Pattern-assisted stacking colloidal quantum dots for photonic integrated circuits

In photonic integrated circuits (PICs), on-chip light sources and other photonic devices are usually made of different materials. The complexity and compatibility brought about by different materials and various structures in a single chip considerably increase the fabrication and integration difficulties. Here, we propose to stack the same nanoscale building blocks [colloidal quantum dots (CQDs) with both large gains and high refractive indices] in predefined trench patterns to address the fabrication and integration problems of PICs. By employing this simple approach of using the same material (CdSe/ZnS CQDs), the on-chip integration of more than 10 CQD-based photonic components (including the laser, low-noise amplifier, bending waveguide, Y-splitter, Mach-Zehnder interferometer, and grating) is experimentally demonstrated. In particular, the integrated low-noise amplifier (net gain coefficient >600 cm^-1) addresses the absorption loss problem brought about by the utilization of the same material. Moreover, the little influence of the CQD layer on the CQD nanophotonic components facilitates the fabrication and is beneficial for large-scale integration. This simple fabrication approach with a flexible integration strategy may provide a possible platform to construct functional PICs.

Single-mode surface-emitting microcylinder/microring laser assisted by a shallowly-etched top grating

Semiconductor lasers based on microcylinder/microring cavities supporting high-quality factor modes are promising candidates of optical sources for optical interconnect. However, their multi-mode lasing performance and non-directional emission characteristic restrict their applications. In this paper, a single mode surface-emitting laser at O-band based on a second-order grating shallowly etched on the top of the microcylinder/microring cavity is proposed and demonstrated. The second-order top grating cannot only scatter the whispering gallery modes vertically to form surface emission but also select a single mode to lase. The laser is electrically pumped and continuous wave operated in a wide temperature range with side-mode suppression-ratio larger than 40 dB. The upward surface-emitting optical power exceeds 1 mW. Except for O-band, the laser can be easily realized at other long-wavelength communication bands, such as C-band and L-band.

Anomalous optical forces in PT-symmetric waveguides

Evanescently coupled passive waveguides experience optical forces of attractive or repulsive nature, depending on the mode of operation. Here we explore the optical forces between parity-time-symmetric coupled waveguides, with balanced levels of gain and loss. We find that, besides the diagonal stress components that result in a pressure normal to the surface of the waveguides, this system exhibits an off-diagonal stress component that creates a shear along the propagation direction. In addition, for a critical value of balanced gain and loss, the normal pressure can be reduced to zero. These anomalous optical forces are related to the unusual power flow in coupled active-passive channels, and open interesting opportunities for microfluidics and micro-optomechanical systems.

Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam

Non-Hermitian parity-time (PT) symmetric systems that possess real eigenvalues have been intensively investigated in quantum mechanics and rapidly extended to optics and acoustics demonstrating a lot of unconventional wave phenomena. Here, a PT symmetric metamaterial beam is designed based on shunted piezoelectric patches and asymmetric wave scattering in the form of flexural waves is demonstrated through analytical and numerical approaches. The gain and loss components in the PT symmetric beam are realized by the introduction of negative and positive resistances into the external shunting circuits, respectively. Effective medium theory and transfer matrix method are employed to determine the effective material parameters and scattering properties of the PT symmetric metamaterial beam. Unidirectional reflectionlessness has been demonstrated analytically and numerically, together with illustrations of the PT phase transition and exceptional points. The tunability of exceptional points is studied by changing the spacing between piezoelectric patches and shunting circuit parameters. The design explores complex material parameters of the beam structure, and could open unique ways to asymmetric wave control, enhanced sensing, amplification, and localization of flexural waves.

How to Compute Spectra with Error Control

Computing the spectra of operators is a fundamental problem in the sciences, with wide-ranging applications in condensed-matter physics, quantum mechanics and chemistry, statistical mechanics, etc. While there are algorithms that in certain cases converge to the spectrum, no general procedure is known that (a) always converges, (b) provides bounds on the errors of approximation, and (c) provides approximate eigenvectors. This may lead to incorrect simulations. It has been an open problem since the 1950s to decide whether such reliable methods exist at all. We affirmatively resolve this question, and the algorithms provided are optimal, realizing the boundary of what digital computers can achieve. Moreover, they are easy to implement and parallelize, offer fundamental speed-ups, and allow problems that before, regardless of computing power, were out of reach. Results are demonstrated on difficult problems such as the spectra of quasicrystals and non-Hermitian phase transitions in optics.

