I. Rotter
It is shown that the two experiments Dembowski et al., PRL 86, 787 (2001), and Lauber et al., PRL 72, 1004 (1994), prove the same topological singularity. The phase changes found in both experiments are related to a second order branch point in the complex plane.
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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 describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier \etal, Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose-Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of s…
Eigenvectors of decaying quantum systems are studied at exceptional points of the Hamiltonian. Special attention is paid to the properties of the system under time reversal symmetry breaking. At the exceptional point the chiral character of the system -- found for time reversal symmetry -- generically persists. It is, however, no longer circular but rather elliptic.
Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through an exceptional point, which is a non-Hermitian degenerate point with coalesced eigenvalues and eigenvectors. In this letter we reveal an anomalous PT transition that takes place away from an exceptional point in a nonlinear system: as the nonlinearity increases, the original linear system evolves along two distinct PT-symmetric trajectories, each of which can…
Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is notoriously difficult. Recently, Q. Zhong et al. [Phys. Rev. Lett. 125, 203602 (2020)] have introduced a robust construction where a unidirectional coupling of two subsystems having exceptional points of the same order leads generically to a single exceptional point of twice the order. Here, we investigate this scheme in a different manner by exploiting the n…
Topologically Protected Exceptional Points and Reentrant $\mathcal{PT}$ Phase in an Exact Ternary Model
本文提出一个精确可解的三元 PT 对称模型，统一呈现重入 PT 相、高阶及各向异性例外点，并以新的拓扑指数揭示其共同起源。
Exceptional points of arbitrary high orders induced by non-Markovian dynamics
本文通过非马尔可夫动力学诱导出任意高阶例外点，突破传统认为例外点阶数受限于系统自由度的观点。
The original versions (1 and 2) of this paper paper contain a fatal error. All my attempts to patch the error have failed. As a service to the community I explain the error in some detail.
Yuan and Shields claim that our data-encryption protocol is entirely equivalent to a classical stream cipher utilizing no quantum phenomena. Their claim is, indeed, false. Yuan and Shields also claim that schemes similar to the one presented in Phys. Rev. Lett. 90, 227901 are not suitable for key generation. This claim is also refuted. In any event, we welcome the opportunity to clarify the situation for a wider audience.
This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]
Exceptional points and phase transitions in non-Hermitian binary systems
本文揭示了非厄米二能级系统中例外点与相变的关系，证明例外点是稳定与不稳定解合并处而非相边界端点，并发现弱耦合区也可发生相变及持续 Rabi 振荡。
We use the exceptional point in Hopfield-Bogoliubov matrix to find the phase transition points in the bosonic system. In many previous jobs, the excitation energy vanished at the critical point. It can be stated equivalently that quantum critical point is obtained when the determinant of Hopfield-Bogoliubov matrix vanishes. We analytically obtain the Hopfield-Bogoliubov matrix corresponding to the general quadratic Hamiltonian. For single-mode system the appearance of the exceptional point in Hopfield-Bogoliubov matrix is equivalent to the disappearance of the determinant of Hopfield-Bogoliubo…
Two subtleties of this paper are discussed.
The inequalities proposed in [Phys. Rev. Lett. 105, 170404 (2010)] are not Bell's inequalities in the usual sense: there are local classical models that violate these inequalities. Thus, their violation demonstrates nonlocality only under assumptions about the physical implementation and moreover they cannot be used as a device-independent test of nonlocality.
We point out the relation between the work of Zheng and ours, APS [G.S. Agarwal, R.R. Puri, and R.P. Singh, Phys. Rev. A 56, 2249 (2001)] and show the important connection between the atomic cat state and the GHZ states.
In a recent letter, Barbosa et al [PRL 90, 227901(2003)] claim that secure communication is possible with bright coherent pulses, by using quantum noise to hide the data from an eavesdropper. We show here that the secrecy in the scheme of Barbosa et al is unrelated to quantum noise, but rather derives from the secret key that sender and receiver share beforehand.
Comment on Chiribella et al., Phys. Rev. Lett. 132 (2024) 190201, arXiv:2301.10885
本文指出 Chiribella 等人对“经典”的定义忽略非对易量子投影子，因而与希尔伯特空间量子理论不一致。
Adjusting exceptional points using saturable nonlinearities
本文研究可饱和非线性对非厄米二聚体系统中奇异点的影响，发现非线性可产生多个本征值，并证明通过调节失谐空间中的非相等可饱和非线性能够精确定位奇异点。
I critize some of the conclusions in the paper by Danan et al, in particular their claim that '(S)ome (of the photons) have been inside the nested interferometer ... but they never entered and never left (it) ...'. A standard quantum-mechanical analysis also casts doubts on their statement that '(o)nly the description with forward and backward evolving quantum states provides a simple and intuitive picture of pre- and postselected quantum particles.'
In Phys. Rev. Lett. 113, 120404 (2014) [arXiv:1403.2362], Ferrie and Combes claim that weak values could be a statistical artifact caused by correlations between the disturbance and the post-selection condition imposed on the output. In this comment, we show that the disturbance caused by a weak measurement is sufficiently low to definitely rule out the model proposed by Ferrie and Combes.
