When non-Hermitian eigenvalue surfaces form intertwined Riemann surfaces, the corresponding non-Hermitian singularities, also know as exceptional points (EPs), are located at the center of this specific topology. Various experimental platforms have recently been presented in which interesting new physics associated with these branch point singularities can be explored. In particular, it has been shown that dynamically encircling EPs may lead to a so-called chiral state transfer. The chirality in this context refers to the fact that in such an encircling protocol, the final state at the end of an EP -enclosing loop solely depends on the encircling direction (clockwise or counterclockwise), but not on the initial state. Such a chiral behavior is intrinsically linked to the state vector deviating from adiabatically following the system's eigenstates associated with the eigenvalue surfaces; instead, due to the non-Hermitian violation of the adiabatic theorem, non-adiabatic jumps let the system undergo transitions from lossy eigenstates to eigenstates with gain. Here, we present two experiments that implement concepts that go beyond this established paradigm.

Shaping the light emission characteristics of laser systems is of great importance in various areas of science and technology. In a typical lasing arrangement, the transverse spatial profile of a laser mode tends to remain self-similar throughout the entire cavity. Going beyond this paradigm, we demonstrate here how to shape a spatially evolving mode such that it faithfully settles into a pair of bi-orthogonal states at the two opposing facets of a laser cavity. This was achieved by purposely designing a structure that allows the lasing mode to encircle a non-Hermitian exceptional point while deliberately avoiding non-adiabatic jumps. The resulting state transfer reflects the unique topology of the associated Riemann surfaces associated with this singularity. Our approach provides a route to developing versatile mode-selective active devices and sheds light on the interesting topological features of exceptional points.

The parametric steering of a non-Hermitian Hamiltonian on closed loops excluding the exceptional point is studied. It is shown that a combination of topology and shape of the Riemann surfaces governs the topological state transfer.

In non-Hermitian settings, the particular position at which two eigenstates coalesce in the complex plane under a variation of a physical parameter is called an exceptional point. An open disordered system is a special class of non-Hermitian system, where the degree of scattering directly controls the confinement of the modes. Herein a non-perturbative theory is proposed which describes the evolution of modes when the permittivity distribution of a 2D open dielectric system is modified, thereby facilitating to steer individual eigenstates to such a non-Hermitian degeneracy. The method is used to predict the position of such an exceptional point between two Anderson-localized states in a disordered scattering medium. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems.

The adiabatic theorem, a corollary of the Schrödinger equation, manifests itself in a profoundly different way in non-Hermitian arrangements, resulting in counterintuitive state transfer schemes that have no counterpart in closed quantum systems. In particular, the dynamical encirclement of exceptional points (EPs) in parameter space has been shown to lead to a chiral phase accumulation, non-adiabatic jumps and topological mode conversion1-8. Recent theoretical studies, however, have shown that contrary to previously established demonstrations, this behaviour is not strictly a result of winding around a non-Hermitian degeneracy9. Instead, it seems to be mostly attributed to the non-trivial landscape of the Riemann surfaces, sometimes because of the presence of an EP in the vicinity9-11. Here, in an effort to bring this counterintuitive aspect of non-Hermitian systems to light and confirm this hypothesis, we provide a set of experiments to directly observe the field evolution and chiral state conversion in an EP-excluding cycle in a slowly varying non-Hermitian system. To do so, a versatile yet unique fibre-based photonic emulator is realized that utilizes the polarization degrees of freedom in a quasi-common-path single-ring arrangement. Our observations may open up new avenues for light manipulation and state conversion, as well as providing a foundation for understanding the intricacies of the adiabatic theorem in non-Hermitian systems.

We report on the first implementation of a photonic emulator platform upon which dynamic encirclement of an exceptional point can be observed. Using two polarization states, an omnipolarizer is realized based on chiral mode conversion.