Sensing with Exceptional Surfaces in Order to Combine Sensitivity with Robustness

Exceptional points (EPs) are singularities that arise in non-Hermitian physics. Current research efforts focus only on systems supporting isolated EPs characterized by increased sensitivity to external perturbations, which makes them potential candidates for building next generation optical sensors. On the downside, this feature is also the Achilles heel of these devices: they are very sensitive to fabrication errors and experimental uncertainties. To overcome this problem, we introduce a new design concept for implementing photonic EPs that combine the robustness required for practical use together with their hallmark sensitivity. Particularly, our proposed structure exhibits a hypersurface of Jordan EPs embedded in a larger space, and having the following peculiar features: (1) A large class of undesired perturbations shift the operating point along the exceptional surface (ES), thus, leaving the system at another EP which explains the robustness; (2) Perturbations due to back reflection or backscattering force the operating point out of the ES, leading to enhanced sensitivity. Importantly, our proposed geometry is relatively easy to implement using standard photonics components and the design concept can be extended to other physical platforms such as microwave or acoustics.

Spectral singularities of a potential created by two coupled microring resonators

Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, the coupling for each microring resonator yields two counter-propagating modes with equal frequencies. We show that such a system enables implementation of many types of scattering peculiarities. The spectral singularities, which are either the second or fourth order, separate parameter regions where the spectrum is either purely real or composed of complex eigenvalues; hence, they represent the points of the phase transition. By modifying the gain-loss relation for the resonators, such an optical scatterer can act as a laser, as a coherent perfect absorber, be unidirectionally reflectionless or transparent, and support bound states either growing or decaying in time. These characteristics are observed for a discrete series of the incident-radiation wavelengths.

High-power edge-emitting laser based on a parity-time-structured Bragg reflection waveguide

A parity-time-structured Bragg reflection waveguide is proposed and analyzed for realizing a high-power laser. A single transverse mode with the optical field confined mainly in the low-index core is discussed to improve the catastrophic optical damage threshold for high output power. The designed scheme can potentially mitigate the heat buildup by moving the injection from the central narrow core to the outer large-area claddings, while suppressing the coupler mode transversely. The structure can achieve high output power with a short cavity length, low lasing threshold, and high power conversion efficiency.

On-chip magnetic-free optical multi-port circulator based on a locally linear parity-time symmetric system

This paper introduces a new type of magnetic-free optical circulator without utilizing a Faraday rotator, polarization beam splitter, and magneto-optic material for the first time, to the best of our knowledge. The designed circulator operates linearly and relies on the parity-time symmetric (PTS) system. The property of the non-Hermitian system (the linear PTS system) plays the key role in the suggested optical circulator so that it can simultaneously support N-ports. The proposed device is integrated, broadband, and operates in the optical telecommunication frequency band. A great value of isolation rate of 47 dB is achieved. The proposed circulator can pave the way for optical integrated circuits and optical networks.

Tailoring exceptional points with one-dimensional graphene-embedded photonic crystals

We theoretically demonstrate that tunable exceptional points (EPs) can be realized by using graphene-embedded one-dimensional (1D) photonic crystals with optical pumping in the terahertz (THz) frequency range. By tuning the Fermi level of graphene sheet, the energy band are altered significantly and the EP appears. In particular, multiple EPs at different frequencies can be selectively produced via subtly adjusting the band structure. Furthermore, topological features of these EPs, such as crossing and anti-crossing of the real and imaginary parts of the eigenvalues, have been analyzed in detail. We expect that tunable EPs can provide an instructive method to design active optical devices based on photoexcited graphene sheets in the THz frequency range.

