non-Hermitian Degeneracy Research Articles

Three types of third-order non-Hermitian interaction of spontaneous six-wave and eight-wave mixing under multi-dressing effects

Non-Hermitian degeneracy, also known as exceptional point, has been recently seen as a new way to engineer the response of open physical systems. Based on natural non-Hermitian atomic coherence, we investigate spontaneous six-wave mixing (SSWM) and eight-wave mixing (SEWM) processes under both parity–time (PT) and anti-parity–time (anti-PT) symmetry, and we obtain high-dimensional coherent channels under third-order energy-level splitting. Finally, we reveal that the third-order non-Hermitian interaction between two dressing fields of the nested scheme is the strongest, and the parallel scheme is the weakest, with the cascade scheme considered intermediate between them. It can also be used to develop quantum memory devices with enhanced sensitivity in the atom-like system.

PT -symmetric non-Hermitian Hopf metal

The Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K theory. In this Letter, we describe the metallic counterpart of the Hopf insulator in non-Hermitian systems. While the Hopf invariant is not a stable topological index due to the additional non-Hermitian degree of freedom, we show that the PT symmetry stabilizes the Hopf invariant even in the presence of the non-Hermiticity. In sharp contrast to the Hopf insulator phase in the Hermitian counterpart, we describe an interesting result that the non-Hermitian Hopf bundle exhibits topologically protected non-Hermitian degeneracy, characterized by the two-dimensional surface of exceptional points. Despite the non-Hermiticity, the Hopf metal has the quantized Zak phase, which results in bulk-boundary correspondence by showing drumheadlike surface states at the boundary. Finally, we show that, by breaking PT symmetry, the nodal surface deforms into knotted exceptional lines. Our description of the Hopf metal phase confirms the existence of the non-Hermitian topological phase outside the framework of the standard topological classifications. Published by the American Physical Society 2024

Observation of the geometry-dependent skin effect and dynamical degeneracy splitting

The non-Hermitian skin effect is a distinctive phenomenon in non-Hermitian systems, which manifests as the anomalous localization of bulk states at the boundary. To understand the physical origin of the non-Hermitian skin effect, a bulk band characterization based on the dynamical degeneracy on an equal frequency contour is proposed, which reflects the strong anisotropy of the spectral function. In this paper, we report the experimental observation of a newly-discovered geometry-dependent non-Hermitian skin effect and dynamical degeneracy splitting in a two-dimensional acoustic crystal and reveal their remarkable correspondence by performing single-frequency excitation measurements. Our work not only provides a controllable experimental platform for studying the non-Hermitian physics, but also confirms the unique correspondence between the non-Hermitian skin effect and the dynamical degeneracy splitting, paving a new way to characterize the non-Hermitian skin effect.

Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains

Many-body interactions give rise to the appearance of exotic phases in Hermitian physics. Despite their importance, many-body effects remain an open problem in non-Hermitian physics due to the complexity of treating many-body interactions. Here, we present a family of exact and numerical phase diagrams for non-Hermitian interacting Kitaev chains. In particular, we establish the exact phase boundaries for the dimerized Kitaev-Hubbard chain with complex-valued Hubbard interactions. Our results reveal that some of the Hermitian phases disappear as non-Hermiticty is enhanced. Based on our analytical findings, we explore the regime of the model that goes beyond the solvable regime, revealing regimes where non-Hermitian topological degeneracy remains. The combination of our exact and numerical phase diagrams provides an extensive description of a family of non-Hermitian interacting models. Our results provide a stepping stone toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.

Non-Hermitian chiral degeneracy of gated graphene metasurfaces

Non-Hermitian degeneracies, also known as exceptional points (EPs), have been the focus of much attention due to their singular eigenvalue surface structure. Nevertheless, as pertaining to a non-Hermitian metasurface platform, the reduction of an eigenspace dimensionality at the EP has been investigated mostly in a passive repetitive manner. Here, we propose an electrical and spectral way of resolving chiral EPs and clarifying the consequences of chiral mode collapsing of a non-Hermitian gated graphene metasurface. More specifically, the measured non-Hermitian Jones matrix in parameter space enables the quantification of nonorthogonality of polarisation eigenstates and half-integer topological charges associated with a chiral EP. Interestingly, the output polarisation state can be made orthogonal to the coalesced polarisation eigenstate of the metasurface, revealing the missing dimension at the chiral EP. In addition, the maximal nonorthogonality at the chiral EP leads to a blocking of one of the cross-polarised transmission pathways and, consequently, the observation of enhanced asymmetric polarisation conversion. We anticipate that electrically controllable non-Hermitian metasurface platforms can serve as an interesting framework for the investigation of rich non-Hermitian polarisation dynamics around chiral EPs.

