Exceptional points in optics and photonics

Science ◽  
2019 ◽  
Vol 363 (6422) ◽  
pp. eaar7709 ◽  
Author(s):  
Mohammad-Ali Miri ◽  
Andrea Alù
Keyword(s):  
Open Systems ◽  
Optical Gain ◽  
Exceptional Point ◽  
Nanoscale Structures ◽  
Exceptional Points ◽  
Time Symmetry ◽  
Applied Technology ◽  
Recent Developments ◽  
Laser Systems ◽  
Distinct Features

Exceptional points are branch point singularities in the parameter space of a system at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become degenerate. Such peculiar degeneracies are distinct features of non-Hermitian systems, which do not obey conservation laws because they exchange energy with the surrounding environment. Non-Hermiticity has been of great interest in recent years, particularly in connection with the quantum mechanical notion of parity-time symmetry, after the realization that Hamiltonians satisfying this special symmetry can exhibit entirely real spectra. These concepts have become of particular interest in photonics because optical gain and loss can be integrated and controlled with high resolution in nanoscale structures, realizing an ideal playground for non-Hermitian physics, parity-time symmetry, and exceptional points. As we control dissipation and amplification in a nanophotonic system, the emergence of exceptional point singularities dramatically alters their overall response, leading to a range of exotic optical functionalities associated with abrupt phase transitions in the eigenvalue spectrum. These concepts enable ultrasensitive measurements, superior manipulation of the modal content of multimode lasers, and adiabatic control of topological energy transfer for mode and polarization conversion. Non-Hermitian degeneracies have also been exploited in exotic laser systems, new nonlinear optics schemes, and exotic scattering features in open systems. Here we review the opportunities offered by exceptional point physics in photonics, discuss recent developments in theoretical and experimental research based on photonic exceptional points, and examine future opportunities in this area from basic science to applied technology.

scholarly journals Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Arik Bergman ◽  
Robert Duggan ◽  
Kavita Sharma ◽  
Moshe Tur ◽  
Avi Zadok ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Brillouin Scattering ◽  
Optical Gain ◽  
Single Mode ◽  
Exceptional Point ◽  
Small Scale ◽  
Time Symmetry ◽  
Topological Features ◽  
Gain And Loss ◽  
Exotic Physics

AbstractThe exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has recently drawn a great deal of attention. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. So far, these principles have been implemented at the expense of precise fabrication and tuning requirements, involving tailored nano-structured devices with controlled optical gain and loss. In this work, anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of single-mode telecommunication fibre, using a setup consisting of off-the-shelf components. Two propagating signals are amplified and coupled through stimulated Brillouin scattering, enabling exquisite control over the interaction-governing non-Hermitian parameters. Singular response to small-scale variations and topological features arising around the exceptional point are experimentally demonstrated with large precision, enabling robustly enhanced response to changes in Brillouin frequency shift.

scholarly journals Exceptional points in oligomer chains

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Charles Andrew Downing ◽  
Vasil Arkadievich Saroka
Keyword(s):  
Open Systems ◽  
Light Transport ◽  
Coupled Modes ◽  
Exceptional Points ◽  
Time Symmetry ◽  
Degree Of Coherence ◽  
Quantum Objects ◽  
Long Range Interactions ◽  
And Control ◽  
Symmetric Systems

AbstractSymmetry underpins our understanding of physical law. Open systems, those in contact with their environment, can provide a platform to explore parity-time symmetry. While classical parity-time symmetric systems have received a lot of attention, especially because of the associated advances in the generation and control of light, there is much more to be discovered about their quantum counterparts. Here we provide a quantum theory which describes the non-Hermitian physics of chains of coupled modes, which has applications across optics and photonics. We elucidate the origin of the exceptional points which govern the parity-time symmetry, survey their signatures in quantum transport, study their influence for correlations, and account for long-range interactions. We also find how the locations of the exceptional points evolve as a function of the chain length and chain parity, capturing how an arbitrary oligomer chain transitions from its unbroken to broken symmetric phase. Our general results provide perspectives for the experimental detection of parity-time symmetric phases in one-dimensional arrays of quantum objects, with consequences for light transport and its degree of coherence.

scholarly journals Exceptional Points for Nonlinear Schroedinger Equations Describing Bose-Einstein Condensates of Ultracold Atomic Gases

10.14311/1418 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
G. Wunner ◽  
H. Cartarius ◽  
P. Koeberle ◽  
J. Main ◽  
S. Rau
Keyword(s):  
Parameter Space ◽  
Open Systems ◽  
Energy Eigenvalue ◽  
Exceptional Point ◽  
Pitaevskii Equation ◽  
Critical Set ◽  
Exceptional Points ◽  
Schroedinger Equations ◽  
Pass Through ◽  
Bose Einstein

