Higher-order exceptional points (EPs), resulting from non-Hermitian degeneracies, have shown greater advantages in sensitive enhancement than second-order EPs (EP2s). Therefore, seeking higher-order EPs in various quantum systems is important for quantum information science. Here we propose a benchmark cavity optomechanical (COM) system consisting of a mechanical resonator (MR) coupled to two cavities via radiation pressure for predicting the third-order exceptional point (EP3). We first give the pseudo-Hermitian condition for the non-Hermitian COM system by taking the bath effects into account. Then we consider the mechanical gain effect and we find that the pseudo-Hermitian COM system without $\mathcal{PT}$ symmetry can host both the EP3 and EP2 for symmetric and asymmetric cavities. In the symmetric case, only the EP3 or EP2 can be predicted in the parameter space, but the EP3 and EP2 can be transformed into each other by tuning the COM coupling strength in the asymmetric case. We further consider the case of one cavity with gain. For this case, the pseudo-Hermitian COM system is $\mathcal{PT}$-symmetric and can also host the EP3 or EP2. The influence of system parameters on them are discussed. Our proposal provides a potential way to realize sensitive detection and study other physical phenomena {around} higher-order EP3 in non-Hermitian COM systems.
We develop a quantum mechanical method of measuring the Newtonian constant of gravitation, G. In this method, an optomechanical system consisting of two cavities and two membrane resonators is used. The added source mass would induce the shifts of the eigenfrequencies of the supermodes. Via detecting the shifts, we can perform our measurement of G. Furthermore, our system can features exceptional point (EP) which are branch point singularities of the spectrum and eigenfunctions. In the paper, we demonstrate that operating the system at EP can enhance our measurement of G. In addition, we deriv…
Higher-order exceptional points (EPs) in non-Hermitian systems have attracted great interest due to their advantages in sensitive enhancement and distinct topological features. However, realization of such EPs is still challenged because more fine-tuning parameters is generically required in quantum systems, compared to the second-order EP (EP2). Here, we propose a non-Hermitian three-mode optomechanical system in the blue-sideband regime for predicting the third-order EP (EP3). By deriving the pseudo-Hermitian condition for the proposed system, one cavity with loss and the other one with gain…
In this manuscript, working with a binary mechanical system, we examine the effect of quantum gravity on the exceptional points of the system. On the one side, we find that the exceedingly weak effect of quantum gravity can be sensed via pushing the system towards a second-order exceptional point, where the spectra of the non-Hermitian system exhibits non-analytic and even discontinuous behavior. On the other side, the gravity perturbation will affect the sensitivity of the system to deposition mass. In order to further enhance the sensitivity of the system to quantum gravity, we extend the sy…
We propose an optomechanical nano-gravimeter based on exceptional points. The system is a coupled cavity optomechanical system, in which the gain and loss are applied by driving the cavities with a blue detuned and red detuned electromagnetic field, respectively. When the gain and loss reach a balance, the system will show the degeneracy of exceptional points, and any perturbation will cause an eigenfrequencies split, which is proportional to the square root of the perturbation strength. Compared with the traditional optomechanical sensors, the sensitivity is greatly enhanced. This work paves …
We study optomechanically induced transparency in a microresonator coupled with nanoparticles. By tuning the relative angle of the nanoparticles, exceptional points (EPs) emerge periodically in this system and thus strongly modify both the transmission rate and the group delay of the signal. As a result, controllable slow-to-fast light switching can be achieved by manipulating external nanoparticles. This provides a new way to engineer EP-assisted optomechanical devices for applications in optical communications and signal processing.
The ground state cooling of Brillouin scattering optomechanical system is limited by defects in practical sample. In this paper, we propose a new compensatory cooling mechanism for Brillouin scattering optomechanical system with exceptional points (EPs). By using the EPs both in optical and mechanical modes, the limited cooling process is compensated effectively. The dual-EPs system, which is discovered in this work for the first time, can be induced by two defects with specific relative angles and has function of not only actively manipulating the coupling strength of optical modes but also t…
Exceptional points associated with non-hermitian operators, i.e. operators being non-hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within the domain of real parameters the exceptional points are the points where eigenvalues switch from real to complex values. These and other results are exemplified by a classical problem leading to exceptional points of a non-hermitian matrix.
