Exceptional Points Research Articles

Photon blockade in a high-damping cavity via a gain-type coupler

Abstract We propose a scheme to implement photon blockade in a non-Hermitian circuit quantum electrodynamics (circuit-QED) system where a single-mode cavity interacts with a two-level emitter through virtual photon excitation mediated by a coupler resonator. A damping compensation regime is introduced by the phase-lag arising from the medium mode, thereby the periodic exceptional points (EPs) are observed at which the system achieves gain-damping balance. This regime enables photon blockade to occur within the single-mode cavity with high-damping rate by controlling the gain circuit of the coupler, which breaks the limitation of a low-damping rate for photon blockade under weak drive and relaxes the stringent requirements on the quality of the cavity. The numerical simulations for the second-order correlation function, obtained using reported experimental parameters, exhibit excellent agreement with our analytical results. The findings of this study provide a circuit-QED solution for single-quantum devices based on the high-damping cavities, which is of great significance for integrated quantum computing networks.

Higher-order exceptional points and enhanced polarization sensitivity in anisotropic photonic time-Floquet crystals

We realized fourth-order exceptional points (EP-4s) in the quasienergy bands of anisotropic photonic time-Floquet crystals (APTCs), where the full in-plane permittivity tensors are periodically modulated in time. We developed the Floquet matrix method for APTCs, which provides a comprehensive study of the generation and characteristics of EP-4s. It is shown that an EP-4 is formed by the coalescence of three second-order exceptional points (EP-2s), which are classified into two types based on the band slopes near them. Additionally, the helicities of the four coalescing bands converge rapidly to zero at any given time when approaching the EP-4, following the ϵ1/4-dependence. Therefore, a strong polarization sensitivity is observed at the EP-4, which could inspire applications relevant to electromagnetic spins in APTCs.

Observation of parity-time symmetry for evanescent waves

Parity-time (PT) symmetry has enabled the demonstration of fascinating wave phenomena in non-Hermitian systems characterized by precisely balanced gain and loss. Until now, the exploration and observation of PT symmetry in scattering settings have largely been limited to propagating waves. Here, we demonstrate a versatile coupled-resonator acoustic waveguide (CRAW) system that enables the observation of PT-symmetric scattering responses for evanescent waves within a bandgap. By examining the generalized scattering matrix in the evanescent wave regime, we observe hallmark PT-symmetric phenomena—including phase transitions at an exceptional point, anisotropic transmission resonances, and laser-absorber modes—in systems that do not require balanced distributions of gain and loss. Owing to the peculiar energy transfer features of evanescent waves, our results not only demonstrate a distinct pathway for observing PT symmetry, but also enable strategies for exotic energy tunneling mechanisms, paving fresh directions for wave engineering grounded in non-Hermitian physics.

Suppression of the Petermann noise factor in a chiral optical mode converter without encircling an exceptional point

The engineering of exceptional points (EP) in gain-loss-assisted optical systems has recently garnered considerable attention for the development of unconventional photonic components. Moreover, the substantial noise associated with EPs poses a significant challenge to realizing their full potential in applications. There is a gap in the exploration of asymmetric mode conversion phenomena in the close proximity of the dynamical encirclement around an EP. In response, we propose the design of a fabrication-feasible dual-mode optical planar waveguide. Non-Hermiticity, in terms of a customized gain-loss profile, is introduced to modulate the interaction between the coupled modes. Contrary to previous assumptions, we establish that the dynamical encirclement of an EP is not a prerequisite for achieving asymmetric mode conversion. Furthermore, we calculate the Petermann factor (K) near the EP and demonstrate a significant two orders of magnitude reduction in the Petermann noise factor when we do not dynamically encircle the EP. Hence, we propose a new scheme to reduce the inherent noise.

Low-gain generalized PT symmetry for electromagnetic impurity-immunity via non-Hermitian doped zero-index materials

Parity-time-symmetric (PT-symmetric) metasurfaces exhibit a plethora of fascinating exceptional-point-induced phenomena, including unidirectional negative refraction and electromagnetic impurity-immunity. However, practical realization of these effects is often impeded by the high demand for gain metasurfaces (gain tangent ∼102). Here, we propose a solution to this challenge by constructing a low-gain generalized PT-symmetric system. This is achieved by transforming the high-gain metasurface into a bulky slab and then realizing it utilizing zero-index materials doped with low-gain dopants. Within this generalized PT-symmetric system, the required gain tangent of the dopants is only ∼10−1 for the emergence of a coalesced exceptional point, where the remarkable property of electromagnetic impurity-immunity effect—perfect wave transmission regardless of impurities—appears. Furthermore, we observe a further decrease in demand for gain materials in an asymmetric environment. To validate this approach, a microwave implementation is demonstrated in full-wave simulations. This work provides a feasible strategy for substantially reducing requirements on gain materials in PT-symmetric systems, thereby enabling advanced electromagnetic wave control.

