Cavity optomechanics with ultra-high Q crystalline micro-resonators

We present the first observation of optomechanical coupling in ultra-high Q crystalline whispering-gallery-mode (WGM) resonators. The high purity of the crystalline material enables optical quality factors in excess of 10^{10} and finesse exceeding 10^{6}. Simultaneously, mechanical quality factors greater than 10^{5} are obtained, still limited by clamping losses. Compared to previously demonstrated cylindrical resonators, the effective mass of the mechanical modes can be dramatically reduced by the fabrication of CaF2 microdisc resonators. Optical displacement monitoring at the 10^{-18} m/sqrt{Hz}-level reveals mechanical radial modes at frequencies up to 20 MHz, corresponding to unprecedented sideband factors (>100). Together with the weak intrinsic mechanical damping in crystalline materials, such high sindeband factors render crystalline WGM micro-resonators promising for backaction evading measurements, resolved sideband cooling or optomechanical normal mode splitting. Moreover, these resonators can operate in a regime where optomechanical Brillouin lasing can become accessible

Frequency combs and platicons in optical microresonators with normal GVD

We predict the existence of a novel type of the flat-top dissipative solitonic pulses, "platicons", in microresonators with normal group velocity dispersion (GVD). We propose methods to generate these platicons from cw pump. Their duration may be altered significantly by tuning the pump frequency. The transformation of a discrete energy spectrum of dark solitons of the Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is demonstrated. Generation of similar structures is also possible with bi-harmonic, phase/amplitude modulated pump or via laser injection locking.Comment: 9 pages, 6 figure

Mode spectrum and temporal soliton formation in optical microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the resonator mode spectrum on temporal soliton formation. Using frequency comb assisted diode laser spectroscopy, the measured mode structure of crystalline MgF2 resonators are correlated with temporal soliton formation. While an overal general anomalous dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Mode coupling induced avoided crossings in the resonator mode spectrum are found to prevent soliton formation, when affecting resonator modes close to the pump laser. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations, which reveal the rich interplay of mode crossings and soliton formation

Determination of the vacuum optomechanical coupling rate using frequency noise calibration

The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate \vcr analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe field and knowledge of the mechanical oscillator's occupation. The method is experimentally verified for a micromechanical mode in a toroidal whispering-gallery-resonator and a nanomechanical oscillator coupled to a toroidal cavity via its near field.Comment: 11 pages, 2 figure

Soliton dual comb in crystalline microresonators

We present a novel compact dual-comb source based on a monolithic optical crystalline MgF$_2$ multi-resonator stack. The coherent soliton combs generated in two microresonators of the stack with the repetition rate of 12.1 GHz and difference of 1.62 MHz provided after heterodyning a 300 MHz wide radio-frequency comb. Analogous system can be used for dual-comb spectroscopy, coherent LIDAR applications and massively parallel optical communications.Comment: 5 pages, 5 figure

High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators

The inherent coupling of optical and mechanical modes in high finesse optical microresonators provide a natural, highly sensitive transduction mechanism for micromechanical vibrations. Using homodyne and polarization spectroscopy techniques, we achieve shot-noise limited displacement sensitivities of 10^(-19) m Hz^(-1/2). In an unprecedented manner, this enables the detection and study of a variety of mechanical modes, which are identified as radial breathing, flexural and torsional modes using 3-dimensional finite element modelling. Furthermore, a broadband equivalent displacement noise is measured and found to agree well with models for thermorefractive noise in silica dielectric cavities. Implications for ground-state cooling, displacement sensing and Kerr squeezing are discussed.Comment: 25 pages, 8 figure

Coupling ideality of free electrons with photonic integrated waveguides

Recently, integrated photonics has brought new capabilities to electron microscopy and been used to demonstrate efficient electron phase modulation and electron-photon correlations. Here, we quantitatively analyze the interaction strength between a free electron and a photonic integrated circuit with a heterogeneous structure. We adopt a dissipative QED treatment and show that with proper electron beam positioning and waveguide geometry, one can achieve near-unity coupling ideality to a well-defined spatial-temporal waveguide mode. Furthermore, we show that the frequency and waveform of the coupled mode can be tailored to the application. These features show that photonic integrated waveguides are a promising platform for free-electron quantum optics with applications like high-fidelity electron-photon entanglement, heralded single-electron and photon state synthesis

Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain

We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral formula which applies for arbitrary states of the system with a smooth distribution of Bethe roots, including the ground state and finite temperature Gibbs-states. In the cases K<=4 we perform the explicit factorization of the multiple integral. In the case of K=3 we obtain the recent result of Kormos et.al., whereas our formula for K=4 is new. Numerical results are presented as well.Comment: 23 pages, 2 figures, v2: minor modifications and references adde

Cryogenic properties of optomechanical silica microcavities

We present the optical and mechanical properties of high-Q fused silica microtoroidal resonators at cryogenic temperatures (down to 1.6 K). A thermally induced optical multistability is observed and theoretically described; it serves to characterize quantitatively the static heating induced by light absorption. Moreover the influence of structural defect states in glass on the toroid mechanical properties is observed and the resulting implications of cavity optomechanical systems on the study of mechanical dissipation discussed.Comment: 4 pages, 3 figure

Thermo-optic locking of a semiconductor laser to a microcavity resonance

We experimentally demonstrate thermo-optic locking of a semiconductor laser to an integrated toroidal optical microresonator. The lock is maintained for time periods exceeding twelve hours, without requiring any electronic control systems. Fast control is achieved by optical feedback induced by scattering centers within the microresonator, with thermal locking due to optical heating maintaining constructive interference between the cavity and the laser. Furthermore, the optical feedback acts to narrow the laser linewidth, with ultra high quality microtoroid resonances offering the potential for ultralow linewidth on-chip lasers.Comment: 6 pages, 6 figure