Exceptional points in SSH-like models with a hopping amplitude gradient

<sec> We theoretically and experimentally demonstrate the anisotropic exceptional points (EPs) in the cavity magnonics system where magnons in a one millimeter-diameter yttrium iron garnet (YIG) sphere are coherently coupled with the microwave photons in a three-dimensional microwave cavity. The damping nature makes the cavity magnonics system inherently non-Hermitian. By solving the eigenvalues and eigenvectors of non-Hermitian Hamiltonian, a series of interesting and essential characteristics of the system can be obtained. Therefore, non-Hermitian physics has received more and more attention in both theory and experiment communities. Among them, exceptional points correspond to the non-Hermitian system’s degenerate states where the eigenvalues of the non-Hermitian system are identical, and the eigenvectors are parallel. The coupled cavity photon-magnon system has high tunability of coupling strength and cavity external damping rate, which is very suitable for studying EPs -related physics.</sec><sec> Exceptional points (EPs) are crucial in all kinds of non-Hermitian physical systems, which have both fundamental and applicational importance. For instance, it can be used for sensitive detection by monitoring spectrum splitting of degenerate modes when a perturbation to be sensed occurs. The EPs can be anisotropic, which means that it has a different function relation when the system approaches the EPs along different parameter paths of the system. In this paper, by carefully designing the parameter space, we observe the anisotropic exceptional point in the coupled cavity photon-magnon system. It shows the linear and square-root behavior when the EPs are approached from different directions in the parameter space. One of the parameters is the position of the YIG sphere in the cavity, which determines the coherent coupling strength between the cavity mode and the magnon mode. Another parameter is the number of the gasket between the cavity signal loading port and the cavity external surface, which determines the external damping rate of the cavity mode. Both of these parameters can be easily and accurately adjusted experimentally.</sec><sec> Our study paves the way for exploring anisotropic EPs based sensing technologies and more non-Hermitian related physics in the cavity magnonics system.</sec>

Bound states in the continuum (BICs) and exceptional points (EPs), as two distinct physical singularities represented by complex frequencies in non-Hermitian systems, have garnered significant attention and clear definitions in their respective fields in recent years. They share overlapping applications in areas such as high-sensitivity sensing and laser emission. However, the transition between the two, inspired by these intersections, remains largely unexplored. In this work, we reveal the transition process in a non-Hermitian two-mode system, evolving from one bound singularity to a two-dimensional exceptional ring, where the EP is the coalescent state of the quasi-Friedrich-Wintgen (FW)-BIC. This phenomenon is experimentally validated through pored dielectric metasurfaces in terahertz band. Furthermore, external pumping induced photocarriers as the dissipative perturbation, facilitates the breaking of degeneracy in the complex eigenfrequency and enables dynamic EP switching. Finally, we experimentally demonstrate a switchable terahertz beam deflection driven by the phase singularities of the EP. These findings are instrumental in advancing the development of compact devices for sensing and wavefront control within non-Hermitian systems.

Topological insulators and bound states in the continuum represent two fascinating topics in the optical and photonic domain. The exploration of their interconnection and potential applications has emerged as a current research focus. Here, we investigated non-Hermitian photonics based on a parallel cascaded-resonator system, where both direct and indirect coupling between adjacent resonators can be independently manipulated. We observed the emergence of topological Fabry-Pérot bound states in the continuum in this non-Hermitian system, and theoretically validated its robustness. We also observed topological phase transitions and exceptional points in the same system. By elucidating the relationship between topological insulators and bound states in the continuum, this work will enable various applications that harness the advantages of bound states in the continuum, exceptional points, and topology. These applications may include optical delay and storage, highly robust optical devices, high-sensitivity sensing, and chiral mode switching.