Mechanical exceptional-point-induced transparency and slow light

Recently, the conception of PT symmetry has attracted considerable attention in various fields such as optics, acoustics, and atomic physics because of the existence of exceptional point (EP) and its importance in understanding non-Hermitian physics. Here, we propose a new scheme of investigating the mechanical-EP-induced transparency and tunable fast-to-slow light phenomena in PT-symmetric mechanical systems. We find that (i) the transmission of the probe field changes from singleto double transparency windows via the transition from a broken mechanical PT-symmetric phase to an unbroken mechanical PT-symmetric phase; (ii) the efficiency of transparency can be significantly enhanced about three orders of magnitude in the vicinity of the mechanical EP, compared to passive mechanical resonators system; and (iii) the mechanical EP can not only amplify the group delay, but also manipulate the switch from slow light to fast light, which may offer an approach to achieve the practical application of slow light and relevant to the optical switcher and communication network. Our results reveal that the exotic properties of the mechanical EP can result in enormous enhancement of the transmitted probe power and novel steering of fast and slow light.

Fano resonance and polarization transformation induced by interpolarization coupling of Bloch surface waves

In this work, the resonant coupling behaviors between the transverse-electric (TE) and transverse-magnetic (TM) Bloch surface waves (BSWs) on a dielectric multilayer have been theoretically studied. Due to the different penetration depths in the dielectric multilayer, the TM BSWs and TE BSWs can act as the radiative and dark electromagnetic modes, respectively. By using a rectangular grating on the dielectric multilayer, both Rabi splitting and Fano resonance phenomena based on the coupling of the two BSW modes were demonstrated, through tuning the period of the grating and the azimuthal angle of the incoming wave. Furthermore, by using the temporal coupled-mode theory, we show that the anti-Hermitian coupling between the two BSW modes contributes to the enhanced diffraction and the huge polarization transformation efficiency of incoming waves in the weak coupling regime.

Perfectly Absorbing Exceptional Points and Chiral Absorbers

We identify a new kind of physically realizable exceptional point (EP) corresponding to degenerate coherent perfect absorption, in which two purely incoming solutions of the wave operator for electromagnetic or acoustic waves coalesce to a single state. Such non-Hermitian degeneracies can occur at a real-valued frequency without any associated noise or nonlinearity, in contrast to EPs in lasers. The absorption line shape for the eigenchannel near the EP is quartic in frequency around its maximum in any dimension. In general, for the parameters at which an operator EP occurs, the associated scattering matrix does not have an EP. However, in one dimension, when the S matrix does have a perfectly absorbing EP, it takes on a universal one-parameter form with degenerate values for all scattering coefficients. For absorbing disk resonators, these EPs give rise to chiral absorption: perfect absorption for only one sense of rotation of the input wave.

Parity-time symmetry in coherent asymmetric double quantum wells

A coherently prepared asymmetric double semiconductor quantum well (QW) is proposed to realize parity-time (PT) symmetry. By appropriately tuning the laser fields and the pertinent QW parameters, PT-symmetric optical potentials are obtained by three different methods. Such a coherent QW system is reconfigurable and controllable, and it can generate new approaches of theoretically and experimentally studying PT-symmetric phenomena.

Second-Order Topological Phases in Non-Hermitian Systems

A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes, which are localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down. The winding number (Chern number) based on complex wave vectors is used to characterize the second-order topological phases in 2D (3D). A possible experimental situation with ultracold atoms is also discussed. Our work lays the cornerstone for exploring higher-order topological phenomena in non-Hermitian systems.

Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms

Open physical systems with balanced loss and gain, described by non-Hermitian parity-time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{\cal P}{\cal T}} \right)$$\end{document}PT reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry. Such \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold ⁶Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetric quantum systems.

Ultracold atoms provide controllable platforms to study many quantum mechanical phenomena. Here the authors use noninteracting fermions of ultracold Li atoms with tunable time‐periodic dissipation or coupling to demonstrate the breaking and restoration of parity‐time symmetry.

Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators

Many novel properties of non-Hermitian systems are found at or near the exceptional points—branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional point, which is protected by the transverse spin–momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the exceptional points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the exceptional point is also numerically and analytically demonstrated.

Exceptional points in non-Hermitian systems can enhance the performance of optical sensors. Here, Wang et al. demonstrate theoretically and experimentally that higher-order exceptional points, which would allow for yet higher sensitivities, can be realized in simple photonic resonator chains.

