arXiv subjects

Stefano Longhi

Publications and source records attributed to Stefano Longhi.

At least 73 records · Page 4Linked to original sources

arXiv2022

Non-Hermitian topological mobility edges and transport in photonic quantum walks

In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e. asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice: while ballistic transport is allowed in the former case, pseudo dynamical localization is observed in the latter case. The results are illustrated by considering non-Hermitian photonic quantum walks in synthetic mesh lattices.

quant-ph↗

arXiv2022

Non-Hermitian laser arrays with tunable phase locking

Inspired by the idea of non-Hermitian spectral engineering and non-Hermitian skin effect, a novel design for stable emission of coupled laser arrays with tunable phase locking and strong supermode competition suppression is suggested. We consider a linear array of coupled resonators with asymmetric mode coupling displaying the non-Hermitian skin effect and show that, under suitable tailoring of complex frequencies of the two edge resonators, the laser array can stably emit in a single extended supermode with tunable phase locking and with strong suppression of all other skin supermodes. The proposed laser array design offers strong robustness against both structural imperfections of the system and dynamical instabilities typical of semiconductor laser arrays.

physics.optics↗

arXiv2022

Self-healing of non-Hermitian topological skin modes

A unique feature of non-Hermitian (NH) systems is the NH skin effect, i.e. the edge localization of an extensive number of bulk-band eigenstates in a lattice with open or semi-infinite boundaries. Unlike extended Bloch waves in Hermitian systems, the skin modes are normalizable eigenstates of the Hamiltonian that originate from the intrinsic non-Hermitian point-gap topology of the Bloch band energy spectra. Here we unravel a fascinating property of NH skin modes, namely self-healing, i.e. the ability to self-reconstruct their shape after being scattered off by a space-time potential.

quant-ph↗

arXiv2022

Anomalous mobility edges in one-dimensional quasiperiodic models

Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite band of critical states. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.

cond-mat.dis-nn↗

arXiv2021

Bulk-edge correspondence and trapping at a non-Hermitian topological interface

In Hermitian systems, according to the bulk-edge correspondence interfacing two topological optical media with different bulk topological numbers implies the existence of edge states, which can trap light at the interface. However, such a general scenario can be violated when dealing with non-Hermitian systems. Here we show that interfacing two semi-infinite Hatano-Nelson chains with different bulk topological numbers can result in the existence of infinitely many edge (interface) states, however light waves cannot be rather generally trapped at the interface.

physics.optics↗

arXiv2021

Selective and tunable excitation of topological non-Hermitian skin modes

Non-Hermitian lattices under semi-infinite boundary conditions sustain an extensive number of exponentially-localized states, dubbed non-Hermitian skin modes. Such states can be predicted from the nontrivial topology of the energy spectrum under periodic boundary conditions via a bulk-edge correspondence. However, the selective excitation of the system in one among the infinitely-many topological skin edge states is challenging both from practical and conceptual viewpoints. In fact, in any realistic system with a finite lattice size most of skin edge states collapse and become metastable states. Here we suggest a route toward the selective and tunable excitation of topological skin edge states which avoids the collapse problem by emulating semi-infinite lattice boundaries via tailored on-site potentials at the edges of a finite lattice. We illustrate such a strategy by considering a non-Hermitian topological interface obtained by connecting two Hatano-Nelson chains with opposite imaginary gauge fields, which is amenable for a full analytical treatment.

quant-ph↗

arXiv2021

Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices

Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices are deemed to be protected by chiral symmetry, exhibiting quantized Zak phases and protected edge states, but not for all cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry by engineering one-dimensional zigzag photonic lattices, where the long-range hopping breaks chiral symmetry but ensures the existence of inversion symmetry. By the averaged mean displacement method, we detect topological invariants directly in the bulk through the continuous-time quantum walk of photons. Our results demonstrate that inversion symmetry protects the quantized Zak phase, but edge states can disappear in the topological nontrivial phase, thus breaking the conventional bulk-boundary correspondence. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.

