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Henning Schomerus

Publications and source records attributed to Henning Schomerus.

At least 55 records · Page 3Linked to original sources
arXiv2018

Topological dynamics and excitations in lasers and condensates with saturable gain or loss

We classify symmetry-protected and symmetry-breaking dynamical solutions for nonlinear saturable bosonic systems that display a non-hermitian charge-conjugation symmetry, as realized in a series of recent groundbreaking experiments with lasers and exciton polaritons. In particular, we show that these systems support stable symmetry-protected modes that mirror the concept of zero-modes in topological quantum systems, as well as symmetry-protected power-oscillations with no counterpart in the linear case. In analogy to topological phases in linear systems, the number and nature of symmetry-protected solutions can change. The spectral degeneracies signalling phase transitions in linear counterparts extend to bifurcations in the nonlinear context. As bifurcations relate to qualitative changes in the linear stability against changes of the initial conditions, the symmetry-protected solutions and phase transitions can also be characterized by topological excitations, which set them apart from symmetry-breaking solutions. The stipulated symmetry appears naturally when one introduces nonlinear gain or loss into spectrally symmetric bosonic systems, as we illustrate for one-dimensional topological laser arrays with saturable gain and two-dimensional flat-band polariton condensates with density-dependent loss.

cond-mat.mes-hall↗
arXiv2018

Nonlinear mode competition and symmetry-protected power oscillations in topological lasers

Topological photonics started out as a pursuit to engineer systems that mimic fermionic single-particle Hamiltonians with symmetry-protected modes, whose number can only change in spectral phase transitions such as band inversions. The paradigm of topological lasing, realized in three recent experiments, offers entirely new interpretations of these states, as they can be selectively amplified by distributed gain and loss. A key question is whether such topological mode selection persists when one accounts for the nonlinearities that stabilize such systems at their working point. Here we show that topological defect lasers can indeed stably operate in genuinely topological states. These comprise direct analogues of zero modes from the linear setting, as well as a novel class of states displaying symmetry-protected power oscillations, which appear in a spectral phase transition when the gain is increased. These effects show a remarkable practical resilience against imperfections, even if these break the underlying symmetries, and pave the way to harness the power of topological protection in nonlinear quantum devices.

physics.optics↗
arXiv2018

Bulk and edge-state arcs in non-hermitian coupled-resonator arrays

We describe the formation of bulk and edge arcs in the dispersion relation of two-dimensional coupled-resonator arrays that are topologically trivial in the hermitian limit. Each resonator provides two asymmetrically coupled internal modes, as realized in noncircular open geometries, which enables the system to exhibit non-hermitian physics. Neighboring resonators are coupled chirally to induce non-hermitian symmetries. The bulk dispersion displays Fermi arcs connecting spectral singularities known as exceptional points, and can be tuned to display purely real and imaginary branches. At an interface between resonators of different shape, one-dimensional edge states form that spectrally align along complex arcs connecting different parts of the bulk bands. We also describe conditions under which the edge-state arcs are free standing. These features can be controlled via anisotropy in the resonator couplings.

physics.optics↗
arXiv2017

Topological Hybrid Silicon Microlasers

Topological photonics provides a robust framework for strategically controlling light confinement and propagation dynamics. By exploiting the marriage between this notion and symmetry-constrained mode competition in an active setting, we experimentally demonstrate, for the first time, a hybrid silicon microlaser structure supporting a topologically protected zero-mode lasing. This mode is distributed over an integrated array of optical microrings, each supporting multiple modes that compete for gain. However, the mode competition is diminished in favor of a pre-defined topological state, which reflects the charge conjugation symmetry induced by the gain profile. Robust single-mode operation in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid-implemented on a silicon-on-insulator substrate, thereby readily suitable for integrated silicon photonics with potential applications in optical communication and computing.

physics.optics↗
arXiv2017

One-particle-density-matrix occupation spectrum of many-body localized states after a global quench

The emergent integrability of the many-body localized phase is naturally understood in terms of localized quasiparticles. As a result, the occupations of the one-particle density matrix in eigenstates show a Fermi-liquid-like discontinuity. Here we show that in the steady state reached at long times after a global quench from a perfect density-wave state, this occupation discontinuity is absent, reminiscent of a Fermi liquid at a finite temperature, while the full occupation function remains strongly nonthermal. We discuss how one can understand this as a consequence of the local structure of the density-wave state and the resulting partial occupation of quasiparticles. This partial occupation can be controlled by tuning the initial state and can be described by an effective temperature.

