Observation Of Exceptional Points Research Articles

Non-Hermitian polariton–photon coupling in a perovskite open microcavity

Abstract Exploring the non-Hermitian properties of semiconductor materials for optical applications is at the forefront of photonic research. However, the selection of appropriate systems to implement such photonic devices remains a topic of debate. In this work, we demonstrate that a perovskite crystal, characterized by its easy and low-cost manufacturing, when placed between two distributed Bragg reflectors with an air gap, can form a natural double microcavity. This construction shows promising properties for the realisation of novel, tunable non-Hermitian photonic devices through strong light–matter coupling. We reveal that such a system exhibits double-coupled polariton modes with dispersion including multiple inflection points. Owing to its non-Hermiticity, our system exhibits nonreciprocal properties and allows for the observation of exceptional points. Our experimental studies are in agreement with the theoretical analysis based on coupled mode theory and calculations based on transfer matrix method.

Experimental observation of exceptional points in coupled pendulums

The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that yield defective eigenvalues. These spectral singularities which are typical of non-Hermitian system means that both the eigenvalues and their associated eigenvectors coalesce. The existence of an EP requires an adequate parameterization of the dynamical system. For this aim, the experimental device has been designed with two controllable parameters which are the length of one pendulum and a viscous-like damping which is produced via electromagnetic induction. Thanks to the observation of the free response of the coupled pendulums, most EP properties are experimentally investigated, showing good agreements with theoretical considerations. In contrast with many studies on EPs, mainly in the field of physics, the novelty of the present work is that controllable parameters are restricted to be real-valued, and this requires the use of adequate search algorithms. Furthermore, it offers the possibility of exploiting the existence of EPs in time-domain dynamic problems.

Direct observation of exceptional points in photonic crystal by cross-polarization imaging in momentum space

This study explores exceptional points (EPs) in photonic crystals (PhCs) and introduces an experimental technique for their single-shot observation. Exceptional points are spectral singularities found in non-Hermitian systems, such as leaky PhC slabs. However, directly observing EPs in PhC systems using regular reflectivity spectroscopy is a considerable challenge due to interference between guided resonances and background signals. In this work, we present a simple, nondestructive technique that employs crossed polarizations to directly observe EPs in momentum-resolved resonant scattering. This approach effectively suppresses the background signal, enabling exclusive probing of the guided resonances where EPs manifest. Our results demonstrate the formation of EPs in both energy-momentum mapping and isofrequency imaging. All experimental findings align seamlessly with numerical simulations and analytical models. Our approach holds great potential as a robust tool for studying non-Hermitian physics in the PhC platform.

Observation of Exceptional Points in Thermal Atomic Ensembles.

Exceptional points (EPs) in non-Hermitian systems have recently attracted wide interest and spawned intriguing prospects for enhanced sensing. However, EPs have not yet been realized in thermal atomic ensembles, which is one of the most important platforms for quantum sensing. Here we experimentally observe EPs in multilevel thermal atomic ensembles and realize enhanced sensing of the magnetic field for 1 order of magnitude. We take advantage of the rich energy levels of atoms and construct effective decays for selected energy levels by employing laser coupling with the excited state, yielding unbalanced decay rates for different energy levels, which finally results in the existence of EPs. Furthermore, we propose the optical polarization rotation measurement scheme to detect the splitting of the resonance peaks, which makes use of both the absorption and dispersion properties and shows an advantage with enhanced splitting compared with the conventional transmission measurement scheme. Additionally, in our system both the effective coupling strength and decay rates are flexibly adjustable, and thus the position of the EPs are tunable, which expands the measurement range. Our Letter not only provides a new controllable platform for studying EPs and non-Hermitian physics, but also provide new ideas for the design of EP-enhanced sensors and opens up realistic opportunities for practical applications in the high-precision sensing of magnetic field and other physical quantities.

Observation of exceptional points in helically structured thin films.

Exceptional points (EPs) in the polarization space were observed in reflection on helically structured thin films. These films have form anisotropy at the nanoscale introduced through dynamic control of crystalline growth geometry by changing the orientation of the substrate with respect to the impinging vapor. They are simpler alternatives to metasurfaces, because they can be produced at low cost using conventional thin-film deposition techniques. The EPs were experimentally confirmed by eigenstate swapping on a closed circuit surrounding them and were predicted by numerical calculations. Reflective surfaces operating at an EP could be used to make ultrasensitive sensors.

