Coulomb interaction is of central importance in localized energy levels (bound states) or electronic flat bands and could result in many exotic quantum phases, such as magnetic, superconducting, and topological phases in graphene systems1-14. In graphene monolayer, the relativistic massless Dirac fermion nature of the charge carriers enables us to realize unprecedented quasibound states, which are trapped temporarily via whispering-gallery modes (WGMs) with the lifetime (trapping time) of ~ 10 fs, in circular graphene quantum dots (GQDs)15-20. Here we show that Coulomb interaction still plays a dominating role in determining the electronic properties of the temporarily-confined quasibound states. Our scanning tunneling microscopy (STM) and spectroscopy (STS) measurements demonstrate that the discrete quasibound state in a GQD will split into two peaks when it is partially filled. The energy separation of the two split peaks increases linear with inverse effective radius of the GQDs, indicating that the splitting arises from the Coulomb interaction. Moreover, we show that the real space distribution of the two split states separates in different regions of the GQD to reduce the Coulomb interaction, leading to the breaking of the WGM of the quasibound states.
We demonstrate that yttrium iron garnet microspheres support optical whispering gallery modes similar to those in non-magnetic dielectric materials. The direction of the ferromagnetic moment tunes both the resonant frequency via the Voigt effect as well as the degree of polarization rotation via the Faraday effect. An understanding of the magneto-optical coupling in whispering gallery modes, where the propagation direction rotates with respect to the magnetization, is fundamental to the emerging field of cavity optomagnonics.
The poles of the S-matrix and the wave functions of open 2D quantum billiards with convex boundary of different shape are calculated by the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two and three open channels in each lead. Bands of overlapping resonance states appear which are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes appearing in the classical calculations.
Electronic Whispering Gallery Modes (EWGMs) have been recently observed in several circular graphene junctions, pn and pp0, created in scanning tunnelling microscope experiments. By computing the local density of states within the Dirac-Weyl formalism for massless fermions we demonstrate that the EWGMs may really be emerged in any type of the electrostatic potential induced circular graphene junctions, including uni-junctions (e.g. np- or pp0-junctions) as well as bipolar-junctions (e.g. pnp-heterojunctions). Surprisingly, quantitative analyses show that for all the EWGMs identified (regardles…
We report condensation of hexagonal whispering gallery modes (WGM) at room temperature in ZnO microwires that embody nearly perfect polygonal whispering gallery microresonators. The condensate regime is achieved in the UV spectral range only at energies below the first longitudinal optical (LO) phonon replica of the free ZnO A-exciton transition and at non-zero wave vectors. We demonstrate that the multimodality of the WGM system and the high population of free excitons and phonons with various momenta strongly enhance the probability of an interaction of quasiparticles of the cavity exciton-p…
Magnons in ferrimagnetic insulators such as yttrium iron garnet (YIG) have recently emerged as promising candidates for coherent information processing in microwave circuits. Here we demonstrate optical whispering gallery modes of a YIG sphere interrogated by a silicon nitride photonic waveguide, with quality factors approaching $10^6$ in the telecom c-band after surface treatments. Moreover, in contrast to conventional Faraday setup, this implementation allows input photon polarized colinearly to the magnetization to be scattered to a sideband mode of orthogonal polarization. This Brillouin s…
Anisotropic and inhomogeneous metamaterial shells are studied in order to exploit all their resonant mode richness. These multilayer structures are based on a cylindrical distribution of radially dependent constitutive parameters including an inner void cavity. Shell, cavity and whispering gallery modes are characterized, and special attention is paid to the latter ones. The whispering gallery modes are created at the boundary layers of the shell with the background and energy localization is produced with highly radiative characteristics. These low-Q resonant states have frequencies that are …
Whispering-gallery mode resonators host multiple trapped narrowband circulating optical resonances that find applications in quantum electrodynamics, optomechanics, and sensing. However, the spherical symmetry and low field leakage of dielectric microspheres make it difficult to probe their high-quality optical modes using far-field radiation. Even so, local field enhancement from metallic nanoparticles (MNPs) coupled to the resonators can interface the optical far-field and the bounded cavity modes. In this work, we study the interaction between whispering-gallery modes and MNP surface plasmo…