cond-mat.dis-nn↗
arXiv2017

Random matrix approaches to open quantum systems

Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic Processes and Random Matrices" in July 2015, we review the physical origins and mathematical structures of the underlying models, and collect key predictions which give insight into the typical system behaviour. In particular, we aim to give an idea how the different features are interlinked. The notes mainly focus on elastic scattering but also include a short detour to interacting systems, which we motivate by the overarching question of ergodicity. The first chapters introduce general notions from random matrix theory, such as the ten universality classes and ensembles of hermitian, unitary, positive-definite and non-hermitian matrices. We then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics and transport. The last chapter briefly touches on Anderson localization and localization in interacting systems.

cond-mat.dis-nn↗
arXiv2016

Partial chiral symmetry-breaking as a route to spectrally isolated topological defect states in two-dimensional artificial materials

Bipartite quantum systems from the chiral universality classes admit topologically protected zero modes at point defects. However, in two-dimensional systems these states can be difficult to separate from compacton-like localized states that arise from flat bands, formed if the two sublattices support a different number of sites within a unit cell. Here we identify a natural reduction of chiral symmetry, obtained by coupling sites on the majority sublattice, which gives rise to spectrally isolated point-defect states, topologically characterized as zero modes supported by the complementary minority sublattice. We observe these states in a microwave realization of a dimerized Lieb lattice with next-nearest neighbour coupling, and also demonstrate topological mode selection via sublattice-staggered absorption.

physics.optics↗
arXiv2016

One-particle density matrix characterization of many-body localization

We study a model of interacting fermions in one dimension subject to random, uncorrelated onsite disorder. The model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase (MBL). We propose a single-particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one-particle density matrix (OPDM) in many-body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single-particle states is a many-body effect, since without interactions the single-particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero-temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation-spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally-relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model.

cond-mat.dis-nn↗
arXiv2016

Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials

Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also use the gauge field to design waveguides in which sound propagates robustly, as a consequence of the change in topological polarization that occurs along a domain wall in the bulk of the metamaterial. By introducing dissipation, we can selectively enhance the domain-wall-bound topological sound mode, a feature that may be exploited for the design of sound amplification by stimulated emission of radiation - SASERs, the mechanical analogs of lasers.

cond-mat.mes-hall↗
arXiv2016

Universal sign-control of coupling in tight-binding lattices

We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be universally applied to all lattice configurations, as long as the individual sites can be detuned. We experimentally verify this method in laser-written photonic lattices and confirm both the magnitude and the sign of the coupling by interferometric measurements. Based on these findings, we demonstrate how such universal sign-flipped coupling links can be embedded into extended lattice structures to impose a $\mathbb{Z}_2$-gauge transformation. This opens a new avenue for investigations on topological effects arising from magnetic fields with aperiodic flux patterns or in disordered systems.

physics.optics↗
arXiv2015

Non-equilibrium steady states of ideal bosonic and fermionic quantum gases

We investigate non-equilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also non-trivial two-particle correlations, and quantum-jump-type Monte-Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a non-equilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose selected state.

cond-mat.quant-gas↗
arXiv2015

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.

cond-mat.mes-hall↗
arXiv2015

Many-body localization characterized from a one-particle perspective

We show that the one-particle density matrix $ρ$ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of $ρ$) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of $ρ$) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.

cond-mat.str-el↗
arXiv2014

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.

cond-mat.mes-hall↗
arXiv2014

Strain-induced modifications of transport in gated graphene nanoribbons

We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure, and finally becomes completely suppressed at larger strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudo-magnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which either originate from the coupling into Fabry-Perot states that extend through the system, or from the formation of states that are localized near the contacts, where the pseudo-magnetic field is largest. In particular, the n=0 pseudo-Landau level manifests itself via two groups of conductance resonances close to the charge neutrality point.

cond-mat.mes-hall↗
arXiv2014

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.

physics.optics↗
arXiv2013

From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators

I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions which can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales which govern the spectral transition from real to complex eigenvalues. The possible presence of magneto-optical effects (a finite vector potential) in multichannel systems leads to a variant (termed PTT' symmetry) which imposes the same spectral constraints as PT symmetry. I also provide multichannel versions of generalized flux-conservation laws.

quant-ph↗