Exceptional points and quantum dynamics in a non-Hermitian two-qubit system

We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the systemparameter space into PT-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantumdynamics characteristics. Particularly, in the partially broken regime, while the PT-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the PT-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.

Quantum exceptional points of non-Hermitian Hamiltonian and Liouvillian in dissipative quantum Rabi model

The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.

Fabry–Prot resonance coupling associated exceptional points in a composite grating structure

The exceptional point（EP） is a significant and attractive phenomenon in an open quantum system. The scattering properties of light are similar to those in the open quantum system, which makes it possible to achieve EP in the optic system. Here we investigate the EP in a Fabry–P′erot（F–P） resonant coupling structure. The coupling between different types of F–P resonances leads to a near zero reflection, which results in a degeneration of eigenstates and thus the appearing of EP. Furthermore, the multi-wavelength EPs and unidirectional invisibility can be achieved which may be used in integrated photonics systems.

Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors

Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena,which can be fundamentally traced back to non-unitarity.In this paper,we introduce an interesting quantity(denoted asη)as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics.By tuning the model parameters of underlying non-Hermitian systems,we find that the discontinuity of bothηand its first-order derivative(denoted as■η)pronouncedly captures rich physics that is fundamentally caused by non-unitarity.More concretely,in the 1D non-Hermitian topological systems,two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity ofηas a function of the model parameter,which is dubbed"edge state transition".Through theoretical analysis,we identify that the appearance of edge state transition indicates the existence of exceptional points(EPs)in topological edge states.Regarding the discontinuity of■η,we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of■ηand EPs of bulk states.By studying this connection in more general lattice models,we find that some models have discontinuity of■η,implying the existence of EPs in bulk states.

On-chip single-photon chirality encircling exceptional points

Exceptional points(EPs),which are typically defined as the degener-acy points of a non-Hermitian Hamiltonian,have been investigated in various physical systems such as photonic systems.In particular,the intriguing topological structures around EPs have given rise to novel strategies for manipulating photons and the underlying mechanism is especially useful for on-chip photonic applications.Although some on-chip experiments with the adoption of lasers have been reported,EP-based photonic chips working in the quantum regime largely re-main elusive.In the current work,a single-photon experiment was proposed to dynamically encircle an EP in on-chip photonic waveg-uides possessing passive anti-parity-time symmetry.Photon coinci-dences measurement reveals a chiral feature of transporting single photons,which can act as a building block for on-chip quantum de-vices that require asymmetric transmissions.The findings in the cur-rent work pave the way for on-chip experimental study on the physics of EPs as well as inspiring applications for on-chip non-Hermitian quantum devices.

Design of a high sensitivity and wide range angular rate sensor based on exceptional surface

It is found that when the parity–time symmetry phenomenon is introduced into the resonant optical gyro system and it works near the exceptional point,the sensitivity can in theory be significantly amplified at low angular rate.However,in fact,the exceptional point is easily disturbed by external environmental variables,which means that it depends on harsh experimental environment and strong control ability,so it is difficult to move towards practical application.Here,we propose a new angular rate sensor structure based on exceptional surface,which has the advantages of high sensitivity and high robustness.The system consists of two fiber-optic ring resonators and two optical loop mirrors,and one of the resonators contains a variable ratio coupler and a variable optical attenuator.We theoretically analyze the system response,and the effects of phase and coupling ratio on the system response.Finally,compared with the conventional resonant gyro,the sensitivity of this exceptional surface angular rate sensor can be improved by about 300 times at low speed.In addition,by changing the loss coefficient in the ring resonator,we can achieve a wide range of 600 rad/s.This scheme provides a new approach for the development of ultra-high sensitivity and wide range angular rate sensors in the future.

Spontaneous T-symmetry breaking and exceptional points in cavity quantum electrodynamics systems

Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which an atomic ensemble interacts coherently with a single resonant cavity mode. The interacting system can be effectively described by two coupled oscillators with positive and negative mass, when the two-level atoms are prepared in their excited states. The occurrence of symmetry breaking is controlled by the atomic detuning and the coupling to the cavity mode,which naturally divides the parameter space into the symmetry broken and symmetry unbroken phases.The two phases are separated by a spectral singularity, a so-called exceptional point, where the eigenstates of the Hamiltonian coalesce. When encircling the singularity in the parameter space, the quasiadiabatic dynamics shows chiral mode switching which enables topological manipulation of quantum states.

Reconfigurable metamaterial for asymmetric and symmetric elastic wave absorption based on exceptional point in resonant bandgap

Elastic wave absorption at subwavelength scale is of significance in many engineering applications.Non-Hermitian metamaterials show the ability in high-efficiency wave absorption.However,the single functionality of metamaterials is an important limitation on their practical applications for lack of tunability and reconfigurability.Here,we propose a tunable and reconfigurable non-Hermitian piezoelectric metamaterial bar,in which piezoelectric bars connect with resonant circuits,to achieve asymmetric unidirectional perfect absorption(UPA)and symmetric bidirectional perfect absorption(PA)at low frequencies.The two functions can be arbitrarily switched by rearranging shunted circuits.Based on the reverberation-ray matrix(RRM)method,an approach is provided to achieve UPA by setting an exceptional point(EP)in the coupled resonant bandgap.By using the transfer matrix method(TMM)and the finite element method(FEM),it is observed that a non-Hermitian pseudo-band forms between two resonant bandgaps,and the EP appears at the bottom of the pseudo-band.In addition,the genetic algorithm is used to accurately and efficiently design the shunted circuits for desired low-frequency UPA and PA.The present work may provide new strategies for vibration suppression and guided waves manipulation in wide potential applications.