Robust lasing modes in coupled colloidal quantum dot microdisk pairs using a non-Hermitian exceptional point

Evanescently coupled pairs of microdisk lasers have emerged as a useful platform for studying the non-Hermitian physics of exceptional points. It remains an open question how scalable and versatile such phenomena can be when carried over to other designs. Here we have studied the effect of gain/loss modulation in an evanescently coupled pair of microdisk optical resonators fabricated from solution-processed colloidal quantum dots. The emission spectra of these structures are sensitive to small imperfections, which cause frequency-splitting of the whispering gallery modes. Despite this inherent disorder, we found that when spatially modulating the optical pump to vary the gain differential between the coupled microdisks, the coupling drives the split parasitic intra-cavity modes into coalescence at an exceptional point of the resulting three-mode system. This unusual behavior is rationalized via a Hamiltonian that incorporates the intra-cavity coupling as well as the anisotropic inter-cavity coupling between modes in the microdisk pair.

Pairs of microdisk lasers are one of the most common systems for studying optical PT-symmetry. Here, Lafalce, Zeng et al. study the influence of fabrication imperfections in a disk pair made from colloidal quantum dots and show that the resulting three modes also coalesce at an exceptional point.

Demonstration of a two-dimensional P T -symmetric crystal

With the discovery ofP T -symmetric quantum mechanics, it was shown that even non-Hermitian systems may exhibit entirely real eigenvalue spectra. This finding did not only change the perception of quantum mechanics itself, it also significantly influenced the field of photonics. By appropriately designing one-dimensional distributions of gain and loss, it was possible to experimentally verify some of the hallmark features ofP T -symmetry using electromagnetic waves. Nevertheless, an experimental platform to study the impact ofP T -symmetry in two spatial dimensions has so far remained elusive. We break new grounds by devising a two-dimensionalP T -symmetric system based on photonic waveguide lattices with judiciously designed refractive index landscape and alternating loss. With this system at hand, we demonstrate a non-Hermitian two-dimensional topological phase transition that is closely linked to the emergence of topological mid-gap edge states.

Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics

Topological phases are enriched in non-equilibrium open systems effectively described by non-Hermitian Hamiltonians. While several properties unique to non-Hermitian topological systems were uncovered, the fundamental role of symmetry in non-Hermitian physics has yet to be fully understood, and it has remained unclear how symmetry protects non-Hermitian topological phases. Here we show that two fundamental anti-unitary symmetries, time-reversal and particle-hole symmetries, are topologically equivalent in the complex energy plane and hence unified in non-Hermitian physics. A striking consequence of this symmetry unification is the emergence of unique non-equilibrium topological phases that have no counterparts in Hermitian systems. We illustrate this by presenting a non-Hermitian counterpart of the Majorana chain in an insulator with time-reversal symmetry and that of the quantum spin Hall insulator in a superconductor with particle-hole symmetry. Our work establishes a fundamental symmetry principle in non-Hermitian physics and paves the way towards a unified framework for non-equilibrium topological phases.

Topological phases of matter are determined by its symmetries and dimension. Here the authors show that in non-Hermitian systems, such as those with gain and loss, time-reversal and particle-hole symmetries are equivalent to each other, unifying otherwise distinct topological classes and leading to emergent non-Hermitian topological phases.

Exceptional points in optics and photonics

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.

Exceptional points for photon pairs bound by nonlinear dissipation in cavity arrays

We theoretically study the dissipative Bose-Hubbard model describing the array of tunneling-coupled cavities with non-conservative photon-photon interaction. The bound two-photon states are formed in this system either in the limited range of the center-of-mass wave vectors or in the full Brillouin zone, depending on the strength of the dissipative interaction. Transition between these two regimes is manifested as an exceptional point in the complex energy spectrum. This improves fundamental understanding of the interplay of non-Hermiticity and interactions in the quantum structures and can potentially be used for on-demand nonlinear light generation in photonic lattices.

Asymmetric light diffraction of two-dimensional electromagnetically induced grating with PT symmetry in asymmetric double quantum wells

An asymmetric double semiconductor quantum well is proposed to realize two-dimensional parity-time (PT) symmetry and an electromagnetically induced grating. In such a nontrivial grating with PT symmetry, the incident probe photons can be diffracted to selected angles depending on the spatial relationship of the real and imaginary parts of the refractive index. Such results are due to the interference mechanism between the amplitude and phase of the grating and can be manipulated by the probe detuning, modulation amplitudes of the standing wave fields, and interaction length of the medium. Such a system may lead to new approaches of observing PT-symmetry-related phenomena and has potential applications in photoelectric devices requiring asymmetric light transport using semiconductor quantum wells.