Dynamical encircling exceptional point(EP) shows a number of intriguing physical phenomena and its potential applications. To enrich the manipulations of optical systems in experiment, here, we study the dynamical encircling EP, i.e. state transfer process, in largely detuned multimode optomechanical system. The process of state transfer has been investigated with different factors about the location of start point, the orientation and the initial state of the trajectories around the EP in parameter space. Results show that the nonreciprocal and the chiral topological energy transfer between t…
Exceptional points (EPs) represent a distinct type of spectral singularity in non-Hermitian systems, and intriguing physics concepts have been studied with optical EPs recently. As a system beyond photonics, the mechanical oscillators coupling with many physical systems are expected to be further exploited EPs for mechanical sensing, topology energy transfer, nonreciprocal dynamics etc. In this study, we demonstrated on-chip mechanical EPs with a silicon optomechanical zipper cavity, wherein two near-degenerate mechanical breathing modes are coupled via a single co-localized optical mode. By t…
We show a parameter-dependent $3\times 3$ non-Hermitian matrix that exhibits both degeneracy and coalescence of eigenvalues at an exceptional point (Hermitian and non-Hermitian degeneracies). This simple non-Hermitian model is suitable for the discussion of those concepts in an undergraduate or graduate course on quantum-mechanics. We also study the symmetry group responsible for the degeneracy.
The exceptional points of non-Hermitian systems, where $n$ different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the $ε^{1/n}$ dependence of the energy level splitting on a perturbative parameter $ε$ near an $n$-th order exceptional point stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility $dε^{1/n}/dε$ diverges at the exceptional point. Here we theoretically study the sensitivity of parameter estimation near the exceptional points, using the exact formali…
Non-Hermitian systems with parity-time symmetry have been developed rapidly and hold great promise for future applications. Unlike most existing works considering the symmetry of the free energy terms (e.g., gain-loss system), in this paper, we report that a realizable non-Hermitian interaction between two quantum resonances can also have a real spectrum after the exceptional point. That phenomenon is similar with that in the gain-loss system so that the non-Hermitian interaction can be an excellent substitute for quantum gain. Such a non-Hermitian interaction can be realized in designed optom…
Exceptional points (EPs) have recently attracted considerable attention in the study of non-Hermitian systems and in applications such as sensors and mode switching. In particular, nontrivial topological structures of EPs have been studied intensively in relation to encircling EPs. Thus, EP generation is currently an important issue in several fields. To generate multiple EPs, multiple levels or composite physical systems have been employed with Hermitian couplings. In this study, we generate multiple EPs on two-level systems in a single microcavity by adopting the non-Hermitian coupling of a …
Complex potential and non-Hermitian hopping amplitude are building blocks of a non-Hermitian quantum network. Appropriate configuration, such as PT-symmetric distribution, can lead to the full real spectrum. To investigate the underlying mechanism of this phenomenon, we study the phase diagram of a semi-infinite non-Hermitian system. It consists of a finite non-Hermitian cluster and a semi-infinite lead. Based on the analysis of the solution of the concrete systems, it is shown that it can have the full real spectrum without any requirements on the symmetry and the wave function within the lea…
Topological operations have the merit of achieving certain goals without requiring accurate control over local operational details. To date, topological operations have been used to control geometric phases, and have been proposed as a means for controlling the state of certain systems within their degenerate subspaces[1-8]. More recently, it was predicted that topological operations can be extended to transfer energy between normal modes, provided that the system possesses a specific type of degeneracy known as an exceptional point (EP)[9-11]. Here we demonstrate the transfer of energy betwee…
In contrast to Hermitian systems, eigenstates of non-Hermitian ones are in general nonorthogonal. This feature is most pronounced at exceptional points where several eigenstates are linearly dependent. In this work we show that near this point a new effect takes place. It exhibits in energy increases in the system when its parameters change periodically. This effect resembles parametric resonance in a Hermitian system but there is a fundamental difference. It comes from the unique properties of the exceptional point that leads to parametric instability that occurs almost at any change in a par…
Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formula…
We study quantum phase transitions in non-Hermitian XY and transverse-field Ising spin chains, in which the non-Hermiticity arises from the imaginary magnetic field. Analytical and numerical results show that at exceptional points, coalescing eigenstates in these models close to W, distant Bell and GHZ states, which can be steady states in dynamical preparation scheme proposed by T. D. Lee et. al. (Phys. Rev. Lett. 113, 250401 (2014)). Selecting proper initial states, numerical simulations demonstrate the time evolution process to the target states with high fidelity.