physics.optics↗

arXiv2021

Non-Hermitian skin effect beyond the tight-binding models

The energy bands of non-Hermitian systems exhibit nontrivial topological features that arise from the complex nature of the energy spectrum. Under periodic boundary conditions (PBC), the energy spectrum describes rather generally closed loops in complex plane, characterized by integer nonzero winding numbers. Such nontrivial winding provides the topological signature of the non-Hermitian skin effect (NHSE), i.e. the macroscopic condensation of bulk states at the lattice edges under open boundary conditions (OBC). In spite of the great relevance of band winding in the non-Hermitian topological band theory and the related NHSE, most of current results rely on tight-binding models of non-Hermitian systems, while exact Bloch wave function analysis of the NHSE and related topological band theory is still lacking. While tight-binding models can correctly describe narrow-band electronic states with a relatively weak degree non-Hermiticity, they are not suited to describe high-energy wide-band electronic states and/or regimes corresponding to strong non-Hermiticity. Here we consider the single-particle continuous Schrödinger equation in a periodic potential, in which non-Hermiticity is introduced by an imaginary vector potential in the equation, and show that the NHSE is ubiquitous under OBC and characterized by a non-vanishing integer winding number, even thought the energy spectrum under PBC always comprises an open curve, corresponding to high-energy electronic states. We also show that the interior of the PBC energy spectrum corresponds to the complex eigenenergies sustaining localized (edge) states under semi-infinite boundary conditions.

quant-ph↗

arXiv2021

Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation

Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap, the phase transition is of universal form and described by a non-Hermitian Dirac equation with Lorentz-symmetry violation. A simple photonic system displaying such a phase transition is discussed, which is based on light coupling in co-propagating gratings.

physics.optics↗

arXiv2021

Dispersive bands of bound states in the continuum

Bound states in the continuum (BICs), i.e. highly-localized modes with energy embedded in the continuum of radiating waves, have provided in the past decade a new paradigm in optics and photonics, especially at the nanoscale, with a range of applications from nano photonics to optical sensing and laser design. Here we introduce the idea of a crystal made of BICs, in which an array of BICs are indirectly coupled via a common continuum of states resulting in a tight-binding dispersive energy miniband embedded in the spectrum of radiating waves. The results are illustrated for a chain of optical cavities side-coupled to a coupled-resonator optical waveguide (CROW) with non-local contact points.

physics.optics↗

arXiv2021

Intermittent decoherence blockade in a chiral ring environment

It has long been recognized that emission of radiation from atoms is not an intrinsic property of individual atoms themselves, but it is largely affected by the characteristics of the photonic environment and by the collective interaction among the atoms. A general belief is that preventing full decay and/or decoherence requires the existence of dark states, i.e., dressed light-atom states that do not decay despite the dissipative environment. Here, we show that, contrary to such a common wisdom, decoherence suppression can be intermittently achieved on a limited time scale, without the need for any dark state, when the atom is coupled to a chiral ring environment, leading to a highly non-exponential staircase decay. This effect, that we refer to as intermittent decoherence blockade, arises from periodic destructive interference between light emitted in the present and light emitted in the past, i.e., from delayed coherent quantum feedback.

quant-ph↗

arXiv2021

Non-Hermitian Maryland Model

Non-Hermitian systems with aperiodic order display phase transitions that are beyond the paradigm of Hermitian physics. Unfortunately, owing to the incommensurability of the potential most of known non-Hermitian models are not integrable. This motivates the search for exactly solvable models, where localization/delocalization phase transitions, mobility edges in complex plane and their topological nature can be unraveled. Here we present an exactly solvable model of quasi crystal, which is a non-pertrurbative non-Hermitian extension of a famous integrable model of quantum chaos proposed by Grempel {\it at al.} [Phys. Rev. Lett. {\bf 49}, 833 (1982)] and dubbed the Maryland model. Contrary to the Hermitian Maryland model, its non-Hermitian extension shows a richer scenario, with a localization-delocalization phase transition via topological mobility edges in complex energy plane.

quant-ph↗

arXiv2021

Inverse Anderson transition in photonic cages

Transport inhibition via Anderson localization is ubiquitous in disordered periodic lattices. However, in crystals displaying only flat bands disorder can lift macroscopic band flattening, removing geometric localization and enabling transport in certain conditions. Such a striking phenomenon, dubbed inverse Anderson transition and predicted for three-dimensional flat band systems, has thus far not been directly observed. Here we suggest a simple quasi one-dimensional photonic flat band system, namely an Aharonov-Bohm photonic cage, in which correlated binary disorder induces an inverse Anderson transition and ballistic transport.