White light cavity formation and superluminal lasing near exceptional points

We study theoretically a superluminal laser system comprising active and passive (lossy) coupled micro-resonators with equal gain/loss. It is shown that when the system satisfies the white light cavity (WLC) condition, corresponding to zero group index, it also forms a PT-symmetric system (PTSS) at its exceptional point (EP). Slightly above lasing threshold, in the broken symmetry regime near the EP, the system exhibits "superluminal" lasing - a unique lasing condition which is highly attractive for sensing and precision metrology applications. It is also shown that some of the latest experimental studies involving PTSSs have indirectly demonstrated such superluminal lasing.

Photonic Topological Insulating Phase Induced Solely by Gain and Loss

We reveal a one-dimensional topological insulating phase induced solely by gain and loss control in non-Hermitian optical lattices. The system comprises units of four uniformly coupled cavities, where the successive two have loss; the others experience gain, and they are balanced under two magnitudes. The gain and loss parts are effectively dimerized, and a bulk band gap, topological transition, midgap topological edge, and interface states in finite systems can all be achieved by controlled pumping. We also clarify non-Hermitian topological invariants and edge states in gapless conditions.

Winding around non-Hermitian singularities

Non-Hermitian singularities are ubiquitous in non-conservative open systems. Owing to their peculiar topology, they can remotely induce observable effects when encircled by closed trajectories in the parameter space. To date, a general formalism for describing this process beyond simple cases is still lacking. Here we develop a general approach for treating this problem by utilizing the power of permutation operators and representation theory. This in turn allows us to reveal a surprising result that has so far escaped attention: loops that enclose the same singularities in the parameter space starting from the same point and traveling in the same direction, do not necessarily share the same end outcome. Interestingly, we find that this equivalence can be formally established only by invoking the topological notion of homotopy. Our findings are general with far reaching implications in various fields ranging from photonics and atomic physics to microwaves and acoustics.

A general description of observable effects induced by non-Hermitian singularities is complex. Here, Zhong et al. develop such a formalism, showing that loops around the same exceptional point starting from the same point in the same direction do not need to have the same outcome.

Single-transverse-mode broadband InAs quantum dot superluminescent light emitting diodes by parity-time symmetry

Parity-time (PT) symmetry breaking in counterintuitive gain/loss coupled waveguide designs is numerically and theoretically investigated. The PT symmetry mode selection conditions are determined theoretically. Single-transverse-mode broadband InAs quantum dot (QD) superluminescent light emitting diodes (SLEDs) are fabricated and characterized; the PT symmetric broad-area SLEDs contain laterally coupled gain and loss PT- symmetric waveguides. Single-transverse-mode operation is achieved by parity-time symmetry breaking. The broadband SLEDs exhibit a uniform Gaussian-like emission spectrum with the 3-dB bandwidth of 110 nm. Far-field characteristics of the coupled waveguide SLEDs exhibit a single-lobe far-field pattern when the gain and loss waveguides are biased at the injection current of 600 mA and 60 mA, respectively.

Tunable slow and fast light in parity-time-symmetric optomechanical systems with phonon pump

We study the response of parity-time (PT)-symmetric optomechanical systems with tunable gain and loss to the weak probe field in the presence of a strong control field and a coherent phonon pump. We show that the probe transmission can exceed unity at low control power due to the optical gain of the cavity and it can be further enhanced or suppressed by tuning the amplitude and phase of the phonon pump. Furthermore, the phase dispersion of the transmitted probe field is modified by controlling the applied fields, which allows one to tune the group delay of the probe field. Based on this optomechianical system, we can realize a tunable switch between slow and fast light effect by adjusting the gain-to-loss ratio, power of the control field as well as the amplitude and phase of the phonon pump. Our work provides a platform to control the light propagation in a more flexible way.