We experimentally demonstrate for the first time omnipolarizer action in the optical domain. This is achieved by encircling a non-Hermitian singularity through which the output polarization state can be faithfully and unidirectionally preselected. (C) 2020 The Author(s)

The efficient transfer of excitations between different levels of a quantum system is a task with many applications. Among the various protocols to carry out such a state transfer in driven systems, rapid adiabatic passage (RAP) is one of the most widely used. Here we show both theoretically and experimentally that adding a suitable amount of loss to the driven Hamiltonian turns a RAP protocol into a scheme for encircling an exceptional point including the chiral state transfer associated with it. Our work thus discloses an intimate connection between a whole body of literature on RAP and recent studies on the dynamics in the vicinity of an exceptional point, which we expect to serve as a bridge between the disjoint communities working on these two scenarios.

A non-Hermitian He-Ne ring laser gyroscope (RLG) that operates at an exceptional point is proposed and experimentally realized. Compared to a standard RLG, the device exhibits more than an order of magnitude enhancement in sensitivity.

Gyroscopes are essential to many diverse applications associated with navigation, positioning and inertial sensing1. In general, most optical gyroscopes rely on the Sagnac effect—a relativistically induced phase shift that scales linearly with the rotational velocity2,3. In ring laser gyroscopes (RLGs), this shift manifests as a resonance splitting in the emission spectrum, which can be detected as a beat frequency4. The need for ever more precise RLGs has fuelled research activities aimed at boosting the sensitivity of RLGs beyond the limits dictated by geometrical constraints, including attempts to use either dispersive or nonlinear effects5–8. Here we establish and experimentally demonstrate a method using non-Hermitian singularities, or exceptional points, to enhance the Sagnac scale factor9–13. By exploiting the increased rotational sensitivity of RLGs in the vicinity of an exceptional point, we enhance the resonance splitting by up to a factor of 20. Our results pave the way towards the next generation of ultrasensitive and compact RLGs and provide a practical approach for the development of other classes of integrated sensor. A method based on non-Hermitian singularities, or exceptional points, is established and used to increase the Sagnac scale factor and enhance the sensitivity of ring-laser gyroscopes.

The crystal structure of phases in the pseudo-binary system CeCo1–хNiхC2 (x = 0, 0.33, 0.5, 0.67, 0.79, 0.80, 0.83, 1) was investigated by means of X-ray powder diffraction. Co richer solid solutions CeCo1–хNiхC2 (0≤ x ≤0.5) crystallize in the monoclinic CeCoC2-type structure; a = 5.3968(2) Å, b = 5.4013(3) Å, c = 7.4762(3) Å, β = 102.136(3)°, V = 213.06(3) Å3 for x = 0.5. Ni-rich CeNi1–yCoyC2 (0≤ y ≤0.2) are isotypic with the orthorhombic CeNiC2-type structure, a = 3.8486(2) Å, b = 4.5479(2) Å, c = 6.1531(3) Å, V = 107.70(1) Å3 for y = 0.2. In the intermediate region (0.5< x <0.79) both phases, CeCo0.21Ni0.79C2 and CeCo0.5Ni0.5C2, coexist. The non-isoelectronic substitution of Ni by Co in solid solutions CeNi1–yCoyC2 causes a continuous reduction of the Néel temperature and finally, for CeCoC2, results in a paramagnetic Kondo-lattice ground state.

Magnetic properties of single crystalline HoCoC2 and the evolution of magnetic and structural features in a series of polycrystalline solid solutions HoCo1−xNixC2 (0⩽x⩽1) are investigated by means of X-ray diffraction, magnetization, magnetic susceptibility and specific heat measurements. The crystal structures of all investigated samples refers to the CeNiC2-type structure (space group Amm2 and Pearson symbol oS8). Non-isoelectronic substitution of Co by Ni causes a non-linear increase of the unit cell volume and especially a non-monotonous variation of the a and c lattice parameters as well as a pronounced reduction of the C–C bond length of carbon dimers. Temperature dependent magnetization and specific heat measurements reveal a crossover from a ferromagnetic for HoCoC2 with TC=10.6(1)K to an antiferromagnetic ground state for HoNiC2 with TN=2.78(6)K and a non-monotonous variation of the magnetic ordering temperature with a minimum at intermediate compositions. Crystalline electric field effects of HoCoC2 and HoNiC2 are analysed using combined thermodynamic and magnetic susceptibility data. The electrical resistivity of HoNiC2 displays a distinct anomaly near room temperature which indicates the formation of a charge density wave (CDW) state as earlier reported for several other rare earth nickel dicarbides.