The efficient transfer of excitations between different levels of a quantum system is a task with many applications. Among the various protocols to carry out such a state transfer in driven systems, rapid adiabatic passage (RAP) is one of the most widely used. Here we show both theoretically and experimentally that adding a suitable amount of loss to the driven Hamiltonian turns a RAP protocol into a scheme for encircling an exceptional point including the chiral state transfer associated with it. Our work thus discloses an intimate connection between a whole body of literature on RAP and recent studies on the dynamics in the vicinity of an exceptional point, which we expect to serve as a bridge between the disjoint communities working on these two scenarios.
Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise. Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly, like a state-flip or the accumulation of a geometric phase. Experiments dedicated to this issue could already successfully explore the topological structur…
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…
Dynamically encircling exceptional points (EPs) in two-dimensional Hamiltonian parameter space has enabled intriguing chiral dynamics in which the final state of the system depends on the encircling direction. Here, we show that full Hamiltonian parameter space can be described in a Riemann sphere, and those points on the parameter space boundary with the eigenstates of the system Hamiltonian being convergent, converge to the north vertex. We present that encircling one EP on the Riemann sphere leads to chiral response, and a continuous encircling trajectory passing through the north vertex ca…
Exceptional points are degeneracies in non-Hermitian systems. A two-state system with parity-time (PT) symmetry usually has only one exceptional point beyond which the eigenmodes are PT-symmetry broken. The so-called symmetry recovery, i.e., eigenmodes become PT-symmetric again, typically occurs in multi-state systems. Here we show that a two-state ferromagnetic waveguide system can have an exceptional point and a subsequent symmetry recovery due to the presence of accidental degeneracy points when the system is lossless. By introducing a parameter space where both exceptional points reside, w…
The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directi…
Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric systems shows an interesting chiral dynamics, leading to asymmetric mode switching in which the output modes are different when the encircling direction is reversed. Here we show that the dynamical encircling of an EP in anti-PT-symmetric systems can also result in chiral dynamics if the starting/end point lies in the PT-broken phase, in contrast to PT-symmetric systems where chiral dynamics emerges if the starting/end point lies in the PT-unbroken phase. For many applications, such as signal processing using wavegu…
Dynamically varying system parameters along a path enclosing an exceptional point is known to lead to chiral mode conversion. But is it necessary to include this non-Hermitian degeneracy inside the contour for this process to take place? We show that a slow enough variation of parameters, even away from the system's exceptional point, can also lead to a robust asymmetric state exchange. To study this process, we consider a prototypical two-level non-Hermitian Hamiltonian with a constant coupling between elements. Closed form solutions are obtained when the amplification/attenuation coefficient…
We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate irrespective of initial conditions. Moreover, numerical simulations suggest t…
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 conversion [1- 8]. Recent theoretical studies, however, have shown that contrary to previously established demonstrations, this behavior is not strictly a result of wi…
Eigenmode coalescence imparts remarkable properties to non-hermitian time evolution, culminating in a purely non-hermitian spectral degeneracy known as an exceptional point (EP). Here, we revisit time evolution at the EP and classify two-level non-hermitian Hamiltonians in terms of the Möbius group. We then leverage that classification to study dynamical EP encircling, by applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that Floquet non-hermitian systems exhibit rich physics whose complexity is not captured by an EP-encircling rule. For example, Floquet EPs can occur …
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately describe the evolution of non-Hermitian systems when encircling an exceptional point. This allows us to use the recently proposed Magnus-based strategy for control to design fast non-reciprocal, topological operations whose fidelity error is orders of magnitude smaller than their much slower adiabatic counterparts.