Directional Bistability and Nonreciprocal Lasing with Cold Atoms in a Ring Cavity

We demonstrate lasing into counterpropagating modes of a ring cavity using a gas of cold atoms as a gain medium. The laser operates under the usual conditions of magneto-optical trapping with no additional fields. We characterize the threshold behavior of the laser and measure the second-order optical coherence. The laser emission exhibits directional bistability, switching randomly between clockwise and counterclockwise modes, and a tunable nonreciprocity is observed as the atoms are displaced along the cavity axis.

Unidirectional light emission in PT-symmetric microring lasers

The synergetic use of gain and loss in parity-time symmetric coupled resonators has been shown to lead to single-mode lasing operation. However, at the corresponding resonance frequency, an ideal ring resonator tends to support two degenerate eigenmodes, traveling along the cavity in opposite directions. Here, we show a unidirectional single-moded parity-time symmetric laser by incorporating active S-bend structures with opposite chirality in the respective ring resonators. Such chiral elements break the rotation symmetry of the ring cavities by providing an asymmetric coupling between the clockwise (CW) and the counterclockwise (CCW) traveling modes, hence creating a new type of exceptional point. This property, consequently, leads to the suppression of one of the counter-propagating modes. In this paper, we first measure the extinction ratio between the CW and CCW modes in a single ring resonator in the presence of an S-bend waveguide. We then experimentally investigate the unidirectional emission in PT-symmetric systems below and above the exceptional point. Finally, unidirectional emission will be shown in systems of two S-bend ring resonators coupled through a link structure.

Non-Hermitian Chern Bands

The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example of bulk-boundary correspondence. We show that the chiral edge modes are not strictly tied to the Chern numbers defined by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional bulk-boundary correspondence stems from the non-Bloch-wave behavior of eigenstates (non-Hermitian skin effect), which generates pronounced deviations of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes. The theory is backed up by the open-boundary energy spectra, dynamics, and phase diagram of representative lattice models. Our results highlight a unique feature of non-Hermitian bands and suggest a non-Bloch framework to characterize their topology.

Simultaneous Observation of a Topological Edge State and Exceptional Point in an Open and Non-Hermitian Acoustic System

This Letter reports on the experimental observation of a topologically protected edge state and exceptional point in an open and non-Hermitian (lossy) acoustic system. Although the theoretical underpinning is generic to wave physics, the simulations and experiments are performed for an acoustic system. It has nontrivial topological properties that can be characterized by the Chern number provided that a synthetic dimension is introduced. Unidirectional reflectionless propagation, a hallmark of exceptional points, is unambiguously observed in both simulations and experiments.

Time-asymmetric loop around an exceptional point over the full optical communications band

Topological operations around exceptional points^1-8-time-varying system configurations associated with non-Hermitian singularities-have been proposed as a robust approach to achieving far-reaching open-system dynamics, as demonstrated in highly dissipative microwave transmission³ and cryogenic optomechanical oscillator⁴ experiments. In stark contrast to conventional systems based on closed-system Hermitian dynamics, environmental interferences at exceptional points are dynamically engaged with their internal coupling properties to create rotational stimuli in fictitious-parameter domains, resulting in chiral systems that exhibit various anomalous physical phenomena^9-16. To achieve new wave properties and concomitant device architectures to control them, realizations of such systems in application-abundant technological areas, including communications and signal processing systems, are the next step. However, it is currently unclear whether non-Hermitian interaction schemes can be configured in robust technological platforms for further device engineering. Here we experimentally demonstrate a robust silicon photonic structure with photonic modes that transmit through time-asymmetric loops around an exceptional point in the optical domain. The proposed structure consists of two coupled silicon-channel waveguides and a slab-waveguide leakage-radiation sink that precisely control the required non-Hermitian Hamiltonian experienced by the photonic modes. The fabricated devices generate time-asymmetric light transmission over an extremely broad spectral band covering the entire optical telecommunications window (wavelengths between 1.26 and 1.675 micrometres). Thus, we take a step towards broadband on-chip optical devices based on non-Hermitian topological dynamics by using a semiconductor platform with controllable optoelectronic properties, and towards several potential practical applications, such as on-chip optical isolators and non-reciprocal mode converters. Our results further suggest the technological relevance of non-Hermitian wave dynamics in various other branches of physics, such as acoustics, condensed-matter physics and quantum mechanics.