Photonic topological edge states in one-dimensional dimer chains have long been thought to be robust to structural perturbations by mapping the topological Su–Schrieffer–Heeger model of a solid-state system. However, the edge states at the two ends of a finite topological dimer chain will interact as a result of near-field coupling. This leads to deviation from topological protection by the chiral symmetry from the exact zero energy, weakening the robustness of the topological edge state. With the aid of non-Hermitian physics, the splitting frequencies of edge states can be degenerated again, with topological protection recovered by altering the gain or loss strength of the structure. This point of coalescence is known as the exceptional point (EP). The intriguing physical properties of EPs in topological structures give rise to many fascinating and counterintuitive phenomena. In this work, based on a finite non-Hermitian dimer chain composed of ultra-subwavelength resonators, we propose theoretically and verify experimentally that the sensitivity of topological edge states is greatly affected when the system passes through the EP. Using the EP of a non-Hermitian dimer chain, we realize a new sensor that is sensitive to perturbation of on-site frequency at the end of the structure and yet topologically protected from internal perturbation of site-to-site couplings. Our demonstration of a non-Hermitian topological structure with an EP paves the way for the development of novel sensors that are not sensitive to internal manufacturing errors but are highly sensitive to changes in the external environment.

As a kind of phase singularity in physical systems, exceptional points (EPs) give rise to a plethora of counterintuitive phenomena, such as the asymmetric state transfer and unidirectional reflection. Especially, the eigenvectors of EP are self-orthogonal, and an inherent chirality can be determined because of the “missing dimension.” Beyond traditional wisdom, in this work, we proposed theoretically an effective anti-parity-time symmetry in a non-Hermitian system under the external excitation, and the chirality reversal from resonance EP to absorption EP is demonstrated experimentally. The essence of this phenomenon is that the external input is involved in the establishment of the eigenstates of the system. Moreover, the critical condition of chirality reversal between two types of EPs in the non-Hermitian system is analytically given. This external excitation-controlled EP not only paves an effective way to study the fundamental non-Hermitian physics in an open system but also holds great potential in the applied photonic devices such as the chiral antenna, polarization converter, and wireless communication.

Engineered non-Hermitian systems featuring exceptional points (EPs) can lead to a host of extraordinary phenomena in diverse fields ranging from photonics, acoustics, opto-mechanics, and electronics to atomic physics. In optics, non-Hermitian dynamics are typically realized using dissipation and phase-insensitive gain accompanied by unavoidable fluctuations. Here, we introduce non-Hermitian dynamics of coupled optical parametric oscillators (OPOs) arising from phase-sensitive amplification and de-amplification, and show their distinct advantages over conventional non-Hermitian systems relying on laser gain and loss. OPO-based non-Hermitian systems can benefit from the instantaneous nature of the parametric gain, noiseless phase-sensitive amplification, and rich quantum and classical nonlinear dynamics. We show that two coupled OPOs can exhibit spectral anti-parity-time (anti-PT) symmetry and a EP between its degenerate and nondegenerate operation regimes. To demonstrate the distinct potentials of the coupled OPO system compared to conventional non-Hermitian systems, we present higher-order EPs with two OPOs, tunable Floquet EPs in a reconfigurable dynamic non-Hermitian system, and the generation of a squeezed vacuum around EPs, all of which are not easy to realize in other non-Hermitian platforms. We believe our results show that coupled OPOs are an outstanding non-Hermitian setting with unprecedented opportunities to realize nonlinear dynamical systems for enhanced sensing and quantum information processing.

Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we have investigated entropic uncertainty relation (EUR) in a non-Hermitian system and revealed a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitarity dynamics determined by a Hermitian Hamiltonian, the behaviors of EUR can be well defined in two different ways depending on whether the system is located in unbroken phase or broken phase regimes. In unbroken phase regime, EUR undergoes an oscillatory behavior while in broken phase regime where the oscillation of EUR breaks down. The exceptional points mark the oscillatory and non-oscillatory behaviors of the EUR. In the dynamical limit, we have identified the witness of critical behavior of non-Hermitian systems in terms of the EUR. Our results reveal that the witness can detect exactly the critical points of non-Hermitian systems beyond (anti-) PT-symmetric systems. Our results may have potential applications to witness and detect phase transition in non-Hermitian systems.