Observation of an exceptional point with an LR-shunted resonator

Non-Hermitian physical systems have enriched wave control abilities and dynamics of wave matter, especially around exceptional points (EPs). In this work, we theoretically, numerically, and experimentally studied an LR-shunted mechanical resonator for the observation of the exceptional point. The shunted resonator was composed of a mechanical resonator with a bonded piezoelectric patch and an LR-shunted circuit. A theoretical model for the LR-shunted resonator was first developed, and the exceptional point was identified from this theoretical model via a parameter space study. It was found that by varying the shunting circuit parameters, i.e., inductance and resistance, such a simple design supports the non-Hermitian degeneracy, namely the exceptional point. At the vicinity of the EP, the LR-shunted mechanical resonator had a square-root dependence on the external perturbation related to the nominal resistance. Next, we designed and fabricated a shunted resonator to verify our design through numerical analysis and experimental measurements. Moreover, our proposed LR-shunted resonator provides the possibility to dynamically encircle an exceptional point due to external stimuli. Our approach sheds light on the designs of chiral effect systems and dynamically tailoring losses in elasticity, and it enables alternative solutions for nondestructive structural health monitoring with enhanced sensitivity.

Nonreciprocal slow or fast light in anti- PT -symmetric optomechanics

Non-Hermitian systems with anti-parity-time ($\mathcal{APT}$) symmetry have revealed rich physics beyond conventional systems. Here, we study optomechanics in an $\mathcal{APT}$-symmetric spinning resonator and show that, by tuning the rotating speed to approach the exceptional point (EP) or the non-Hermitian spectral degeneracy, nonreciprocal light transmission with a high isolation ratio can be realized. Accompanying this process, nonreciprocal group delay or advance is also identified in the vicinity of EP. Our work sheds new light on manipulating laser propagation with optomechanical EP devices and, in a broader view, can be extended to explore a wide range of $\mathcal{APT}$-symmetric effects, such as $\mathcal{APT}$-symmetric phonon lasers, $\mathcal{APT}$-symmetric topological effects, and $\mathcal{APT}$-symmetric force sensing or accelerator.

Exceptional Points in a Spiral Ring Cavity for Enhanced Biosensing

The unique point of non-Hermitian degeneracy in an open system, known as exceptional point (EP), holds great potential in cavity quantum electrodynamics, optical signal processing, and sensing applications. For on-chip miniaturized optical cavities, auxiliary means have been employed for steering a non-Hermitian system to an EP, which typically requires either precision post-fabrication tuning or external off-chip components. Here we report a route of engineering non-Hermitian degeneracies in spiral ring microcavities without any external or temporary assistance. In such a deformed whispering gallery mode cavity which can be readily obtained through the self-rolling of pre-strained nanomembranes, the coupling strength of original non-degenerate modes can be fine tailored by spiral edge-induced backscatterings. Our theoretical results suggest that an EP can be reached by adjusting the physical scales and relative positions of inner and outer spiral edges. For EP-enhanced sensing, a functional regime upon a tiny perturbation where splitting scales as the square root of the perturbation and a saturated regime upon a sufficiently large perturbation are distinguished. For EPs in such a single-resonator system, the enhanced sensitivity towards localized perturbations and robustness towards homogenous perturbations are desirable for single-molecule detections. We expect that this work will serve as a generic guideline for realizing compact EP-empowered sensing systems and provide new insights into ultra-sensitive bioanalyses.

Exceptional Points Induced by Time-Varying Mass to Enhance the Sensitivity of Defect Detection

The exceptional point (EP), a non-Hermitian degeneracy at which eigenvalues and eigenvectors coalesce simultaneously, is investigated in mechanical oscillators involving a time-varying mass. A dynamic modulation mechanism is employed to create the time-varying mass, which can potentially develop an EP by acting as an energy source and drain. To fully demonstrate the existence of EPs, the eigenvalue problem for the modulated system is theoretically formulated through two different schemes, based on the state-space and harmonic balance methods. A second-order EP is confirmed by both methods and exists as a result of the coalescence of fundamental and harmonic eigenmodes. As a salient property of this second-order EP, the square-root behavior of the eigenfrequency subject to small perturbations of the system parameters is theoretically demonstrated, and utilized to devise a proof-of-concept model for mechanical sensors with high sensitivity to void defects in elastic solids. The EP behavior induced by a time-varying mass may find potential applications in damage assessment and health monitoring of engineering structures.