Exceptional points are complex-valued spectral singularities that lead to a host of intriguing features such as loss-induced transparency - a counterintuitive process in which an increase in the system's overall loss can lead to enhanced transmission. In general, the associated enhancements scale with the order of the exceptional points. Consequently, it is of great interest to devise new strategies to implement realistic devices capable of exhibiting high-order exceptional points. Here, we show that high-order N-photon exceptional points can be generated by exciting non-hermitian waveguide ar…
The spectral and transport properties of a non-Hermitian tight-binding lattice with unidirectional hopping are theoretically investigated in three different geometrical settings. It is shown that, while for the infinitely-extended (open) and for the ring lattice geometries the spectrum is complex, lattice truncation makes the spectrum real. However, an exceptional point of order equal to the number of lattice sites emerges. When a homogeneous dc force is applied to the lattice, in all cases an equally-spaced real Wannier-Stark ladder spectrum is obtained, corresponding to periodic oscillatory …
We have investigated the exceptional points (EPs) which are degeneracies of a non-Hermitian Hamiltonian, in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely determined when encircling more than two EPs once, we can recover the initial configuration of the modes by encircling two EPs three times or three EPs twice. We confirm our expectation by numerically calculating the modes of an open quantum system, two dielectric microdisks, and 3$\times$3 matrix model.
Non-Hermitian systems exhibit many peculiar dynamic behaviors which never showed up in Hermitian systems. The existence of spectral singularity (SS) for a non-Hermitian scattering center provides a lasing mechanism in the context of quantum mechanics. In this paper we show exactly that a finite system at exceptional point (EP) can also provide an alternative laser solution. We investigate the dynamics of non-Hermitian Su-Schrieffer-Heeger (SSH) model around EP, based on the analysis of parity-time (PT ) and chiral-time (CT ) symmetries of the Hamiltonian. In contrast to the SS lasing mechanism…
We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of {the} two-level system are allowed to decay because of the interaction with the environment, {and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energ…
We show that the author of a recent paper [arXiv:2008.04929] put forward some false statements about the eigenstates of Hermitian and non-Hermitian systems. We conjecture that one of the non-Hermitian Hamiltonians for a one-dimensional lattice is similar to an Hermitian one and, consequently, exhibits real eigenvalues. Present theoretical analysis of the eigenvalue equation suggests that one of the sets of numerical results in the criticized paper may not be correct.