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 quasi-adiabatic dynamics shows chiral mode switching which enables topological manipulation of quantum states.

Edge States and Topological Invariants of Non-Hermitian Systems

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Experimental Demonstration of an Anisotropic Exceptional Point

Exceptional points (EPs) associated with a square-root singularity have been found in many non-Hermitian systems. In most of the studies, the EPs found are isotropic, meaning that the same singular behavior is obtained independent of the direction from which they are approached in the parameter space. In this Letter, we demonstrate both theoretically and experimentally the existence of an anisotropic EP in an acoustic system that shows different singular behaviors when the anisotropic EP is approached from different directions in the parameter space. Such an anisotropic EP arises from the coalescence of two square-root EPs having the same chirality.

Incident Direction Independent Wave Propagation and Unidirectional Lasing

We propose an incident direction independent wave propagation generated by properly assembling different unidirectional destructive interferences (UDIs), which is a consequence of the appropriate match between synthetic magnetic fluxes and the incident wave vector. Single-direction lasing at spectral singularity is feasible without introducing nonlinearity. UDI allows unidirectional lasing and unidirectional perfect absorption; when they are combined in a parity-time-symmetric manner, the spectral singularities vanish with bounded reflections and transmissions. Furthermore, the simultaneous unidirectional lasing and perfect absorption for incidences from opposite directions is created. Our findings provide insights into light control and may shed light on the explorations of desirable functionality in fundamental research and practical applications.

Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

Quantum walks often provide telling insights about the structure of the system on which they are performed. In \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today’s experimental systems.

Controllable and selective single-mode lasing in polymer microbottle resonator

We report a single-mode dye-doped polymer microbottle resonator (MBR) laser. The selective single-mode lasing from different order whispering gallery modes is achieved by precisely controlling the axial and radial coupling position between a tapered nanofiber and an MBR, respectively. The side-mode suppression ratio is above 20 dB. By doping different fluorescence dyes into the MBR, single-mode lasers at various colors are demonstrated.

Exceptional points and photonic catastrophe

Exceptional points (EPs) with a global collapse of pairs of eigenfunctions are shown to arise in two locally coupled and spatially extended optical structures with balanced gain and loss. The global collapse at the EP deeply changes light propagation, which becomes very sensitive to small changes of initial conditions or system parameters, similar to what happens in models of classical or quantum catastrophes. The implications of global collapse for light behavior are illustrated by considering discrete beam diffraction and Bloch oscillation catastrophe in coupled waveguide lattices.

Observation of an anti-PT-symmetric exceptional point and energy-difference conserving dynamics in electrical circuit resonators

Parity-time (PT) symmetry and associated non-Hermitian properties in open physical systems have been intensively studied in search of new interaction schemes and their applications. Here, we experimentally demonstrate an electrical circuit producing key non-Hermitian properties and unusual wave dynamics grounded on anti-PT (APT) symmetry. Using a resistively coupled amplifying-LRC-resonator circuit, we realize a generic APT-symmetric system that enables comprehensive spectral and time-domain analyses on essential consequences of the APT symmetry. We observe an APT-symmetric exceptional point (EP), inverse PT-symmetry breaking transition, and counterintuitive energy-difference conserving dynamics in stark contrast to the standard Hermitian dynamics keeping the system’s total energy constant. Therefore, we experimentally confirm unique properties of APT-symmetric systems, and further development in other areas of physics may provide new wave-manipulation techniques and innovative device-operation principles.

The study of parity-time (PT) symmetric optical systems has recently attracted much attention. Here, the authors experimentally study an anti-PT symmetric circuit system and observe an exceptional point with an inverse PT symmetry breaking transition and energy-difference conserving dynamics.

