Vicinity Of Exceptional Point Research Articles

Non-Hermitian Chiral Heat Transport.

Exceptional point (EP) has been captivated as a concept of interpreting eigenvalue degeneracy and eigenstate exchange in non-Hermitian physics. The chirality in the vicinity of EP is intrinsically preserved and usually immune to external bias or perturbation, resulting in the robustness of asymmetric backscattering and directional emission in classical wave fields. Despite recent progress in non-Hermitian thermal diffusion, all state-of-the-art approaches fail to exhibit chiral states or directional robustness in heat transport. Here we report the first discovery of chiral heat transport, which is manifested only in the vicinity of EP but suppressed at the EP of a thermal system. The chiral heat transport demonstrates significant robustness against drastically varying advections and thermal perturbations imposed. Our results reveal the chirality in heat transport process and provide a novel strategy for manipulating mass, charge, and diffusive light.

Enhanced Biomolecule Concentration Sensing by Using Exceptional Points in a Microtube Cavity With Multiple Layers

Biosensors have important implications for medical research and disease prevention. High-quality optical microcavities with whispering-gallery modes can enhance light-matter interactions in small volumes, making them ideal for making biosensors. However, the sensitivity of the optical microcavity biosensors can further improve. The sensing performance of the biosensor based on a microtube or microbubble can be further improved by exceptional points in Non-Hermitian physics. Non-Hermitian systems are open systems, exchanging energy with the external environment. Exceptional points (EPs) as one representative feature of Non-Hermitian systems are a branch point singularity, where eigenvalues and their corresponding eigenvectors coalesce in the parameter space of the system. In the vicinity of EPs, the eigenvalues exhibit non-trivial topology, which can be exploited for highly sensitive detections. Based on this principle, a novel configuration with multiple layers is proposed, where coupling of modes can be tailored for EPs by choosing the thickness of layers. Simulated results demonstrated that the design has strong biosensing performance. The sensitivity can be enhanced by 1000 times more than that of conventional methods. The ability to prevent environmental interference has also been improved. This is significant for highly sensitive low concentration biomolecule detection in microtubes in the future.

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.

Non-Hermitian tunable exceptional point system based on coupled fiber-optic Fabry-Pérot microcavities for broadband microwave signal generation

Appearance of exceptional points (EPs) in photonics arises enormous attention as a result of the counterintuitive phenomena occurring around EP. In particular, adiabatically encircling EP contributes to accumulation of Berry phase, leading to mode switching and strong chirality. Therefore, it would be of significance to develop a photonic system with tunable EP states, which helps to implement versatile functionalities for various applications. Here we propose a non-Hermitian tunable system based on coupled fiber-optic Fabry-Pérot microcavities with distributed gain/loss to host quasi-static EP-encirclement and parity-time (PT) symmetry schemes. Analytical calculations for the case of EP encircling along the path in the vicinity of EP are compared with their counterparts on the boundaries of the parameter space based on quasi-adiabatic theory, revealing mode switching and chirality relevant to the system singularity. And moreover, tunable coupling between microcavities enables tunability of EPs under PT symmetry regime, based on which generation of broadband microwave signals ranging from 0 to 75GHz could be achieved and the maximum frequency tuning sensitivity up to the magnitude of 106GHz/RIU could be reached for specific refractive index ranges, providing clues for manipulating EPs in non-Hermitian fiber-optic systems and designing novel EP-based photonic devices.

Light-Controlled Exceptional Point Sensor Based on Azo-Functionalized Whispering Gallery Mode Microcavity

Nonlinear topological responses in the vicinity of exceptional points (EPs) significantly enhance mode splitting sensitivity of non-Hermitian systems to external perturbations. In this paper, a new method is proposed to flexibility control EP state of the whispering gallery mode microcavity integrated with photo-sensitive azobenzene coating, which provides a simple, efficient and stabilized scheme to prepare and tune the EP state with no need to delicately control the interaction between the nanoscatters and the microcavity. By introducing one pair of defects infiltrated with liquid samples, refractive index sensing could be realized when the system is operating around EP and the measurement range of 1.33 to 1.4 covers the RI range of most biological analytes. And moreover, performances of the proposed system in nanoparticle detection are also investigated. In comparison with its counterpart operating around diabolic points, our proposed system exhibits more than quadruple increase in sensitivity. Our proposed EP sensor based on light-controlled tuning of the system state makes it a promising candidate for applications in the field of optical sensing and paves a way toward developing tunable EP-based photonic devices.