Tuning topological phases and exceptional points in a non-Hermitian Rice Mele model beyond nearest neighbors
Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Chemistry Faculty (UPV/EHU)（巴斯克地区理工大学化学学院）；IKERBASQUE, Basque Foundation for Science（伊克拉巴斯基奎巴斯克科学基金会）；Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）
The balance of gain and loss in an open system may maintain certain Hermitian dynamical behaviors, which can be hardly observed in a popular Hermitian system. In this paper, we systematically study a 1D PT -symmetry non-Hermitian SSH model with open boundary condition based on exact approximate solution. We show that the long-wave length standing-wave modes can be achieved within the linear dispersion region when the system is tuned at the exceptional point (EP). The whole Hilbert space can be decomposed into two quasi-Hermitian subspaces, which are consisted of positive and negative energy le…
Non-Hermitian quantum systems with explicit time dependence are of ever-increasing importance. There are only a handful of models that have been analytically studied in this context. Here, a PT-symmetric non-Hermitian $N$-level Landau-Zener type problem with two exceptional points of $N$th order is introduced. The system is Hermitian for asymptotically large times, far away from the exceptional points, and has purely imaginary eigenvalues between the exceptional points. The full Landau-Zener transition probabilities are derived, and found to show a characteristic binomial behaviour. In the adi…
Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays
University of Ngaoundere（恩冈代雷大学）；Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University（斯坦伦布什大学高级研究所（STIAS），瓦伦伯格研究中心）；University of Bisha（比沙大学）；University of Business and Technology（商业与技术大学）；University of Maroua（马鲁阿大学）；University of Yaounde I（雅温得第一大学）
We systematically study the topology of the exceptional point (EP) in the finite non-Hermitian system. Based on the concrete form of the Berry connection, we demonstrate that the exceptional line (EL), at which the eigenstates coalesce, can act as a vortex filament. The direction of the EL can be identified by the corresponding Berry curvature. In this context, such a correspondence makes the topology of the EL clear at a glance. As an example, we apply this finding to the non-Hermitian Rice-Mele (RM) model, the non-Hermiticity of which arises from the staggered on-site complex potential. The …
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 quantu…
We study the energy-level evolution and ground-state cooling of mechanical resonators under a synthetic phononic gauge field. The tunable gauge phase is mediated by the phase difference between the $\mathcal{PT}$- and anti-$\mathcal{PT}$-symmetric mechanical couplings in a multimode optomechanical system. The transmission spectrum then exhibits the asymmetric Fano line shape or double optomechanically induced transparency by modulating the gauge phase. Moreover, the eigenvalues will collapse and become degenerate although the mechanical coupling is continuously increased. Such counterintuitive…
Exceptional points (EPs), the degeneracy point of non-Hermitian systems, have recently attracted great attention after its ability to greatly enhance the sensitivity of micro-cavities is demonstrated experimentally. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although some of the exotic properties and potential applications of EPs are explored, the range of EPs studied is largely limited by the experimental capability. Some of the systems, e.g. with higher-order EPs, are hard to achieve with conventional simulations. Here we pro…
Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt ech…
Sympathetic Cooling of Levitated Optomechanics through Nonreciprocal Coupling
Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology（北京理工大学物理学院量子技术研究中心及先进光电子量子架构与测量教育部重点实验室）
Engineered non-Hermitian systems featuring exceptional points can lead to a host of extraordinary phenomena in diverse fields ranging from photonics, acoustics, opto-mechanics, electronics, to atomic physics. Here we introduce and present 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-sen…
We present the observation of diabolic points in Hermitian and non-Hermitian electronics dimers. The condition of unbreakable Parity-time symmetry is established for both PT-symmetric ZRC and RLC dimers. We show how appears non-Hermitian degeneracy points in the spectrum and how they are protected against a Hermitian perturbation. When a non- Hermitian perturbation is added in the setup, the non-Hermitian diabolic point (NHDP) turns into a ring of exceptional points as in some Dirac and Weyl semimetals. Some experimental simulations of oscillations around these particular points in LTspice are…
Level repulsion - the opening of a gap between two degenerate modes due to coupling - is ubiquitous anywhere from solid state theory to quantum chemistry. In contrast, if one mode has negative energy, the mode frequencies attract instead. They converge and develop imaginary components, leading to an instability; an exceptional point marks the transition. This, however, only occurs if the dissipation rates of the two modes are comparable. Here we expose a theoretical framework for the general phenomenon and realize it experimentally through engineered dissipation in a multimode superconducting …