Exceptional point in a metal-graphene hybrid metasurface with tunable asymmetric loss

Observation of exceptional points (EPs) in non-Hermitian parity-time (PT) symmetric systems has led to various nontrivial physics and exotic phenomena. Here, a metal-graphene hybrid non-Hermitian metasurface is proposed in the terahertz regime, whose unit cell is composed of two orthogonally oriented split-ring resonators (SRRs) with identical dimensions but only one SRR containing a graphene patch at the gap. An EP in polarization space is theoretically observed at a certain Fermi level of the graphene patch, where the induced asymmetric loss and the coupling strength between the two SRRs match a certain relation predicted by a coupled mode theory. The numerical fittings using the coupled mode theory agree well with the simulations. Besides, an abrupt phase flip around the EP frequency is observed in the transmission in circular polarization basis, which can be very promising in ultra-sensitive sensing applications.

Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing

Singularities of open systems, known as exceptional points (EPs), have been shown to exhibit increased sensitivities, but the observation of EPs has so far been limited to wavelength-scaled systems subject to the diffraction limit. Plasmons, the collective oscillations of free electrons coupled to photons, shrink the wavelength of light to electronic and molecular length scales. We propose a novel approach to EPs based on spatial symmetry breaking and report their observation in plasmonics at room temperature. The plasmonic EPs are based on the hybridization of detuned resonances in multilayered plasmonic structures to reach a critical complex coupling rate between nanoantenna arrays, resulting in the simultaneous coalescence of the resonances and loss rates. Their utility as sensors of anti-immunoglobulin G, the most abundant immunoglobulin isotype in human serum, is evaluated. Our work opens the way to a new class of nanoscale devices, sensors and imagers based on topological polaritonic effects. The hybridized modes of an asymmetric plasmonic dimer show avoided crossing of both the real and imaginary parts. This can lead to plasmonic exceptional points, which are used for biosensing with very high sensitivity.

Observation of exceptional points in magnonic parity-time symmetry devices.

Non-Hermitian Hamiltonians may still have real eigenvalues, provided that a combined parity-time (ƤƮ) symmetry exists. The prospect of ƤƮ symmetry has been explored in several physical systems such as photonics, acoustics, and electronics. The eigenvalues in these systems undergo a transition from real to complex at exceptional points (EPs), where the ƤƮ symmetry is broken. Here, we demonstrate the existence of EP in magnonic devices composed of two coupled magnets with different magnon losses. The eigenfrequencies and damping rates change from crossing to anti-crossing at the EP when the coupling strength increases. The magnonic dispersion includes a strong "acoustic-like" mode and a weak "optic-like" mode. Moreover, upon microwave radiation, the ƤƮ magnonic devices act as magnon resonant cavity with unique response compared to conventional magnonic systems.

Many-body exceptional points in colliding condensates

ABSTRACTExceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.

Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains.

Although counter-intuitive features have been observed in non-Hermitian optical systems based on micrometre-sized cavities, the achievement of a simplified but unambiguous approach to enable the efficient access of exceptional points (EPs) and the phase transition to desired lasing modes remains a challenge, particularly in wavelength-scale coupled cavities. Here, we demonstrate coupled photonic-crystal (PhC) nanolasers with asymmetric optical gains, and observe the phase transition of lasing modes at EPs through tuning of the area of graphene cover on one PhC cavity and systematic scanning photoluminescence measurements. As the gain contrast between the two identical PhC cavities exceeds the intercavity coupling, the phase transition occurs from the bonding/anti-bonding lasing modes to the single-amplifying lasing mode, which is confirmed by the experimental measurement of the mode images and the theoretical modelling of coupled cavities with asymmetric gains. In addition, we demonstrate active tuning of EPs by controlling the optical loss of graphene through electrical gating.

Observation of exceptional points in reconfigurable non-Hermitian vector-field holographic lattices.

Recently, synthetic optical materials represented via non-Hermitian Hamiltonians have attracted significant attention because of their nonorthogonal eigensystems, enabling unidirectionality, nonreciprocity and unconventional beam dynamics. Such systems demand carefully configured complex optical potentials to create skewed vector spaces with a desired metric distortion. In this paper, we report optically generated non-Hermitian photonic lattices with versatile control of real and imaginary sub-lattices. In the proposed method, such lattices are generated by vector-field holographic interference of two elliptically polarized pump beams on azobenzene-doped polymer thin films. We experimentally observe violation of Friedel's law of diffraction, indicating the onset of complex lattice formation. We further create an exact parity-time symmetric lattice to demonstrate totally asymmetric diffraction at the spontaneous symmetry-breaking threshold, referred to as an exceptional point. On this basis, we provide the experimental demonstration of reconfigurable non-Hermitian photonic lattices in the optical domain and observe the purest exceptional point ever reported to date.

Exceptional Points in Atomic Spectra

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an experiment with atoms is proposed.

Observation of exceptional points in electronic circuits

Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly match the mathematical predictions at the exceptional point. A discussion about the universal occurrence of exceptional points -- connecting dissipation with spatial orientation -- concludes the paper.