Calculating eigenvalues and eigenvectors of parameter-dependent Hamiltonians using an adaptative wave operator method

We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices using an adaptative active subspace. We consider a Hamiltonian that depends on external adjustable or adiabatic parameters, using adaptative projectors that follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-Hermitian Hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive; it converges within a few dozens of iterations at constant memory cost. We first illustrate the abilities of the method on a 4D-coupled oscillator model Hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H2 + in the vicinity of exceptional points are calculated as an illustrative example.

Strong absorption near exceptional points in plasmonic waveguide arrays

We investigate the exceptional points (EPs) in plasmonic waveguide arrays, including metallic waveguide arrays (MWAs) and graphene sheet arrays (GSAs). The EPs emerge at the boundary of strong and weak coupling ranges in both systems. The cross conversion of Bloch modes and variation of geometric phase can be observed by encircling an EP in the parametric space. We also show the Bloch modes exhibit strong absorption in the vicinity of EPs in GSAs, which originates from the enhanced longitude electric field along the propagation direction. The abnormal absorption and field enhancement also arise in ultrathin MWAs and disappear when the thickness of metal film increases. Our results may find applications in optical switches and sensors at the nanoscale.

Chiral Modes at Exceptional Points in Exciton-Polariton Quantum Fluids.

We demonstrate the generation of chiral modes-vortex flows with fixed handedness in exciton-polariton quantum fluids. The chiral modes arise in the vicinity of exceptional points (non-Hermitian spectral degeneracies) in an optically induced resonator for exciton polaritons. In particular, a vortex is generated by driving two dipole modes of the non-Hermitian ring resonator into degeneracy. Transition through the exceptional point in the space of the system's parameters is enabled by precise manipulation of real and imaginary parts of the closed-wall potential forming the resonator. As the system is driven to the vicinity of the exceptional point, we observe the formation of a vortex state with a fixed orbital angular momentum (topological charge). This method can be extended to generate higher-order orbital angular momentum states through coalescence of multiple non-Hermitian spectral degeneracies. Our Letter demonstrates the possibility of exploiting nontrivial and counterintuitive properties of waves near exceptional points in macroscopic quantum systems.

Unidirectional reflectionless phenomena in a non-Hermitian quantum system of quantum dots coupled to a plasmonic waveguide.

Unidirectional reflectionless phenomena are investigated theoretically in a non-Hermitian quantum system composed of several quantum dots and a plasmonic waveguide. By adjusting the phase shifts between quantum dots, single- and dual-band unidirectional reflectionlessnesses are realized at exceptional points based on two and three quantum dots coupled to a plasmonic waveguide, respectively. In addition, single- and dual-band unidirectional perfect absorptions with high quality factors are obtained at the vicinity of exceptional points.

Switching the unidirectional reflectionlessness by polarization in non-ideal PT metamaterial based on the phase coupling

An effective scheme on switching the exceptional point(EP) where unidirectional reflectionlessness occurs is firstly proposed in non-ideal PT metamaterial via the polarization of incident light. The unidirectional reflectionlessness could be effectively controlled only by adjusting the phase coupling of the two resonators which are consisted of two identical but vertically placed crosses and are excited by incident light as an effective gain. Besides, the unidirectional perfect absorber occurs in the vicinity of EP.

Next-nearest-neighbor resonance coupling and exceptional singularities in degenerate optical microcavities

We report a specially configured non-Hermitian optical microcavity, imposing spatially imbalanced gain-loss profile, to host an exclusively proposed next nearest neighbor resonances coupling scheme. Adopting scattering matrix (S-matrix) formalism, the effect of interplay between such proposed resonance interactions and the incorporated non-Hermiticity in the microcavity is analyzed drawing a special attention to the existence of hidden singularities, namely exceptional points (EPs); where at least two coupled resonances coalesce. We establish adiabatic flip-of-states phenomena of the coupled resonances in the complex frequency plane (k-plane) which is essentially an outcome of the fact that the respective EP is being encircled in system parameter plane. Encountering such multiple EPs, the robustness of flip-of-states phenomena have been analyzed via continuous tuning of coupling parameters along a special hidden singular line which connects all the EPs in the cavity. Such a numerically devised cavity, incorporating the exclusive next neighbor coupling scheme, have been designed for the first time to study the unconventional optical phenomena in the vicinity of EPs.