Topological Switching via Exceptional Point Pairs in an Optical Microcavity Laser
Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University（庆熙大学数学系与基础科学研究院）；Research Institute of Mathematics, Seoul National University（首尔大学数学研究院）；Korea Research Institute of Standards and Science（韩国计量科学研究院）；Digital Technology Research Center, Kyungpook National University（庆北国立大学数字技术中心）；School of Computational Sciences, Korea Institute for Advanced Study（韩国高等科学研究院计算科学学院）
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyse this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasi-stationarity interrupted by abrupt non-adiabatic transitions, and we present a qualitative and quant…
We investigate a parity-time (PT) symmetric system that consists of two symmetrically coupled asymmetric dimers. The enclosed magnetic flux controls the PT phase transition. The system can reenter the exact PT-symmetric phase from a broken PT-symmetric phase with large non-Hermiticity. Two-state coalescence may have one or two defective eigenstates. The topology of exceptional points is reflected by the magnetic flux independent phase rigidity scaling exponents. The topology changes when exceptional points coincide. The geometric phases accumulate when encircling the exceptional points and var…
We demonstrate general classifications of Riemann surface topology generated by multiple arbitrary-order exceptional points of quasi-stationary states. Our studies reveal all possible product permutations of holonomy matrices that describe a stroboscopic encircling of 2nd order exceptional points. The permutations turn out to be categorized into a finite number of classes according to the topological structures of the Riemann surfaces. We further show that the permutation classes can be derived from combinations of cyclic building blocks associated with higher-order exceptional points. Our res…
Non-Hermitian systems have recently attracted significant attention in photonics. One of the hallmarks of these systems is the possibility of realizing asymmetric mode switching and omnipolarizer action through the dynamic encirclement of exceptional points (EP). Here, we offer a new perspective on the operating principle of these devices, and we theoretically and experimentally show that asymmetric mode switching and omni-polarizer action can be easily realized with the same performance and limitations, using simple configurations that emulate the physics involved in encircling EPs without th…
We investigate the exceptional points (EPs) in a non-Hermitian system composed of a pair of graphene sheets with different losses. There are two surface plasmon polaritons (SPP) modes in the graphene waveguide. By varying the distance between two graphene sheets and chemical potential of graphene, the EPs appear as the eigenvalues, that is, the wave vectors of the two modes coalesce. The cross conversion of eigenmodes and variation of geometric phase can be observed by encircling the EP in the parametric space formed by the geometric parameters and chemical potential of graphene. At the same t…
Exceptional Points in Photonics: From Non-Hermitian Physics to Applications
Harbin Engineering University（哈尔滨工程大学）；ITMO University（ITMO大学）；Siberian Federal University（西伯利亚联邦大学）；LV Kirensky Institute of Physics, Federal Research Center KSC SB RAS（LV基伦斯基物理研究所，俄罗斯科学院西伯利亚分院克拉斯诺亚尔斯克科学中心联邦研究中心）；University of California, Irvine（加州大学尔湾分校）；The Hong Kong University of Science and Technology（香港科技大学）
When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called "Exceptional Point" occurs which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such "non-Hermitian degeneracies", since they feature resonant modes and a gain material as their basic constituents. Here we show that Exceptional Points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled micro-disk quantum cascade lasers, we demonstrat…
$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by scattering matrices. A multilayer structure, as a simplest example of the open system, has no certain definition of the scattering matrix, since the output ports can be permuted. The uncertainty in definition of the exceptional points bordering $\mathcal{PT}$-symmetric and $\mathcal{PT}$-symmetry-broken states poses an important problem, because the exception…
Stimulated Raman adiabatic passage (STIRAP) describes adiabatic population transfer between two states coherently coupled via a mediating state that remains unoccupied. This renders STIRAP robust against loss in the mediating state, leading to profound applications in atomic- and molecular-beam research, trapped-ion physics, superconducting circuits, other solid-state systems, optics, in entanglement generation and qubit operations. STIRAP in optomechanics has been considered for optical frequency conversion where a mechanical mode provides the mediating state. Given the advances of optomechan…
Enantiosensitive exceptional points in open chiral systems
Max-Born-Institut（马克斯·玻恩研究所）；Attosecond Quantum Physics Laboratory, Physics Department, King’s College London（伦敦国王学院物理学院阿秒量子物理实验室）；Technion-Israel Institute of Technology（以色列理工学院）；Institute of Advanced Studies in Theoretical Chemistry, Technion-Israel Institute of Technology（以色列理工学院理论化学高级研究所）；Department of Physics, Humboldt Universität zu Berlin（柏林洪堡大学物理系）；Department of Physics, Imperial College London（伦敦帝国理工学院物理系）；Technische Universität Berlin（柏林工业大学）
Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (i.e., non-Hermitian) quantum system: it requires constant pumping of energy and continuously decays releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and los…
Observation of Restored Adiabatic State Transfer in Time-Modulated Non-Hermitian Systems
Beijing Computational Science Research Center（北京计算科学研究中心）；Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University（帕尔卡大学与捷克科学院物理研究所联合光学实验室，帕尔卡大学理学院）；School of Physics, Southeast University（东南大学物理学院）；Quantum Information Physics Theory Research Team, Quantum Computing Center, RIKEN（理研量子计算中心量子信息物理理论研究组）