Parity-time-symmetric optoelectronic oscillator

An optoelectronic oscillator (OEO) is a hybrid microwave and photonic system incorporating an amplified positive feedback loop to enable microwave oscillation to generate a high-frequency and low-phase noise microwave signal. The low phase noise is ensured by the high Q factor of the feedback loop enabled by the use of a long and low-loss optical fiber. However, an OEO with a long fiber loop would have a small free spectral range, leading to a large number of closely spaced oscillation modes. To ensure single-mode oscillation, an ultranarrowband optical filter must be used, but such an optical filter is hard to implement and the stability is poor. Here, we use a novel concept to achieve single-mode oscillation without using an ultranarrowband optical filter. The single-mode operation is achieved based on parity-time (PT) symmetry by using two identical feedback loops, with one having a gain and the other having a loss of the same magnitude. The operation is analyzed theoretically and verified by an experiment. Stable single-mode oscillation at an ultralow phase noise is achieved without the use of an ultranarrowband optical filter. The use of PT symmetry in an OEO overcomes the long-existing mode-selection challenge that would greatly simplify the implementation of OEOs for ultralow-phase noise microwave generation.

Ring quantum cascade lasers with twisted wavefronts

We demonstrate the on-chip generation of twisted light beams from ring quantum cascade lasers. A monolithic gradient index metamaterial is fabricated directly into the substrate side of the semiconductor chip and induces a twist of the light's wavefront. This significantly influences the obtained beam pattern, which changes from a central intensity minimum to a maximum depending on the discontinuity count of the metamaterial. Our design principle provides an interesting alternative to recent implementations of microlasers operating at an exceptional point.

Spatial solitons and stability in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with fourth-order diffraction and parity-time-symmetric potentials

We investigate the existence and stability of solitons in parity-time (PT)-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT-breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.

Bohmian Photonics for Independent Control of the Phase and Amplitude of Waves

The de Broglie-Bohm theory is one of the nonstandard interpretations of quantum phenomena that focuses on reintroducing definite positions of particles, in contrast to the indeterminism of the Copenhagen interpretation. In spite of intense debate on its measurement and nonlocality, the de Broglie-Bohm theory based on the reformulation of the Schrödinger equation allows for the description of quantum phenomena as deterministic trajectories embodied in the modified Hamilton-Jacobi mechanics. Here, we apply the Bohmian reformulation to Maxwell's equations to achieve the independent manipulation of optical phase evolution and energy confinement. After establishing the deterministic design method based on the Bohmian approach, we investigate the condition of optical materials enabling scattering-free light with bounded or random phase evolutions. We also demonstrate a unique form of optical confinement and annihilation that preserves the phase information of incident light. Our separate tailoring of wave information extends the notion and range of artificial materials.

Deep-Ultraviolet Hyperbolic Metacavity Laser

Given the high demand for miniaturized optoelectronic circuits, plasmonic devices with the capability of generating coherent radiation at deep subwavelength scales have attracted great interest for diverse applications such as nanoantennas, single photon sources, and nanosensors. However, the design of such lasing devices remains a challenging issue because of the long structure requirements for producing strong radiation feedback. Here, a plasmonic laser made by using a nanoscale hyperbolic metamaterial cube, called hyperbolic metacavity, on a multiple quantum-well (MQW), deep-ultraviolet emitter is presented. The specifically designed metacavity merges plasmon resonant modes within the cube and provides a unique resonant radiation feedback to the MQW. This unique plasmon field allows the dipoles of the MQW with various orientations into radiative emission, achieving enhancement of spontaneous emission rate by a factor of 33 and of quantum efficiency by a factor of 2.5, which is beneficial for coherent laser action. The hyperbolic metacavity laser shows a clear clamping of spontaneous emission above the threshold, which demonstrates a near complete radiation coupling of the MQW with the metacavity. This approach shown here can greatly simplify the requirements of plasmonic nanolaser with a long plasmonic structure, and the metacavity effect can be extended to many other material systems.

Spectral engineering for circular-side square microlasers

Spectral engineering has been demonstrated for the circular-side square microlasers with an output waveguide butt-coupled to one vertex. By carefully optimizing deformation parameter and waveguide connection angle, undesired high-order transverse modes are suppressed while the mode Q factors and the transverse-mode intervals are enhanced simultaneously for the low-order transverse modes. Dual-mode lasing with pure lasing spectra is realized experimentally for the circular-side square microlasers with side lengths of 16 μm, and the transverse mode intervals can be adjusted from 0.54 to 5.4 nm by changing the deformation parameter. Due to the enhanced mode confinement, single-mode lasing with a side-mode suppression-ratio of 36 dB is achieved for a 10μm-side-length circular-side square microlaser with a 1.5μm-wide waveguide.