reducing the quality of squeezing. Here, by introducing the topological phase, we experimentally demonstrate the topologically protected nonlinear process of four-wave mixing, enabling the generation of squeezed light on a silica chip. We measure the cross-correlations at different evolution distances for various topological sites and verify the nonclassical features with high fidelity. The squeezing parameters are measured to certify the protection of cavity-free, strongly squeezed states. The demonstration of topological protection for squeezed light on a chip brings new opportunities for quantum integrated photonics, opening novel approaches for the design of advanced multi-photon circuits.