Exceptional points in the microcavity with phonon pump enhance the transparency and slow light

We theoretically investigated optomechanically induced transparency (OMIT) and slow light in a microcavity optomechanical system containing three nanoparticles, where the pump-probe field drives the cavity and a weak phonon pump drives the mechanical resonator. When the phonon pump frequency matches the pump-probe field frequency difference, adjusting the phonon pump's amplitude and phase can result in the transparency window exceeding unity. Tuning the relative positions of nanoparticles can periodically steer the system to exceptional points (EPs), further enhancing and modulating the transparency window. Furthermore, the phonon pump causes the phase dispersion at the transparency window to become highly steep, resulting in a large value and tunable group delay. Notably, when the system is at EPs, the slow light can be enhanced by approximately two times compared to when the system is not at EPs. Our research demonstrates a way to control optical transmission with potential applications in quantum communications and optical buffers.

Braids and higher-order exceptional points from the interplay between lossy defects and topological boundary states

We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEP). Depending on the location of the defect, third- and fourth-order exceptional points (EP3 and EP4) appear in the space of Hamiltonian parameters. On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (EL) in parameter space. Namely, the HOEPs lie at intersections of mutually noncommuting ELs. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states. These can then coalesce together into an EP3. When the defect lies at the midpoint of the chain, a special symmetry of the full spectrum can lead to an EP4. In this way, our model illustrates the emergence of interesting non-Abelian topological properties in the multiband structure of non-Hermitian perturbations of topological phases. Published by the American Physical Society 2024

Dynamic gain and frequency comb formation in exceptional-point lasers

Exceptional points (EPs)—singularities in the parameter space of non-Hermitian systems where two nearby eigenmodes coalesce—feature unique properties with applications such as sensitivity enhancement and chiral emission. Existing realizations of EP lasers operate with static populations in the gain medium. By analyzing the full-wave Maxwell–Bloch equations, here we show that in a laser operating sufficiently close to an EP, the nonlinear gain will spontaneously induce a multi-spectral multi-modal instability above a pump threshold, which initiates an oscillating population inversion and generates a frequency comb. The efficiency of comb generation is enhanced by both the spectral degeneracy and the spatial coalescence of modes near an EP. Such an “EP comb” has a widely tunable repetition rate, self-starts without external modulators or a continuous-wave pump, and can be realized with an ultra-compact footprint. We develop an exact solution of the Maxwell–Bloch equations with an oscillating inversion, describing all spatiotemporal properties of the EP comb as a limit cycle. We numerically illustrate this phenomenon in a 5-μm-long gain-loss coupled AlGaAs cavity and adjust the EP comb repetition rate from 20 to 27 GHz. This work provides a rigorous spatiotemporal description of the rich laser behaviors that arise from the interplay between the non-Hermiticity, nonlinearity, and dynamics of a gain medium.

Experimental encircling of an exceptional point in a two degrees of freedom system: overview and application to noise control

When a resonator is added to an acoustic cavity or a vibrating structure, a new resonance frequency, or pole, is created in the system. When dissipation is present, this may breakdown when some parameters are finely tuned. This phenomenon, typical of non-Hermitian dynamics is called an exceptional point in the parametric space where two (or more) eigenvalues, as well as their associated eigenvectors, coalesce. In the recent years, EPs have gained interest in physics because of the counter-intuitive concepts associated with them. In the fields of acoustics and vibration, understanding EP may lead to a better comprehension of modal energy exchanges and decay. This work aims at exploring the key concepts related to EPs by revisiting the well-known coupled pendulums problem in the presence of damping. First, the free response of the experimental system is investigated after tuning it on an EP. Then an encircling is performed by varying the parameters through time. Our experimental results illustrate in a pedagogical manner nearly-optimal dissipation, energy exchange and chirality effects which have been recently evidenced in physics.

Manipulating one-way quantum steering in a mechanical gain-loss optomechanical system

Based on the phenomenon of exceptional points (EPs) in the optomechanically induced mechanical PT-symmetric binary and ternary systems, we propose a mechanism to generate the perfect one-way quantum steering between two totally symmetric modes, respectively. By investigating the quantum steering behavior in the close vicinity of EP, we find that the optimal one-way quantum steering can be successfully generated at the EP in the PT-symmetric binary mechanical system. When pushing the system towards the EP, we show that not only is the broadest region of the one-way quantum steering achieved, but the robustness against the thermal noise can be significantly enhanced. In addition, the direction of the one-way quantum steering can be precisely controlled only by altering the sign of the detuning of the cavity field. What’s more, we analyze the mean populations of the involved modes to further support our findings and find that the occurrence of the one-way quantum steering depends mainly on the difference in the populations between the two target modes. We also successfully extend our findings to the high-order EP, and the desired one-way quantum steering can still be generated in the PT-symmetric ternary mechanical system when it operates at the EP. Our scheme opens up an alternative manipulation method to explore the various novel quantum effects exploiting the EPs and has significant potential applications in quantum nonreciprocal devices.