Encircling the Liouvillian exceptional points: a brief review
本文简要综述了通过参数环绕Liouvillian例外点引起的手性态转移，涵盖理论描述、实验观察及多体效应下的集体动力学现象，并探讨其量子应用潜力。
We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system. We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to swept the eigenstates through the exceptional points in parameter space. The non-trivial Berry phases of the eigenstates obtained in this loop from the exceptional points can be measured by the a…
The claim that Kuwahara et al. [1] have reported the observation of a Hanbury Brown-Twiss electron antibunching dip (their Fig. 3) could possibly be explained as an electron source emission rate dependency on the light polarization. Strain on their GaAs/GaAsP sample is uniaxial, and one would expect a linear dichroism in the photoemission possibly as large as 15% [7] - much larger than the 0.1% reported effect. The same concern exist for circular polarized light.
Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities
研究分析了多模玻色子系统中量子例外、魔鬼和混合点的特性及动力学行为，揭示了其退化性和复杂动态。
Gao applied LeRoy and Bernstein semi-classical analysis for the energy levels in a potential of the form -C/r^n to sequences of scaled energy differences progressing towards low lying states and found a better agreement with the semi-classical prediction. We checked that for the energy levels obtained by Stwalley et al. with the same potential, the agreement with the semi-classical approximation is better for higher vibrational quantum numbers in agreement with Bohr's correspondence principle.
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, …
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 report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and non-symmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity.
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival is shown to take place in the corresponding quantum walks.
Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic topologically stable exceptional points according to two types of complex-energy gaps and fundamental symmetries of charge conjugation, parity, and time reversal. This classification reveals unique non-Hermitian gapless structures with no Hermitian analogs and systematically predicts unknown non-Hermitian semimetals and nodal superconductors; a topological dumbbe…
Comment on Hess et al. Phys. Rev. Lett. {\bf 130}, 207001 (2023)
本评论指出 Hess 等人 2023 年提出的模型未通过拓扑能隙协议 TGP，并结合该协议的基准检验背景讨论其意义。
Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
本文证明Lindbladian PT对称性可普遍产生持续周期振荡，涵盖耗散连续时间晶体模型和空间扩展玻色系统，并揭示PT对称相中的周期轨道为中心型，依赖初始态。
Exceptional points in non-Hermitian Photonics: Applications and Recent Developments
本文综述了非厄米光子平台中例外点的近期发展，并探讨了光学非线性和例外束缚态对未来非厄米光子学的潜在影响。
We study the parity and time-reversal ($\mathcal{PT}$) symmetric quantum physics in a non-Hermitian non-relativistic hydrogen molecule with local (Hubbard type) Coulomb interaction. We consider non-Hermiticity generated from both kinetic and orbital energies of the atoms and encounter the existence of two different types of exceptional points (EPs) in pairs. These two kinds of EP are characteristically different and depend differently on the interaction strength. Our discovery may open the gates of a rich physics emerging out of a simple Hamiltonian resembling a two-site Hubbard model.
The Comment by Xiong et al. (arXiv:1610.06275) criticizing my Letter [Phys. Rev. Lett. 116, 133903 (2016)] was rejected by Physical Review Letters. In this Reply, I show that all their claims are wrong.
Toida et al. claim in their recent article [Phys. Rev. Lett. 110, 066802 (2013)] that they `report a direct observation of vacuum Rabi splitting in a GaAs/AlGaAs double quantum dot (DQD) based charge qubit coupled with a superconducting coplanar waveguide (CPW) resonator'. In this comment, we challenge the main claims made in their paper and show that their results: a) do not provide any evidence of vacuum Rabi oscillations and b) do not provide any direct evidence of vacuum Rabi splitting.
Constructing Non-Hermitian Theories with Tunable Exceptional Points and Controlled State Purification
该研究以动量空间形变为通用原理，构建了含可调例外点的非厄米理论，可实现混合量子态纯化与非厄米量子物质的逆向工程，为多体非厄米系统设计提供了统一途径。
Exceptional swallowtail degeneracies in driven-dissipative quadrature squeezing
本文发现双模驱动耗散正交压缩系统中存在燕尾简并结构，该结构可实现复特征值的非平凡编织，为高斯态的拓扑控制提供新途径。
Boundary-Driven Exceptional Points in Photonic Waveguide Lattices
该研究通过侧耦合缺陷在无限长光子波导晶格中诱导边界驱动的异常点，揭示了非马尔可夫记忆核对共振轨迹和共扼条件的影响，为探索记忆增强的非Hermitian物理提供了实验平台。
Crossing exceptional points in non-Hermitian quantum systems
本文利用不可区分双光子输入探测有损定向耦合器，实验揭示非厄米系统跨越奇异点时量子关联变化及奇异点处Hong-Ou-Mandel干涉由凹陷到峰值的切换。
We present a reinterpretation of our previous results on the radial compression mode of a degenerate quantum gas in the BEC-BCS crossover in [1]. We show that our former data are consistent with other experimental and theoretical work, when the ellipticity of the optical trapping potential in [1] is properly taken into account.
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