Dissipation driven degeneracies

Dissipation alone can produce counterintuitive topological wave transport that is otherwise absent in a non-dissipative system. This work demonstrates the influence of dissipation on degeneracies that arise in the context of elastic wave transport. The conditions on the parameters necessary to observe non-Hermitian degeneracies in the Bloch spectrum are precisely derived. It will be shown—contrary to the expectation from singularity theory of a linear eigenvalue problem—that a proportionally damped system with commutative damping does not exhibit non-Hermitian degeneracies. The necessity of a non-commutative and non-proportional dissipation model to observe non-Hermitian degeneracies (or exceptional points) is emphasized. Non-proportional dissipation is used to induce a non-Hermitian degeneracy in a local resonance sub-Bragg bandgap of a linear chain, without using negative damping. While Bloch waves are chosen to illustrate the influence of dissipation, the results readily extend to waves in non-periodic media as well as other wave and vibration transport problems.

Far-Field Correlations Verifying Non-Hermitian Degeneracy of Optical Modes.

An experimental verification of an exceptional point (EP) in a stand-alone chaotic microcavity is a tough issue because as deformation parameters are fixed the traditional frequency analysis methods cannot be applied any more. Through numerical investigations with an asymmetric Reuleaux triangle microcavity (ARTM), we find that the eigenvalue difference of paired modes can approach near-zero regardless of nonorthogonality of the modes. In this case, for a definite verification of EPs in experiments, wave function coalescence should be confirmed. For this, we suggest the method of exploiting correlation of far-field patterns (FFPs), which is directly related to spatial mode patterns. In an ARTM, we demonstrate that the FFP correlation of paired modes can be used to confirm wave function coalescence when an eigenvalue difference approaches near zero.

Observation of chiral state transfer without encircling an exceptional point.

The adiabatic theorem, a corollary of the Schrödinger equation, manifests itself in a profoundly different way in non-Hermitian arrangements, resulting in counterintuitive state transfer schemes that have no counterpart in closed quantum systems. In particular, the dynamical encirclement of exceptional points (EPs) in parameter space has been shown to lead to a chiral phase accumulation, non-adiabatic jumps and topological mode conversion1-8. Recent theoretical studies, however, have shown that contrary to previously established demonstrations, this behaviour is not strictly a result of winding around a non-Hermitian degeneracy9. Instead, it seems to be mostly attributed to the non-trivial landscape of the Riemann surfaces, sometimes because of the presence of an EP in the vicinity9-11. Here, in an effort to bring this counterintuitive aspect of non-Hermitian systems to light and confirm this hypothesis, we provide a set of experiments to directly observe the field evolution and chiral state conversion in an EP-excluding cycle in a slowly varying non-Hermitian system. To do so, a versatile yet unique fibre-based photonic emulator is realized that utilizes the polarization degrees of freedom in a quasi-common-path single-ring arrangement. Our observations may open up new avenues for light manipulation and state conversion, as well as providing a foundation for understanding the intricacies of the adiabatic theorem in non-Hermitian systems.

Coalescence of Anderson-localized modes at an exceptional point in 2D random media.

In non-Hermitian settings, the particular position at which two eigenstates coalesce in the complex plane under a variation of a physical parameter is called an exceptional point. An open disordered system is a special class of non-Hermitian system, where the degree of scattering directly controls the confinement of the modes. Herein a non-perturbative theory is proposed which describes the evolution of modes when the permittivity distribution of a 2D open dielectric system is modified, thereby facilitating to steer individual eigenstates to such a non-Hermitian degeneracy. The method is used to predict the position of such an exceptional point between two Anderson-localized states in a disordered scattering medium. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems.

Non-Hermitian spectrum and multistability in exciton-polariton condensates

We investigate non-Hermitian spectrum and multistability of exciton-polariton condensates excited by a nonresonant pump. An increase in pumping power moves the system away from non-Hermitian spectrum degeneracy toward bifurcation through an exceptional point, which induces a transition from monostability to multistability. The spectrum can be used as a universal method for detecting this transition. In the region of multistability, the system contains one steady and two metastable states. The analyses of stability show that metastable states maintain a finite lifetime and eventually evolve into steady states, which are induced by non-Hermitian skin effects. We also discover a steady state with multipeak soliton for attractive polariton-polariton interaction, which is different from general single-peak soliton for repulsive interaction. Our results open up exciting possibilities for controlling non-Hermitian quantum multistable states, which may be useful for designing polariton-based devices exploiting optical multistability.

