192 | NATURE | VOL 548 | 10 AUGUST 2017 LETTER doi:10.1038/nature23281 Exceptional points enhance sensing in an optical microcavity Weijian Chen 1 , Şahin Kaya Özdemir 1 , Guangming Zhao 1 , Jan Wiersig 2 & Lan Yang 1 Sensors play an important part in many aspects of daily life such as infrared sensors in home security systems, particle sensors for environmental monitoring and motion sensors in mobile phones. High-quality optical microcavities are prime candidates for sensing applications because of their ability to enhance light–matter interactions in a very confined volume. Examples of such devices include mechanical transducers 1 , magnetometers 2 , single-particle absorption spectrometers 3 , and microcavity sensors for sizing single particles 4 and detecting nanometre-scale objects such as single nanoparticles and atomic ions 5–7 . Traditionally, a very small perturbation near an optical microcavity introduces either a change in the linewidth or a frequency shift or splitting of a resonance that is proportional to the strength of the perturbation. Here we demonstrate an alternative sensing scheme, by which the sensitivity of microcavities can be enhanced when operated at non-Hermitian spectral degeneracies known as exceptional points 8–16 . In our experiments, we use two nanoscale scatterers to tune a whispering- gallery-mode micro-toroid cavity, in which light propagates along a concave surface by continuous total internal reflection, in a precise and controlled manner to exceptional points 12,13 . A target nanoscale object that subsequently enters the evanescent field of the cavity perturbs the system from its exceptional point, leading to frequency splitting. Owing to the complex-square-root topology near an exceptional point, this frequency splitting scales as the square root of the perturbation strength and is therefore larger (for sufficiently small perturbations) than the splitting observed in traditional non-exceptional-point sensing schemes. Our demonstration of exceptional-point-enhanced sensitivity paves the way for sensors with unprecedented sensitivity. The time evolution of classical and quantum systems with loss and/or gain is described by non-Hermitian Hamiltonians. Such Hamiltonians exhibit special spectral degeneracies known as excep- tional points, at which two or more eigenvalues and the correspond- ing eigenvectors coalesce. However, the rich physics at and around exceptional points has been elucidated only recently, after the physical existence of exceptional points was experimentally demonstrated in microwave cavities 10 . Exceptional points were subsequently observed in optical microcavities 11–13 , coupled atom–cavity systems 14 , photonic crystal slabs 15 , exciton–polariton billiards 16 , parity–time-symmetric systems 17–19 and acoustic systems 20 . Several counterintuitive effects related to exceptional points have been observed. For example, in coupled laser cavities, an exceptional point is responsible for pump-induced 21 or loss-induced 22 revival of lasing. Dynamically encir- cling an exceptional point in parameter space can lead to asymmetric mode switching in microwave waveguides 23 —a phenomenon that can be used for topological energy transfer in optomechanical systems 24 . In whispering-gallery microcavities, the asymmetric backscattering of counter-propagating optical waves can be related to exceptional points. In the vicinity of an exceptional point, the modes exhibit strong chiral behaviour, with an unbalanced contribution of clockwise- and anticlockwise-travelling modes leading to directional lasing 13 . One key difference between exceptional points and conventional degeneracies known as diabolic points is their sensitivity to pertur- bations. In a system operating around a diabolic point, the resulting eigenvalue splitting is proportional to the perturbation strength . In contrast, for a system with an Nth-order exceptional point, at which N eigenvalues and the corresponding eigenvectors coalesce, the splitting induced by the perturbation scales as  1/N . Hence, for a sufficiently small perturbation , the splitting at the exceptional point is larger. This particular characteristic of exceptional points has been proposed for use in sensor applications 25–27 . Here we experimentally demonstrate such an exceptional-point sensor, highlighting the enhancement of the sensitivity. Our system 12,13 consists of a silicon dioxide (silica) micro-toroid cavity coupled to a fibre-taper waveguide for in- and out-coupling of light (Extended Data Fig. 1). With its circular geometry, the micro-toroid cavity supports clockwise- and anticlockwise-travelling modes with degenerate eigen- frequencies but orthogonal eigenvectors—that is, the cavity operates at a diabolic point. To set up an exceptional-point sensor, we use two silica nano-tips as Rayleigh scatterers within the mode volume of the cavity to tune the coupling between clockwise- and anticlockwise-travelling modes to steer the system to an exceptional point. In the experiments, we first located an optical resonance mode with no observable mode splitting in the transmission spectrum. The absence of mode splitting was also confirmed by the absence of a reflection signal, that is, no modal coupling between the clockwise- and anticlockwise-travelling modes. We then introduced a scatterer into the mode volume of the cavity to induce modal coupling between the clockwise- and anticlockwise-travelling modes, which led to mode splitting and a reflection signal. Afterwards, a second scatterer was introduced to the mode volume, the relative position and effective size of which were finely tuned to bring the system to an exceptional point. At an exceptional point, owing to fully asymmetric backscattering between the clockwise- and anticlockwise-travelling waves, only one of the travelling directions is dominant 13 ; for example, the reflection spectrum shows a strong resonance peak for light injection in the anticlockwise direction, whereas it vanishes for light injection in the clockwise direction (Extended Data Fig. 2). Optical cavities that operate at exceptional points can be exploited for enhanced nanoparticle sensing using the mode-splitting technique 25,26 . When a nanoparticle enters the mode volume it perturbs the system, pushing it away from the exceptional point and conse- quently lifting the non-Hermitian degeneracy of the eigenfrequencies and the corresponding eigenvectors, triggering a complex frequency splitting. For example, for second-order (N = 2) exceptional points the system has square-root topology at the complex frequency eigensurface; therefore, eigenfrequency splitting induced by a small perturbation of strength  ( ≪  1 ) is proportional to  1/2 (Fig. 1b). In contrast, conven- tional cavity-based nanoparticle sensors 4–6 utilize diabolic rather than exceptional points, at which only the eigenfrequencies are degenerate and the corresponding eigenvectors can be chosen to be orthogonal, 1 Department of Electrical and Systems Engineering, Washington University, St Louis, Missouri 63130, USA. 2 Institute for Theoretical Physics, Otto-von-Guericke University Magdeburg, D-39016 Magdeburg, Germany. © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.