Exceptional points (EPs) are special spectral degeneracies of non-Hermitian Hamiltonians governing the dynamics of open systems. At the EP two or more eigenvalues and the corresponding eigenstates coalesce 1-3 . Recently, it has been proposed that EPs can enhance the sensitivity of optical gyroscopes 4,5 . Here we report measurement of rotation sensitivity boost by over 4× resulting from operation of a chip-based stimulated Brillouin gyroscope near an exceptional point. A second-order EP is identified in the gyroscope and originates from the dissipative coupling between the clockwise and counterclockwise lasing modes. The modes experience opposing Sagnac shifts under application of a rotation, but near the exceptional point new modal admixtures dramatically increase the Sagnac shift. Modeling confirms the measured enhancement. Besides the ability to operate an optical gyroscope with enhanced sensitivity, this result provides a new platform for study of non-Hermitian physics and nonlinear optics with precise control.High-Q optical microresonators have received considerable attention as sensors across a wide range of applications including biomolecule 6-8 and nanoparticle detection 9 , temperature measurement 10 , and rotation measurement [11][12][13][14][15] . In recent years, a new approach to enhance the sensitivity of microresonator sensors using the physics of exceptional points is being studied 4,5,16-20 . Traditionally, for precise sensing, a perturbation to an optical microcavity (or to its reference frame as in the case of a gyroscope) introduces either a linewidth change, a frequency shift, or a frequency splitting of a resonance that monotonically changes with the strength of the perturbation. However, operation of these systems near an exceptional point changes this situation by introduction of a square-root dependence into the transduction that can boost the sensor's ability to transduce perturbations 16 .In this work, we experimentally and theoretically demonstrate the existence of EPs in a microresonatorbased laser gyroscope, and then measure the enhanced rotation-rate transduction sensitivity near the EP. The laser gyroscope is described elsewhere 11 and uses counterpropagating Brillouin lasers in a high-quality-factor (Q ≈ 10 8 ) silica wedge resonator 21 . As shown in Fig. 1a pump light at frequencies ω pj (j = 1, 2) determined by radio-frequency modulation of a single laser (∼1552.5 nm) is coupled into the resonator from both ends of a fiber taper 22,23 . One of the pump frequencies is Pound-Drever-Hall locked to a resonator mode by feedback control to the laser. The second pump frequency is then varied to affect pump detuning change as described below. The two pump powers are stabilized via power feedback. Brillouin scattering causes a pump photon with frequency ω pj to scatter from a co-propagating acoustic phonon with frequency Ω phonon into a backwardpropagating Stokes photon with frequency ω sj . In the context of a resonator (and as illustrated in Fig. 1b), the associated phase matching con...

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The Peierls Hamiltonian band matrix is developed to investigate magnetoelectronic properties of bilayer Bernal graphene. A uniform perpendicular magnetic field creates many dispersionless Landau levels ͑LLs͒ at low and high energies and some oscillatory LLs at moderate energy. State degeneracy of the low LLs is two times as much as that of the high LLs. Wave functions and state energies are dominated by the interlayer atomic interactions and field strength ͑B 0 ͒. The former induce two groups of LLs, more low LLs, the asymmetric energy spectrum about the Fermi level, and the change of level spacing. Two sets of effective quantum numbers, n 1 ef f 's and n 2 ef f 's, are required to characterize all the wave functions. They are determined by the strongest oscillation modes of the dominant carrier densities; furthermore, they rely on the specific interlayer atomic hoppings. The dependence of the quite low Landau-level energies on B 0 and n 1 ef f is approximatelylinear. An energy gap is produced by the magnetic field and interlayer atomic hoppings. E g grows with increasing field strength, while it is reduced by the Zeeman effect. The main features of magnetoelectronic structures are directly reflected in the density of states. The predicted electronic properties could be verified by the experimental measurements on absorption spectra and transport properties.

Orbiting planets induce a weak radial velocity (RV) shift in the host star that provides a powerful method of planet detection. Importantly, the RV technique provides information about the exoplanet mass, which is unavailable with the complementary technique of transit photometry. However, RV detection of an Earth-like planet in the ‘habitable zone’ 1 requires extreme spectroscopic precision that is only possible using a laser frequency comb (LFC) 2 . Conventional LFCs require complex filtering steps to be compatible with astronomical spectrographs, but a new chip-based microresonator device, the Kerr soliton microcomb 3 – 8 , is an ideal match for astronomical spectrograph resolution and can eliminate these filtering steps. Here, we demonstrate an atomic/molecular line-referenced soliton microcomb as a first in-the-field demonstration of microcombs for calibration of astronomical spectrographs. These devices can ultimately provide LFC systems that would occupy only a few cubic centimetres 9 , 10 , thereby greatly expanding implementation of these technologies into remote and mobile environments beyond the research lab.