Entanglement entropy and topological properties in a long-range non-Hermitian Su–Schrieffer–Heeger model

Exceptional points (EPs) in non-Hermitian systems offer a remarkably strong response to weak perturbations, but the nonorthogonal nature of the corresponding eigenvectors causes noise to diverge, hindering EPs practical application. Here, we report a twelve-fold enhancement of signal-to-noise ratio (SNR) in magnetic field sensing enabled by a third-order EP of coherent perfect absorption (CPA EP3) in a passive cavity magnonic system. This non-Hermitian magnonic platform comprises two identical yttrium iron garnet (YIG) spheres coherently coupled to a cavity mode, in which the CPA EP3 is realized by engineering the three-mode loss to form a pseudo-Hermitian absorption Hamiltonian. By independently tailoring the absorption EP apart from the resonance EP, the system circumvents the noise divergence caused by eigenbasis collapse. Notably, we harness the sensitivity of the minimum output intensity near CPA to perturbations, yielding a seventy-fold SNR improvement and a 400-fold increase in responsivity compared with non-CPA system. A comprehensive noise analysis over one hundred repeated measurements confirms the suppression of frequency noise near the CPA EP3. This demonstrates that our scheme not only avoids the noise divergence plaguing conventional higher-order EP sensors but also provides a general strategy to exploit both CPA and EP for SNR enhancement in passive non-Hermitian systems.

Radiative emission experienced by a subwavelength particle near a resonant cavity is typically characterized by the well-known Purcell factor figure of merit. In recent work, we presented a generalization of Purcell enhancement that applies to situations involving exceptional points (EP)---spectral singularities in non-Hermitian systems where two or more eigenvectors and their corresponding complex eigenvalues coalesce, leading to a non-diagonalizable, defective Hamiltonian. EPs are attended by many intriguing physical effects and have been studied in various contexts, including lasers, atomic and molecular systems, photonic crystals, parity-time symmetric lattices, and optomechanical resonators. Thus far, the main focus of these works has been on analyzing the impact of second-order exceptional points on scattering from eternally incident light, e.g. for unidirectional transmission. An important but little explored property of EPs related to light-matter interactions is their ability to modify and enhance the local density of states (LDOS). Recently, we showed that EPs can modify the spontaneous emission rate or Purcell factor of narrow-band emitters embedded in resonant cavities. In this talk, we show that EPs can have an even greater impact on nonlinear optical processes like frequency conversion. In particular, we derive a general formula quantifying radiative emission from a subwavelength emitter in the vicinity of a triply resonant χ(2) cavity that supports an EP near the emission frequency and a bright mode at the second harmonic. We show that the resulting frequency up-conversion process can be enhanced by up to two orders of magnitude compared to nondegenerate scenarios and that, in contrast to the recently predicted spontaneous-emission enhancements, nonlinear EP enhancements can persist even when considering spatial distributions of broadband emitters, provided that the cavity satisfies special nonlinear selection rules. This is demonstrated via a two-dimensional proof-of-concept PhC designed to partially fulfill the various criteria needed to approach the derived bounds on the maximum achievable up-conversion efficiencies. Along these lines, we show that similar enhancements can arise in quantum systems consisting of single and multi-level atoms embedded in photonic cavities. Our predictions suggest an indirect but practically relevant route to experimentally observe the impact of EPs on spontaneous emission and related light–matter interactions, with implications to quantum information science.

We introduce non-Hermitian plasmonic waveguide-cavity systems with topological edge states (TESs) at singular points. The compound unit cells of the structures consist of metal-dielectric-metal (MDM) stub resonators side-coupled to an MDM waveguide. We show that we can realize both a TES and an exceptional point at the same frequency when a proper amount of loss is introduced into a finite three-unit-cell structure. We also show that the finite structure can exhibit both a TES and a spectral singularity when a proper amount of gain is introduced into the structure. In addition, we show that we can simultaneously realize a unidirectional spectral singularity and a TES when proper amounts of loss and gain are introduced into the structure. We finally show that this singularity leads to extremely high sensitivity of the reflected light intensity to variations of the refractive index of the active materials in the structure. TESs at singular points could potentially contribute to the development of singularity-based plasmonic devices with enhanced performance.

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, ‘skin-effect’, and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

This Letter reports on the experimental observation of a topologically protected edge state and exceptional point in an open and non-Hermitian (lossy) acoustic system. Although the theoretical underpinning is generic to wave physics, the simulations and experiments are performed for an acoustic system. It has nontrivial topological properties that can be characterized by the Chern number provided that a synthetic dimension is introduced. Unidirectional reflectionless propagation, a hallmark of exceptional points, is unambiguously observed in both simulations and experiments.

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.

Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 − 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 − 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.