Structural and electronic properties of oligothiophene nano-wires and rings synthesized on a Au(111) surface are investigated by scanning tunneling microscopy. The spectroscopic data of the linear and cyclic oligomers show remarkable differences which, to a first approximation, can be accounted by considering electronic states confinement to one-dimensional (1D) boxes having respectively fixed and periodic boundary conditions. A more detailed analysis shows that polythiophene must be treated as a ribbon (i.e. having an effective width) rather than a purely 1D structure. A fascinating consequen…
We report the study of interactions between cavity photons and paramagnetic Cr$^{3+}$ spins in a ruby (Cr$^{3+}$:Al$_2$O$_3$) Whispering Gallery mode (WGM) resonator. Examining the system at microwave frequencies and millikelvin temperatures, spin-photon couplings up to 610 MHz or about 5% of photon energy are observed between the impurity spins and high quality factor ($Q > 10^5$) WGM. Large tunability and spin-spin interaction allows operation in the strong coupling regime. The system exhibits behaviour not predicted by the usual Tavis-Cummings model because of interactions within the two-le…
Brillouin light scattering is an established technique to study magnons, the elementary excitations of a magnet. Its efficiency can be enhanced by cavities that concentrate the light intensity. Here, we theoretically study inelastic scattering of photons by a magnetic sphere that supports optical whispering gallery modes in a plane normal to the magnetization. Magnons with low angular momenta scatter the light in the forward direction with a pronounced asymmetry in the Stokes and the anti-Stokes scattering strength, consistent with earlier studies. Magnons with large angular momenta constitute…
Interaction of Whispering Gallery Modes (WGM) with dilute spin ensembles in solids is an interesting paradigm of Hybrid Quantum Systems potentially beneficial for Quantum Signal Processing applications. In the present work, WGM spectroscopy of Rare-Earth doped YSO crystal reveals the existence of Iron Group Ion (IGI) co-dopings with concentration levels of order 100 ppb. The IGI spin ensembles demonstrate large Zero Field Splittings at 14.7GHz, 18.4GHz and 25.4GHz, considerable anisotropy of the \textrm{g}-tensors, as well as two inequivalent lattice sites. Strong coupling regimes between an e…
Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-sized quantum corrals, depend on careful positioning of adatoms at clean surfaces. Here we demonstrate an entirely different approach, inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphene's unique properties, namely gate-tunable light-like carriers, we create Whispering Gallery Mode (WGM) resonators defined by circular pn-junctions, induced by a scanning tunneling probe. We …
We report direct observation of the strong exciton-photon coupling in ZnO tapered whispering gallery (WG) microcavity at room temperature. By scanning excitations along the tapered arm of ZnO tetrapod using micro-photoluminescence spectrometer with different polarizations, we observed a transition from the pure WG optical modes in the weak interaction regime to the excitonic polariton in the strong coupling regime. The experimental observations are well described by using the plane wave model including excitonic polariton dispersion relation. This provides a direct mapping of the polariton dis…
Herein, we report sub-wavelength propagation and directional out-coupling of whispering gallery modes (WGMs) of a fluorescent silica microsphere resonator mediated via plasmon polaritons in a single crystalline silver nanowire. Fluorescent spectral signatures of emission from the nanowire ends confirm efficient guiding of WGMs via nanowire plasmons. By employing Fourier plane optical microscopy, we reveal and quantify the directional fluorescence emission of WGMs from the ends of the nanowire. Given that the discussed geometry is self-assembled from a solution-phase, our results will find rele…
Transmission electron microscopy is an excellent experimental tool to study the interaction of free electrons with nanoscale light fields. However, up to now, applying electron microscopy to quantum optical investigations was hampered by the lack of experimental platforms which allow a strong coupling between fast electrons and high-quality resonators. Here, as a first step, we demonstrate the broad-band excitation of optical whispering-gallery modes in silica microresonators by fast electrons. In the emitted coherent cathodoluminescence spectrum, a comb of equidistant peaks is observed, resul…
We present the design, fabrication and characterization of cubic (3C) silicon carbide microdisk resonators with high quality factor modes at visible and near infrared wavelengths (600 - 950 nm). Whispering gallery modes with quality factors as high as 2,300 and corresponding mode volumes V ~ 2 (λ/n)^3 are measured using laser scanning confocal microscopy at room temperature. We obtain excellent correspondence between transverse-magnetic (TM) and transverse-electric (TE) polarized resonances simulated using Finite Difference Time Domain (FDTD) method and those observed in experiment. These stru…