physics.optics↗

arXiv2021

Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model

We derive analytical results on energy spectral phase transitions and deformations in the simplest model of one-dimensional lattice displaying the non-Hermitian skin effect, namely the Hatano-Nelson model with unidirectional hopping, under on-site potential uncorrelated disorder in complex energy plane. While the energy spectrum under open boundary conditions (OBC) exactly reproduces the distribution of on-site potential disorder, the energy spectrum under periodic boundary conditions (PBC) undergoes spectral deformations, from one or more closed loops in the fully delocalized phase, with no overlap with the OBC spectrum, to a mixed spectrum (closed loops and some OBC energies) in the mobility edge phase, to a complete collapse toward the OBC spectrum in the bulk localized phase. Such transitions are observed as the strength of disorder is increased. Depending on the kind of disorder, different interesting behaviors are found. In particular, for continuous disorder with a radial distribution in complex energy plane it is shown that in the delocalized phase the energy spectrum under PBC is locked and fully insensitive to disorder, while transition to the bulk localized phase is signaled by the change of a topological winding number. When the disorder is described by a discrete distribution, the bulk localization transition never occurs, while topological phase transitions associated to PBC energy spectral splittings can be observed.

cond-mat.dis-nn↗

arXiv2021

Rabi oscillations of bound states in the continuum

Photonic bound states in the continuum (BICs) are special localized and non-decaying states of a photonic system with a frequency embedded into the spectrum of scattered states. The simplest photonic structure displaying a single BIC is provided by two waveguides side-coupled to a common waveguide lattice, where the BIC is protected by symmetry. Here we consider such a simple photonic structure and show that, breaking mirror symmetry and allowing for non-nearest neighbor couplings, a doublet of quasi-BIC states can be sustained, enabling weakly-damped embedded Rabi oscillations of photons between the waveguides.

physics.optics↗

arXiv2021

Phase transitions in a non-Hermitian Aubry-André-Harper model

The Aubry-André-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value $V_c$ of the quasiperiodic potential amplitude $V$. In terms of dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent $δ$ of wave packet spreading, with $δ=1$ in the delocalized phase $V V_c$ (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed $v(V)$ of excitation transport in the lattice, which is a continuous function of potential amplitude $V$ and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-André-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous not only in the diffusion exponent $δ$, but also in the speed $v$ of ballistic transport. This means that, even very close to the spectral phase transition point, rather counter-intuitively ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as $V$ is increased above zero, i.e. surprisingly disorder in the lattice can result in an enhancement of transport.

cond-mat.dis-nn↗

arXiv2021

Maryland model in optical waveguide lattices

The Maryland model was introduced more than 30 years ago as an integrable model of localization by aperiodic order. Even though quite popular and rich of fascinating mathematical properties, this model has so far remained quite artificial, as compared to other models displaying dynamical localization like the periodically-kicked quantum rotator or the Aubry-Andre$^{\prime}$ model. Here we suggest that light propagation in a polygonal optical waveguide lattice provides a photonic realization of the Maryland model and enables to observe a main prediction of this model, namely fragility of wave localization in the commensurate potential limit.

physics.optics↗

arXiv2020

Chiral excitation and effective bandwidth enhancement in tilted coupled optical waveguide lattices

Light escape from an optical waveguide side-coupled to a waveguide lattice provides a photonic analogue of the spontaneous emission process of an excited two-level atom in a one-dimensional array of cavities. According to the Fermi golden rule the decay process is prevented when the atomic resonance frequency falls in a stop band of the lattice, while time-reversal symmetry ensures that the spontaneously emitted photon has equal probability to propagate in opposite directions of the array. This scenario is drastically modified when the quantum emitter drifts along the lattice at a constant speed. In the waveguide optics analogue the atomic drift is emulated by the introduction of a slight geometric tilt of the waveguide axis from the lattice axis. In this setting light excitation in the array is chiral, i.e. light propagates in a preferred direction of the lattice, and coupling is allowed even though the waveguide is far detuned from the tight-binding lattice band.

physics.optics↗