The coalescence of two eigenfunctions with the same energy eigenvalue is not possible in Hermitian Hamiltonians. It is, however, a phenomenon well known from non-hermitian quantum mechanics. It can appear, e.g., for resonances in open systems, with complex energy eigenvalues. If two eigenvalues of a quantum mechanical system which depends on two or more parameters pass through such a branch point singularity at a critical set of parameters, the point in the parameter space is called an exceptional point. We will demonstrate that exceptional points occur not only for non-hermitean Hamiltonians but also in the nonlinear Schroedinger equations which describe Bose-Einstein condensates, i.e., the Gross-Pitaevskii equation for condensates with a short-range contact interaction, and with additional long-range interactions. Typically, in these condensates the exceptional points are also found to be bifurcation points in parameter space. For condensates with a gravity-like interaction between the atoms, these findings can be confirmed in an analytical way.

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

Anomalous Heat Conduction, Diffusion and Heat Rectification in Nanoscale Structures

2009 ◽  
Author(s):  
Gang Zhang ◽  
Nuo Yang ◽  
Gang Wu ◽  
Baowen Li
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Transport ◽  
Nano Materials ◽  
Fourier Law ◽  
Nanoscale Structures ◽  
Recent Developments ◽  
Theoretical Results ◽  
Good Agreement ◽  
Anomalous Heat

In this paper, we report the recent developments in the study of heat transport in nano materials. First of all, we show that phonon transports in nanotube super-diffusively which leads to a length dependence thermal conductivity, thus breaks down the Fourier law. Then we discuss how the introduction of isotope doping can reduce the thermal conductivity efficiently. The theoretical results are in good agreement with experimental ones. Finally, we will demonstrate that nanoscale structures are promising candidates for heat rectification.

scholarly journals Pexophagy: The Selective Degradation of Peroxisomes

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Andreas Till ◽  
Ronak Lakhani ◽  
Sarah F. Burnett ◽  
Suresh Subramani
Keyword(s):  
Mammalian Cells ◽  
Current Knowledge ◽  
Cell Types ◽  
Model Systems ◽  
Eukaryotic Cells ◽  
Organelle Biogenesis ◽  
Selective Degradation ◽  
Future Challenges ◽  
Recent Developments ◽  
Distinct Features

Peroxisomes are single-membrane-bounded organelles present in the majority of eukaryotic cells. Despite the existence of great diversity among different species, cell types, and under different environmental conditions, peroxisomes contain enzymes involved inβ-oxidation of fatty acids and the generation, as well as detoxification, of hydrogen peroxide. The exigency of all eukaryotic cells to quickly adapt to different environmental factors requires the ability to precisely and efficiently control peroxisome number and functionality. Peroxisome homeostasis is achieved by the counterbalance between organelle biogenesis and degradation. The selective degradation of superfluous or damaged peroxisomes is facilitated by several tightly regulated pathways. The most prominent peroxisome degradation system uses components of the general autophagy core machinery and is therefore referred to as “pexophagy.” In this paper we focus on recent developments in pexophagy and provide an overview of current knowledge and future challenges in the field. We compare different modes of pexophagy and mention shared and distinct features of pexophagy in yeast model systems, mammalian cells, and other organisms.

scholarly journals Observation of non-Bloch parity-time symmetry and exceptional points

2020 ◽  
Author(s):  
Peng Xue ◽  
Lei Xiao ◽  
Tianshu Deng ◽  
Kunkun Wang ◽  
Zhong Wang ◽  
...  
Keyword(s):  
Brillouin Zone ◽  
Skin Effect ◽  
Quantum Walks ◽  
Pt Symmetry ◽  
Great Promise ◽  
Single Photons ◽  
Band Theory ◽  
Exceptional Points ◽  
Time Symmetry ◽  
Transition Points

Abstract Parity-time (PT)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A PT-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigen spectrum, while the transition points in between, the so-called exceptional points, give rise to a host of critical behaviors that holds great promise for applications. For spatially periodic non-Hermitian systems, PT symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. Here, in non-unitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These "non-Bloch exceptional points" originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Our finding opens the avenue toward a generalized PT-symmetry framework, and reveals the intriguing interplay among PT symmetry, non-Hermitian skin effect, and non-Hermitian topology.

The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis

2020 ◽  
Author(s):  
Felicitas Schäfer ◽  
Shuai Guo ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Large Sets ◽  
Training Samples ◽  
Numerical Stability Analysis ◽  
Increased Sensitivity ◽  
Positive Growth Rate ◽  
Input Uncertainties ◽  
The Impact

Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.

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