Highly Chiral Exceptional Point in Perturbed Coupled Resonators

Exceptional point (EP) is a non-Hermitian spectral degeneracy that has application in ultrasensitive sensors and laser mode selectivity. By employing strong chirality in an optical system, the direction of light propagation can be controlled and subwavelength particles can be detected. Here, we show that EP with high chirality can appear in the coupled resonators perturbed by a scatterer, in which both the distance and position of the scatterer can be tuned. We achieve strong chiral EP in two different distances between the resonators, with chirality around 0.99 in both cases.

Non-Hermitian time evolution: From static to parametric instability

Eigenmode coalescence imparts remarkable properties to non-hermitian time evolution, culminating in a purely non-hermitian spectral degeneracy known as an exceptional point (EP). Here, we revisit time evolution at the EP and classify two-level non-hermitian Hamiltonians in terms of the M\"obius group. We then leverage that classification to study dynamical EP encircling, by applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that Floquet non-hermitian systems exhibit rich physics whose complexity is not captured by an EP-encircling rule. For example, Floquet EPs can occur without encircling and vice-versa. Instead, we show that the elaborate interplay between non-hermitian and modulation instabilities is better understood through the lens of parametric resonance.

Phase diagram and quantum criticality of a non-Hermitian XY model with a complex transverse field

We study a one dimensional non-Hermitian quantum XY model with a complex transverse field, where the imaginary transverse field can be generated by three-level atoms with spontaneous decay. Many-body spectrum can be obtained analytically. The phase diagram in thermodynamical limit indicates that the imaginary transverse field induces non-Hermitian degeneracy and shrinks the ferromagnetic phase for anisotropic interaction. We also analyze the effect of imaginary field on quantum criticality through ground state geometry phase. It causes a shift of transition point but does not change the order of phase transition in anisotropic interaction region. However, the phase transition is related to the original Hermitian degeneracy in anisotropic interaction region, which indicates that the imaginary transverse field cannot change phase boundary and critical behavior.

Dynamically Encircling an Exceptional Point in a Real Quantum System.

The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly intriguing behavior is the mode switch phenomenon induced by dynamically encircling an exceptional point in the parameter space. While these mode switches have been explored in classical systems, the experimental investigation in the quantum regime remains elusive due to the difficulty of constructing time-dependent non-Hermitian Hamiltonians in a real quantum system. Here we experimentally demonstrate dynamically encircling the exceptional point with a single nitrogen-vacancy center in diamond. The time-dependent non-Hermitian Hamiltonians are realized utilizing a dilation method. Both the asymmetric and symmetric mode switches have been observed. Our Letter reveals the topological structure of the exceptional point and paves the way to comprehensively explore the exotic properties of non-Hermitian Hamiltonians in the quantum regime.

Exceptional Points in Plasmonic Waveguides Do Not Require Gain or Loss

Exceptional points (EPs) in photonics are associated with non-Hermitian Hamiltonians with energy gain or loss, a notable example is EPs in parity-time symmetric Hamiltonians. We show that, counterintuitively, actual energy gain or loss is not required to generate this type of non-Hermitian degeneracy, since the eigenvalue of the optical Hamiltonian is the mode's propagation constant and not the energy. This is demonstrated by a simple three-layer insulator-metal-insulator (I-M-I) plasmonic waveguide, the eigenmodes of which are known to experience degeneracy at a certain point in the parametric space suggested to be used for rainbow trapping. We identify this point to be, in fact, an EP with the coalescence of the eigenmodes, despite the system having neither parity nor time symmetry. Furthermore, we demonstrate the manifestation of a third-order EP, which is generated by merging two separate EPs in the parametric space of the I-M-I waveguide. The presented results reveal unconventional properties of the Hamiltonian of a simple plasmonic waveguide and provide an insight into the nature of EPs in non-Hermitian plasmonic systems in general, suggesting the possibility of accessing even higher-order EP regimes in simple photonic structures without the need for optical gain or loss.

Subharmonic Entrainment Breather Solitons in Ultrafast Lasers

We study theoretically and experimentally the subharmonic entrainment (SHE) breather soliton in mode-locked lasers for the first time, in which the ratio of the breather period to the round-trip time is an integer. We build a non-Hermitian degeneracy map of breather soliton, and illustrate that SHE arises between the two exceptional points (EPs). We obtain SHE at the ratio of 20, observe the evolution of breather soliton when tuning the gain and/or cavity loss, and prove that this phenomenon can improve the stability of breather soliton. Our research brings insight into the EP physics of ultrafast lasers and makes the mode-locked laser a powerful test bed for non-Hermitian degeneracy, which may open a new course in ultrafast laser research.