non-Hermitian Effects Research Articles

Linear response theory for transport in non-Hermitian [formula omitted]-symmetric models

We analyzed the influence of dissipative non-Hermitian terms on electrical transport in one-dimensional non-Hermitian PT-symmetric models, which presents chiral symmetry. The combination of periodic modulation and non-Hermitian effects opens up exciting avenues for exploring new phases of matter and understanding of the role of non-Hermitian physics in topological systems. The effective Hermitian Hamiltonian has always a higher dimension than the corresponding non-Hermitian one. We analyzed the effect of periodic hopping modulation on Su-Schrieffer-Heeger chain, that exhibits the non-Hermiticity in the presence of an complex staggered potential, where this dissipative non-Hermitian extension modifies the features of the topological trivial phase and the topological nontrivial phase.

Bending immunity in valley edge states and non-Hermitian supercoupling effects

Bending immunity in valley edge states and non-Hermitian supercoupling effects

Pseudospin-orbit coupling and non-Hermitian effects in the quantum geometric tensor of a plasmonic lattice

Pseudospin-orbit coupling and non-Hermitian effects in the quantum geometric tensor of a plasmonic lattice

Topological phases and non-Hermitian topology in tunable nonreciprocal cyclic three-mode optical systems

We propose a method for simulating a 1D non-Hermitian Su-Schrieffer-Heeger model with modulated nonreciprocal hopping using a cyclic three-mode optical system. The current system exhibits different localization of topologically nontrivial phases, which can be characterized by the winding number. We find that the eigenenergies of such a system undergo a real-complex transition as the nonreciprocal hopping changes, accompanied by a non-Bloch parity-time symmetry breaking. We explain this phase transition by considering the evolution of saddle points on the complex energy plan and the ratio of complex eigenenergies. Additionally, we demonstrate that the skin states resulting from the non-Hermitian skin effect possess higher-order exceptional points under the critical point of the non-Bloch parity-time phase transition. Furthermore, we investigate the non-Hermitian skin phase transition by the directional mean inverse participation ratio and the generalized Brillouin zone. This work provides an alternative way to investigate the novel topological and non-Hermitian effects in nonreciprocal optical systems.

Dynamical localization in a non-Hermitian Floquet synthetic system

We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain. The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation. In the Hermitian case, strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy. We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization. Moreover, the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter. Interestingly, the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value. The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most. The exponential localization length decreases with the increase of the non-Hermitian parameter, unveiling the underlying mechanism of the enhancement of the dynamical localization by non-Hermiticity.

Photonic Floquet Skin-Topological Effect.

Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.

Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice.

Recent studies of non-Hermitian periodic lattices unveiled the non-Hermitian skin effect (NHSE), in which the bulk modes under the periodic boundary conditions (PBC) become skin modes under open boundary conditions. The NHSE is a topological effect owing to the nontrivial spectral winding, and such spectral behaviors appear naturally in nonreciprocal systems. Hence prevailing approaches rely on nonreciprocity to achieve the NHSE. Here, we report the experimental realization of the geometry-dependent skin effect in a two-dimensional reciprocal system, in which the skin effect occurs only at boundaries whose macroscopic symmetry mismatches with the lattice symmetry. The role of spectral reciprocity and symmetry is revealed by connecting reflective channels at given boundaries with the spectral topology of the PBC spectrum. Our work highlights the vital role of reciprocity, symmetry, and macroscopic geometry on the NHSE in dimensionality larger than one and opens new routes for wave structuring using non-Hermitian effects.

Extended topological mode in a one-dimensional non-Hermitian acoustic crystal

In Hermitian topological systems, topological modes (TMs) are bound to interfaces or defects of a lattice. Recent discoveries show that non-Hermitian effects can reshape the wavefunctions of the TMs and even turn them into extended modes occupying the entire bulk lattice. In this letter, we experimentally demonstrate such an extended TM (ETM) in a one-dimensional (1D) non-Hermitian acoustic topological crystal. The acoustic crystal is formed by a series of coupled acoustic resonant cavities, and the non-Hermiticity is introduced as a non-reciprocal coupling coefficient using active electroacoustic controllers (AECs). Our work highlights the potential universality of ETMs in different physical systems and resolves the technical challenges in the further study of ETMs in acoustic waves.

Topological Microlaser with a Non-Hermitian Topological Bulk.

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While bulk-edge correspondence has been extensively studied in Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian topological band theory due to the interplay between non-Hermiticity and topology, and its effect on bulk-edge correspondence is still an ongoing pursuit. Importantly, including non-Hermicity can significantly expand the horizon of topological states of matter and lead to a plethora of unique properties and device applications, an example of which is a topological laser. However, the bulk topology, and thereby the bulk-edge correspondence, in existing topological edge-mode lasers is not well defined. Here, we propose and experimentally probe topological edge-mode lasing with a well-defined non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring resonators. By modeling the Hamiltonian with an additional degree of freedom (referred to as synthetic dimension), our 1D structure is equivalent to a 2D non-Hermitian Chern insulator with precise mapping. Our Letter may open a new pathway for probing non-Hermitian topological effects and exploring non-Hermitian topological device applications.