Dynamic of time-independent and time-dependent asymmetric Gross-Pitaevskii equation around exceptional point

Systems operating at exceptional points (EPs) are highly sensitive to small perturbations, making it challenging to work near an EP. Eigenvalue analysis of the Gross-Pitaevskii equation has shown that asymmetric nonlinearity can compensate for detuning effects. However, an experimentally feasible system based on asymmetric nonlinear coupled resonators has not yet been explored. Additionally, some intriguing features of such a system are hidden in time domain analysis, which is rarely investigated. In this study, we demonstrate this feature using a full-wave simulation of an asymmetric nonlinear coupled resonator based on the finite-element method in Comsol. The time-dependent analysis reveals that detuning can shift the system from PT-symmetric to broken PT-symmetric (or vice versa), and nonlinearity can reverse this dynamic. This study provides an experimental framework for examining exceptional points (EPs) in nonlinear detuned coupled resonators and opens up new avenues for fundamental research into the influence of nonlinearity and detuning on the system’s state during EP encirclement.

Exotic spin-Hall effect in non-Hermitian optical systems

Abstract We systematically explore the origin and evolution of the exceptional points (EP) when a light beam is scattered by a parity-time (PT)-symmetric system using a scattering matrix approach and a full-wave theory. It is demonstrated that the PT-symmetric system switches between symmetry and symmetry-breaking phases at the EPs, giving rise to singular features in the Fresnel coefficients and causing the spin-Hall effect (SHE) near the EPs to exhibit anomalous features such as significantly enhanced transverse spin-Hall shifts and additional in-plane spin-Hall shifts. This exotic SHE can be explained by the significant beam intensity distortion caused by the destructive interference between the spin-maintained normal modes and the spin-reversed abnormal modes in the scattered light. This phenomenon can further be understood in terms of vortex mode decomposition, wherein it can be interpreted as the competition and superposition of three vortex modes with topological charges of −1, 0, and 1, respectively. These findings elucidate the mechanism of the unusual SHE around the EPs and offer potential avenues for EP-based sensing and structured light manipulation.

Quantum entanglement assisted via Duffing nonlinearity

We propose a scheme to enhance quantum entanglement in an optomechanical system by exploiting the so-called Duffing nonlinearity. Our model system consists of two mechanically coupled mechanical resonators, both driven by an optical field. One resonator supports Duffing nonlinearity, while the other does not. The resonators are coupled to each other via the so-called phonon-hopping mechanism. The hopping rate is θ-phase dependent that induces exceptional point singularities in the system. Interestingly, while the resonator with Duffing nonlinearity exhibits vanishing entanglement with light, we observe an increase in entanglement between light and the other mechanical resonator. This enhanced entanglement persists longer against thermal fluctuations compared to the one without the nonlinearity. Additionally, this entanglement features a sudden death and revival phenomenon, where the peaks happen at multiples of θ=π2. This work opens another avenue for exploiting nonlinear resources to generate strong quantum entanglement, paving the way for advancements in quantum information processing, quantum sensing, and quantum computing within complex systems. Published by the American Physical Society 2024

Three types of third-order non-Hermitian interaction of spontaneous six-wave and eight-wave mixing under multi-dressing effects

Non-Hermitian degeneracy, also known as exceptional point, has been recently seen as a new way to engineer the response of open physical systems. Based on natural non-Hermitian atomic coherence, we investigate spontaneous six-wave mixing (SSWM) and eight-wave mixing (SEWM) processes under both parity–time (PT) and anti-parity–time (anti-PT) symmetry, and we obtain high-dimensional coherent channels under third-order energy-level splitting. Finally, we reveal that the third-order non-Hermitian interaction between two dressing fields of the nested scheme is the strongest, and the parallel scheme is the weakest, with the cascade scheme considered intermediate between them. It can also be used to develop quantum memory devices with enhanced sensitivity in the atom-like system.

Simple reciprocal electric circuit exhibiting exceptional point of degeneracy

Simple reciprocal electric circuit exhibiting exceptional point of degeneracy

Angular excitation of exceptional points and pseudospetra of photonic lattices

Abstract Optical parity-time ( PT ) symmetry has triggered a plethora of theoretical and experimental studies, and as a result non-Hermitian photonics is one of the frontiers of optics today. From unidirectional invisibility and coherent perfect absorbers to wireless power transfer and ultrasensitive sensors, non-hermiticity led to numerous important applications that rely on gain-loss synthetic structures. In particular, one such structure is that of complex photonic lattices that may exhibit exceptional points (EPs) around which the corresponding sensitivity is increased by orders of magnitude. Here, we investigate a new multiparametric family of non-Hermitian lattices that respects PT -symmetry, and examine their spectral sensitivity in terms of pseudospectra, as well, the angular excitation of the underlying EPs.