Nonlinear perturbation of a high-order exceptional point:Skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.

Majorana tunneling in a one-dimensional wire with non-Hermitian double quantum dots

The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneling and interdot tunneling in a non-Hermitian double quantum dots system. It is found that in the weak-coupling regime the Majorana tunneling has pronounced effects on the transport properties of such a system, manifested as splitting of the single peak into three and a reduced 1/4 peak in the transmission function. In the presence of the PT-symmetric complex potentials and interdot tunneling, the 1/4 central peak is robust against them, while the two side peaks are tuned by them. The interdot tunneling only induces asymmetry, instead of moving the conductance peak, due to the robustness of the Majorana modes. There is an exceptional point induced by the union of Majorana tunneling and interdot tunneling. With increased PT-symmetric complex potentials, the two side peaks will move towards each other. When the exceptional point is passed through, these two side peaks will disappear. In the strong-coupling regime, the Majorana fermion induces a 1/4 conductance dip instead of the three-peak structure. PT-symmetric complex potentials induce two conductance dips pinned at the exceptional point. These effects should be accessible in experiments.

Mode coupling with Fabry-Perot modes in photonic crystal slabs

Fabry–Perot(FP)modes are a class of fundamental resonances in photonic crystal(PhC)slabs.Owing to their low quality factors,FP modes are frequently considered as background fields with their resonance nature being neglected.Nevertheless,FP modes can play important roles in some phenomena,as exemplified by their coupling with guided resonance(GR)modes to achieve bound states in the continuum(BIC).Here,we further demonstrate the genuine resonance mode capability of FP modes PhC slabs.Firstly,we utilize temporal coupled-mode theory to obtain the transmittance of a PhC slab based on the FP modes.Secondly,we construct exceptional points(EPs)in both momentum and parameter spaces through the coupling of FP and GR modes.Furthermore,we identify a Fermi arc connecting two EPs and discuss the far-field polarization topology.This work elucidates that the widespread FPs in PhC slabs can serve as genuine resonant modes,facilitating the realization of desired functionalities through mode coupling.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

Observation of the exceptional point in superconducting qubit with dissipation controlled by parametric modulation

Open physical systems described by the non-Hermitian Hamiltonian with parity-time-reversal(PT)symmetry show peculiar phenomena,such as the presence of an exceptional point(EP)at which the PT symmetry is broken and two resonant modes of the Hamiltonian become degenerate.Near the EP,the system could be more sensitive to external perturbations and this may lead to enhanced sensing.In this paper,we present experimental results on the observation of PT symmetry broken transition and the EP using a tunable superconducting qubit.The quantum system of investigation is formed by the two levels of the qubit and the energy loss of the system to the environment is controlled by a method of parametric modulation of the qubit frequency.This method is simple with no requirements for additional elements or qubit device modifications.We believe it can be easily implemented on multi-qubit devices that would be suitable for further exploration of non-Hermitian physics in more complex and diverse systems.

Theory of complex-coordinate transformation acoustics for non-Hermitian metamaterials

Transformation acoustics(TA)has emerged as a powerful tool for designing several intriguing conceptual devices,which can manipulate acoustic waves in a flexible manner,yet their applications are limited in Hermitian materials.In this work,we propose the theory of complex-coordinate transformation acoustics(CCTA)and verify the effectiveness in realizing acoustic non-Hermitian metamaterials.Especially,we apply this theory for the first time to the design of acoustic parity-time(PT)and antisymmetric parity-time(APT)metamaterials and demonstrate two distinctive examples.First,we use this method to obtain the exceptional points(EPs)of the PT/APT system and observe the spontaneous phase transition of the scattering matrix in the transformation parameter space.Second,by selecting the Jacobian matrix's constitutive parameters,the PT/APT-symmetric system can also be configured to approach the zero and pole of the scattering matrix,behaving as an acoustic coherent perfect absorber and equivalent laser.We envision our proposed CCTAbased paradigm to open the way for exploring the non-Hermitian physics and finding application in the design of acoustic functional devices such as absorbers and amplifiers whose material parameters are hard to realize by using the conventional transformation method.

Coherent Perfect Absorption in Higher Order Systems

We investigate the phenomenon of coherent perfect absorption in a high-order system with three passive resonators coupled to a super-surface to form this three-state coherent perfect absorber. The effective parity time (PT) symmetry in the passive system has received much attention, and in this open three-state PT symmetric system, the incident wave is used as the effective gain instead of balancing the material gain and loss. We analyze the variation of coherent perfect absorption of this system with the coupling coefficient of the system by simulation.