Non-Hermitian optics and photonics: from classical to quantum

Non-Hermitian optics is a burgeoning field at the intersection of quantum physics, electrodynamics, and nanophotonics. It provides a new perspective of the role of gain and loss in optical systems. Leveraging the advanced designs inspired by non-Hermitian physics, classical optical platforms have been widely investigated to unveil novel physical concepts, such as parity-time symmetry and exceptional points, which have no counterparts in the conventional Hermitian settings. These investigations have yielded a plethora of new phenomena in optical wave scattering, optical sensing, and nonlinear optical processes. Non-Hermitian effects also have a profound impact on the lasing behaviors in the semiclassical framework of lasers, allowing for novel ways to engineer single-mode lasers, chiral laser emission, laser noise, linewidth, etc. Furthermore, over recent years, there has been increasing interest in the explorations of non-Hermitian physics in quantum optics, which addresses photon statistics, entanglement, decoherence, and quantum sensing in non-Hermitian systems. In this review, we review the most recent theoretical and experimental advances in non-Hermitian optics and photonics, covering the significant progress in both classical and quantum optics regimes.

Wireless Power Transfer and Sensing Based on Non-Hermitian Topological Effects

Wireless Power Transfer and Sensing Based on Non-Hermitian Topological Effects

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.

Operator growth and Krylov construction in dissipative open quantum systems

Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.

Uniform optical gain as a non-Hermitian control knob

Non-Hermitian optics utilizes judicious engineering of the spatial and spectral distribution of gain and loss in order to tailor the behavior of photonic systems in ways that could not be achieved by modulating only the real part of the refractive index. In this respect, a question that has never been addressed is whether a uniform distribution of gain or loss can also lead to nontrivial non-Hermitian effects in linear systems, beyond just signal amplification or decay. Here, we investigate this problem and demonstrate that the application of uniform gain to a symmetric photonic molecule (PM) can reverse the optical energy distribution inside the structure. For a PM composed of two coupled resonators, this translates into changing the optical energy distribution inside the resonators. For a PM formed through scattering or defect-induced intermodal coupling in a ring resonator, the applied gain, despite being uniform and symmetric, can impose a strong chirality and switch the direction of light propagation from dominantly clockwise to dominantly counterclockwise. These predictions are confirmed by using both coupled mode formalism and full-wave finite-element simulations. Our work establishes a different direction in the field of non-Hermitian optics where interesting behavior can be engineered not only by unbalancing the non-Hermitian parameter but also by changing its average value---a feature that was overlooked in previous works.

Driving-induced multiple PT -symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals

The cooperation between time-periodic driving fields and non-Hermitian effects could endow systems with distinctive spectral and transport properties. In this paper, we uncover an intriguing class of non-Hermitian Floquet matter in one-dimensional quasicrystals, which is characterized by the emergence of multiple driving-induced $\mathcal{PT}$-symmetry breaking/restoring transitions, mobility edges, and reentrant localization transitions. These findings are demonstrated by investigating the spectra, level statistics, inverse participation ratios, and wave-packet dynamics of a periodically quenched nonreciprocal Harper model. Our results not only unveil the richness of localization phenomena in driven non-Hermitian quasicrystals but also highlight the advantage of the Floquet approach in generating unique types of nonequilibrium phases in open systems.

Gain-Loss-Induced Hybrid Skin-Topological Effect.

Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the PT phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the PT symmetries belonging to different edges. Moreover, we discover the PT phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and PT phase transition in higher-dimensional systems.

Observation of non-Hermitian aggregation effects induced by strong interactions

Non-Hermiticity greatly expands existing physical laws beyond the Hermitian framework, revealing various phenomena with unique properties. To date, most exotic non-Hermitian effects, such as exceptional points and non-Hermitian skin effects, have been discovered in single-particle systems. The interplay between non-Hermitian and particle interactions is expected to be a more fascinating but much less explored area. Here, we report an experimental simulation of a strongly correlated non-Hermitian few-body system and reveal a type of non-Hermitian skin state toward effective boundaries in Hilbert space induced by strong interactions. Such an interaction-induced non-Hermitian effect represents the aggregation of bosonic clusters with nonidentical occupations in the periodic lattice, and we call it the non-Hermitian aggregation effect. By mapping the eigenstates of three correlated bosons to modes of the designed three-dimensional electric circuit, the interaction-induced non-Hermitian aggregation effects in Hilbert space are verified by measuring the spatial impedance response. Our finding not only discloses a physical effect in the non-Hermitian system but also suggests a flexible platform to further investigate other non-Hermitian correlated phases in experiments.

Quantum Squeezing and Sensing with Pseudo-Anti-Parity-Time Symmetry.

The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.

Dimerization-induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals

Non-Hermitian effects could create rich dynamical and topological phase structures. In this work, we show that the collaboration between lattice dimerization and non-Hermiticity could generally bring about mobility edges and multiple localization transitions in one-dimensional quasicrystals. Non-Hermitian extensions of the Aubry-Andr\'e-Harper model with staggered on-site potential and dimerized hopping amplitudes are introduced to demonstrate our results. Reentrant localization transitions due to the interplay between quasiperiodic gain/loss and lattice dimerization are found. Quantized winding numbers are further adopted as topological invariants to characterize transitions among phases with distinct spectrum and transport nature. Our study thus enriches the family of non-Hermitian quasicrystals by incorporating effects of lattice dimerization, and offering a convenient way to modulate localization transitions and mobility edges in non-Hermitian systems.

Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.