Improvement of the chirality near avoided resonance crossing in optical microcavity

Chirality is one of the important phenomena at the vicinity of exceptional point (EP). The conventional understanding is that the chirality is determined by asymmetrical scattering efficiency (η), which reaches to zero only when the resonance approaches EP. Here we study the possibility to enhance the chirality in open systems with a more robust mechanism. By combining chirality with avoided resonance crossing, we show that the chirality and η can be dramatically modified. Taking a spiral shaped annular cavity as an example, we show that the chirality of optical resonances can be significantly improved when two sets of chiral states approach each other. The imbalance between counterclockwise (CCW) components and clockwise (CW) components has been enhanced by more than an order of magnitude. Our research provides a new route to tailor and control the chirality in open systems.

Quantum noise and mode nonorthogonality in non-HermitianPT-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 lineshape 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 to spontaneous PT-symmetry breaking). The calculations are carried out in the scattering input-output formalism, and are illustrated for a quasi one-dimensional resonator set-up. In our derivations we also allow for the more general case of a resonator in which the amplifying and absorbing regions are not related by symmetry.

Complex magnetic monopoles, geometric phases and quantum evolution in the vicinity of diabolic and exceptional points

We consider the geometric phase and quantum tunneling in the vicinity of diabolic and exceptional points. We show that the geometric phase associated with the degeneracy points is defined by the flux of complex magnetic monopoles. In the limit of weak coupling, the leading contribution to the real part of the geometric phase is given by the flux of the Dirac monopole plus a quadrupole term, and the expansion of the imaginary part starts with a dipole-like field. For a two-level system governed by a generic non-Hermitian Hamiltonian, we derive a formula to compute the non-adiabatic, complex, geometric phase by integrating over the complex Bloch sphere. We apply our results to study a dissipative two-level system driven by a periodic electromagnetic field and show that, in the vicinity of the exceptional point, the complex geometric phase behaves like a step-function. Studying the tunneling process near and at the exceptional point, we find two different regimes: coherent and incoherent. The coherent regime is characterized by Rabi oscillations, with a one-sheeted hyperbolic monopole emerging in this region of the parameters. The two-sheeted hyperbolic monopole is associated with the incoherent regime. We show that the dissipation results in a series of pulses in the complex geometric phase which disappear when the dissipation dies out. Such a strong coupling effect of the environment is beyond the conventional adiabatic treatment of the Berry phase.

Projective Hilbert space structures at exceptional points

A non-Hermitian complex symmetric 2 × 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseux-expanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular behaviour in the EP-limit can be resolved by projectively extending the original Hilbert space. The complementary normalization conditions correspond then to two different affine charts of this enlarged projective Hilbert space. Geometric phase and phase-jump behaviour are analysed, and the usefulness of the phase rigidity as measure for the distance to EP configurations is demonstrated. Finally, EP-related aspects of -symmetrically extended quantum mechanics are discussed and a conjecture concerning the quantum brachistochrone problem is formulated.

Asymmetric Polarity Reversals, Bimodal Field Distribution, and Coherence Resonance in a Spherically Symmetric Mean-Field Dynamo Model

Using a mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha which is algebraically quenched and disturbed by additional noise, the basic features of geomagnetic polarity reversals are shown to be generic consequences of the dynamo action in the vicinity of exceptional points of the spectrum. This simple paradigmatic model yields long periods of constant polarity which are interrupted by self-accelerating field decays leading to asymmetric polarity reversals. It shows the recently discovered bimodal field distribution, and it gives a natural explanation of the correlation between polarity persistence time and field strength. The dependence of the persistence time on the noise shows typical features of coherence resonance.