Exceptional point enhanced nanoparticle detection in deformed Reuleaux‑triangle microcavity

In this paper,we propose a deformed Reuleaux-triangle resonator(RTR)to form exceptional point(EP)which results in the detection sensitivity enhancement of nanoparticle.After introducing single nanoparticle to the deformed RTR at EP,frequency splitting obtains an enhancement of more than 6 times compared with non-deformed RTR.In addition,EP induced a result that the far feld pattern of chiral mode responses signifcantly to external perturbation,corresponding to the change in internal chirality.Therefore,single nanoparticle with far distance of more than 4000 nm can be detected by measuring the variation of far feld directional emission.Compared to traditional frequency splitting,the far feld pattern produced in deformed RTR provides a cost-efective and convenient path to detect single nanoparticle at a long distance,without using tunable laser and external coupler.Our structure indicates great potential in high sensitivity sensor and label-free detector.

Reconfigurable exceptional point-based sensing with 0.001λsensitivity using spoof localized surface plasmons

Recent breakthroughs in the field of non-Hermitian physics present unprecedented opportunities,from fundamental theories to cutting-edge applications such as multimode lasers,unconventional wave transport,and high-performance sensors.The exceptional point,a spectral singularity widely existing in non-Hermitian systems,provides an indispensable route to enhance the sensitivity of optical detection.However,the exceptional point of the forementioned systems is set once the system is built or fabricated,and machining errors make it hard to reach such a state precisely.To this end,we develop a highly tunable and reconfigurable exceptional point system,i.e.,a single spoof plasmonic resonator suspended above a substrate and coupled with two freestanding Rayleigh scatterers.Our design offers great flexibility to control exceptional point states,enabling us to dynamically reconfigure the exceptional point formed by various multipolar modes across a broadband frequency range.Specifically,we experimentally implement five distinct exceptional points by precisely manipulating the positions of two movable Rayleigh scatterers.In addition,the enhanced perturbation strength offers remarkable sensitivity enhancement for detecting deep-subwavelength particles with the minimum dimension down to 0.001λ(withλto be the free-space wavelength).

Anti-PT-symmetric Kerr gyroscope

Non-Hermitian systems can exhibit unconventional spectral singularities called exceptional points(EPs).Various EP sensors have been fabricated in recent years,showing strong spectral responses to external signals.Here we propose how to achieve a nonlinear anti-parity-time(PT)gyroscope by spinning an optical resonator.We show that,in the absence of any nonlinearity,the sensitivity or optical mode splitting of the linear device can be magnified up to 3 orders compared to that of the conventional device without EPs.Remarkably,the PT symmetry can be broken when including the Kerr nonlinearity of the materials and,as a result,the detection threshold can be significantly lowered,i.e.,much weaker rotations which are well beyond the ability of a linear gyroscope can now be detected with the nonlinear device.Our work shows the powerful ability of PT gyroscopes in practice to achieve ultrasensitive rotation measurement.

Chiral exceptional point and coherent suppression of backscattering in silicon microring with low loss Mie scatterer

Non-Hermitian systems with their spectral degeneracies known as exceptional points(EPs)have been explored for lasing,controlling light transport,and enhancing a sensor’s response.A ring resonator can be brought to an EP by controlling the coupling between its frequency degenerate clockwise and counterclockwise traveling modes.This has been typically achieved by introducing two or more nanotips into the resonator’s mode volume.While this method provides a route to study EP physics,the basic understanding of how the nanotips’shape and size symmetry impact the system’s non-Hermicity is missing,along with additional loss from both in-plane and out-of-plane scattering.The limited resonance stability poses a challenge for leveraging EP effects for switches or modulators,which requires stable cavity resonance and fixed laser-cavity detuning.Here we use lithographically defined asymmetric and symmetric Mie scatterers,which enable subwavelength control of wave transmission and reflections without deflecting to additional radiation channels.We show that those pre-defined Mie scatterers can bring the system to an EP without post tuning,as well as enable chiral light transport within the resonator.Counterintuitively,the Mie scatterer results in enhanced quality factor measured on the transmission port,through coherently suppressing the backscattering from the waveguide surface roughness.The proposed device platform enables pre-defined chiral light propagation and backscattering-free resonances,needed for various applications such as frequency combs,solitons,sensing,and other nonlinear optical processes such as photon blockade,and regenerative oscillators.

Microscale vortex laser with controlled topological charge

A microscale vortex laser is a new type of coherent light source with small footprint that can directly generate vector vortex beams. However, a microscale laser with controlled topological charge, which is crucial for virtually any of its application, is still unrevealed. Here we present a microscale vortex laser with controlled topological charge. The vortex laser eigenmode was synthesized in a metamaterial engineered non-Hermitian micro-ring cavity system at exceptional point. We also show that the vortex laser cavity can operate at exceptional point stably to lase under optical pumping. The microscale vortex laser with controlled topological charge can serve as a unique and general building block for next- generation photonic integrated circuits and coherent vortex beam sources. The method we used here can be employed to generate lasing eigenmode with other complex functionalities.