Nonhermitian transport effects in coupled-resonator optical waveguides

Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., nonhermitian degeneracies at which not only the frequencies and decay rates coalesce but also the eigenmodes themselves. The non-hermitian corrections to the group velocity are largest in the regions around the exceptional points.Comment: 11 pages, 9 figure

Helical scattering and valleytronics in bilayer graphene

We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60° over a large energetic range in one of the valleys, and down to −60° in the other. In a Y-junction geometry, this can be used to create and detect valley polarization

Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices

We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The spectral properties of the higher Landau levels are constrained by a generalized time-reversal symmetry. In the setting of two-dimensional photonic crystal lasers, the anomaly directly affects the mode selection and lasing threshold while in three-dimensional photonic lattices it can be probed via beam dynamics.Comment: 5 pages, 2 figures, submitted to journal in May 2012. v2: final version, including supplemental material (5+2 pages, 2+3 figures

Nonreciprocal response theory of non-Hermitian mechanical metamaterials:response phase transition from the skin effect of zero modes

Nonreciprocal non-Hermitian systems provide an unconventional localization mechanism of topological zero modes via the non-Hermitian skin effect. While fundamental theoretical characterizations of this effect involve the biorthogonal system of right and left eigenmodes, the recent demonstration of this effect for a zero mode in a robotic metamaterial (Ghatak et al., arXiv:1907.11619) is based on the direct experimental observation of the conventional right eigenvectors. Here I show that such nonreciprocal mechanical metamaterials reveal their underlying biorthogonality in the directly observable response of the system to external excitation. Applied to the experiment, this nonreciprocal response theory predicts that the zero-mode skin effect coincides with an extended phase where the system is highly sensitive to physical perturbations, leading to a diverging response in the limit of a large system

Asymptotic boundary layer method for unstable trajectories : Semiclassical expansions for individual scar wavefunctions.

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field

Fundamental constraints on the observability of non-Hermitian effects in passive systems

Utilizing scattering theory, we quantify the consequences of physical constraints that limit the visibility of non-Hermitian effects in passive devices. The constraints arise from the fundamental requirement that the system obeys causality, and can be captured concisely in terms of an internal time-delay operator, which furthermore provides a direct quantitative measure of the visibility of specific non-Hermitian phenomena in the density of states. We illustrate the implications by contrasting different symmetry classes and non-Hermitian effects, including exceptional points and the non-Hermitian skin effect, whose underlying extreme mode nonorthogonality turns out to be effectively disguised

Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry

We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation-symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-hermitian versions of time-reversal symmetry, chirality and charge-conjugation) emerge dynamically.Comment: 4++ page

Degeneracy doubling and sublattice polarization in strain-induced pseudo-Landau levels

The degeneracy and spatial support of pseudo-Landau levels (pLLs) in strained honeycomb lattices systematically depends on the geometry -- for instance, in hexagonal and rectangular flakes the 0th pLL displays a twofold increased degeneracy, while the characteristic sublattice polarization of the 0th pLL is only fully realized in a zigzag-terminated triangle. These features are dictated by algebraic constraints in the atomistic theory, and signify a departure from the standard picture in which all qualitative differences between pLLs and Landau levels induced by a magnetic field trace back to the valley-antisymmetry of the pseudomagnetic field.Comment: 5 pages, 2 figure

Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators

PT-symmetric optical resonators combine absorbing regions with active, amplifying regions. The latter are the source of radiation generated via spontaneous and stimulated emission, which embodies quantum noise and can result in lasing. We calculate the frequency-resolved output radiation intensity of such systems and relate it to a suitable measure of excess noise and mode nonorthogonality. The line shape differs depending on whether the emission lines are isolated (as for weakly amplifying, almost-Hermitian systems) or overlapping (as for the almost-degenerate resonances in the vicinity of exceptional points associated with spontaneous PT-symmetry breaking). The calculations are carried out in the scattering input-output formalism, and are illustrated for a quasi-one-dimensional resonator setup. In our derivations, we also consider the more general case of a resonator in which the amplifying and absorbing regions are not related by symmetry