Nodal spectral functions stabilized by non-Hermitian topology of quasiparticles

In quantum materials, basic observables such as spectral functions and susceptibilities are determined by Green's functions and their complex quasiparticle spectrum rather than by bare electrons. Even in closed many-body systems, this makes a description in terms of effective non-Hermitian (NH) Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance and stability of nodal phases is drastically affected by NH topology. While previous work has mostly considered complex degeneracies known as exceptional points as the NH counterpart of nodal points, we propose to relax this assumption by only requiring a crossing of the real part of the complex quasiparticle spectra, which entails a band crossing in the spectral function, i.e., a nodal spectral function. Interestingly, such real crossings are topologically protected by the braiding properties of the complex Bloch bands, and thus generically occur already in one-dimensional systems without symmetry or fine tuning. We propose and study a microscopic lattice model in which a sublattice-dependent interaction stabilizes nodal spectral functions. Besides the gapless spectrum, we identify nonreciprocal charge transport properties after a local potential quench as a key signature of nontrivial band braiding. Finally, in the limit of zero interaction on one of the sublattices, we find a perfectly ballistic unidirectional mode in a nonintegrable environment, reminiscent of a chiral edge state known from quantum Hall phases. Our analysis is corroborated by numerical simulations both in the framework of exact diagonalization and within the conserving second Born approximation. Published by the American Physical Society 2024

Dual Orthogonally Polarized Lasing Assisted by Imaginary Fermi Arcs in Organic Microcavities.

The polarization control of micro- and nanolasers is an important topic in nanophotonics. Up to now, the simultaneous generation of two distinguishable orthogonally polarized lasing modes from a single organic microlaser remains a critical challenge. Here, we demonstrate simultaneously orthogonally polarized dual lasing from a microcavity filled with an organic single crystal exhibiting selective strong coupling. We show that the non-Hermiticity due to polarization-dependent losses leads to the formation of real and imaginary Fermi arcs with exceptional points. Simultaneous orthogonally polarized lasing becomes possible thanks to the eigenstate mixing by the photonic spin-orbit coupling at the imaginary Fermi arcs. Our work provides a novel way to develop linearly polarized lasers and paves the way for the future fundamental research in topological photonics, non-Hermitian optics, and other fields.

Storing light near an exceptional point

Photons with zero rest mass are impossible to be stopped. However, a pulse of light can be slowed down and even halted through strong light-matter interaction in a dispersive medium in atomic systems. Exceptional point (EP), a non-Hermitian singularity point, can introduce an abrupt transition in dispersion. Here we experimentally observe room-temperature storing light near an exceptional point induced by nonlinear Brillouin scattering in a chip-scale 90-μm-radius optical microcavity, the smallest platform up to date to store light. Through nonlinear coupling, a Parity-Time (PT) symmetry can be constructed in optical-acoustical hybrid modes, where Brillouin scattering-induced absorption (BSIA) can lead to both slow light and fast light of incoming pulses. A subtle transition of slow-to-fast light reveals a critical point for storing a light pulse up to half a millisecond. This compact and room-temperature scheme of storing light paves the way for practical applications in all-optical communications and quantum information processing.

Parametrically enhancing sensor sensitivity at an exceptional point

We propose a scheme to enhance the sensitivity of non-Hermitian optomechanical mass sensors. The benchmark system consists of two coupled optomechanical systems where the mechanical resonators are mechanically coupled. The optical cavities are driven either by a blue-detuned or red-detuned laser to produce gain and loss, respectively. Moreover, the mechanical resonators are parametrically driven through the modulation of their spring constant. For a specific strength of the optical driving field and without parametric driving, the system features an exceptional point (EP). Any perturbation to the mechanical frequency (dissipation) induces a splitting (shifting) of the EP, which scales as the square root of the perturbation strength, resulting in a sensitivity-factor enhancement compared with conventional optomechanical sensors. The sensitivity enhancement induced by the shifting scenario is weak as compared to the one based on the splitting phenomenon. By switching on parametric driving, the sensitivity of both sensing schemes is greatly improved, yielding to a better performance of the sensor. We have also confirmed these results through an analysis of the output spectra and the transmissions of the optical cavities. In addition to enhancing EP sensitivity, our scheme also reveals nonlinear effects on sensing under splitting and shifting scenarios. This work sheds light on mechanisms of enhancing the sensitivity of non-Hermitian mass sensors, paving a way to improve sensors performance for better nanoparticles or pollutants detection and for water treatment. Published by the American Physical Society 2024