Photonic systems and technologies traditionally relegated to table-top experiments are poised to make the leap from the laboratory to real-world applications through integration, leading to a dramatic decrease in size, weight, power, and cost 1 . In particular, photonic integrated ultra-narrow linewidth lasers are a critical component for applications including coherent communications 2 , metrology 3-5 , microwave photonics 6 , spectroscopy 7 , and optical synthesizers 1 . Stimulated Brillouin scattering (SBS) lasers, through their unique linewidth narrowing properties 8 , are an ideal candidate to create highly-coherent waveguide integrated sources. In particular, cascaded-order Brillouin lasers show promise for multi-line emission 14 , low-noise microwave generation 6 and other optical comb applications. To date, compact, very-low linewidth SBS lasers have been demonstrated using discrete, tapered-fiber coupled chip-scale silica 9,10 or CaF2 11 microresonators. Photonic integration of these lasers can dramatically improve their stability to environmental and mechanical disturbances, simplify their packaging, and lower cost through wafer-scale photonics foundry processes. While single-order silicon 12 and cascade-order chalcogenide 13 waveguide SBS lasers have been demonstrated, these lasers produce modest emission linewidths of 10-100 kHz and are not compatible with waferscale photonics foundry processes. Here, we report the first demonstration of a sub-Hz (~0.7 Hz) fundamental linewidth photonic-integrated Brillouin cascaded-order laser, representing a significant advancement in the state-of-the-art in integrated waveguide SBS lasers. This laser is comprised of a bus-ring resonator fabricated using an ultra-low loss (< 0.5 dB/m) Si3N4 waveguide platform. To achieve a sub-Hz linewidth, we leverage a high-Q, large mode volume, single polarization mode resonator that produces photon generated acoustic waves without phonon guiding. This approach greatly relaxes phase matching conditions between polarization modes and optical and acoustic modes. By using a theory for cascaded-order Brillouin laser dynamics 14 , we determine the fundamental emission linewidth of the first Stokes order by measuring the beat-note linewidth between and the relative powers of the first and third Stokes orders. Extension of these high performance lasers to the visible and near-IR wavebands is possible due to the low optical loss of silicon nitride waveguides from 405 nm to 2350 nm 15 , paving the way to photonic-integrated sub-Hz lasers for visible-light applications including atomic clocks and precision spectroscopy.

We use general concepts of statistical mechanics to compute the quantum frictional force on an atom moving at constant velocity above a planar surface. We derive the zero-temperature frictional force using a non-equilibrium fluctuation-dissipation relation, and show that in the large-time, steady-state regime quantum friction scales as the cubic power of the atom's velocity. We also discuss how approaches based on Wigner-Weisskopf and quantum regression approximations fail to predict the correct steady-state zero temperature frictional force, mainly due to the low frequency nature of quantum friction.Comment: 5+1 pages, 1 figur

Brillouin laser oscillators offer powerful and flexible dynamics as the basis for mode-locked lasers, microwave oscillators, and optical gyroscopes in a variety of optical systems. However, Brillouin interactions are markedly weak in conventional silicon photonic waveguides, stifling progress toward silicon-based Brillouin lasers. The recent advent of hybrid photonic-phononic waveguides has revealed Brillouin interactions to be one of the strongest and most tailorable nonlinearities in silicon. In this study, we have harnessed these engineered nonlinearities to demonstrate Brillouin lasing in silicon. Moreover, we show that this silicon-based Brillouin laser enters a regime of dynamics in which optical self-oscillation produces phonon linewidth narrowing. Our results provide a platform to develop a range of applications for monolithic integration within silicon photonic circuits.

Electrostatic patch potentials give rise to forces between neutral conductors at distances in the micrometer range and must be accounted for in the analysis of Casimir force experiments. In this paper we develop a quasi-local model for describing random potentials on metallic surfaces. In contrast to some previously published results, we find that patches may provide a significant contribution to the measured signal, and may render the experimental data at distances below 1 micrometer compatible with theoretical predictions based on the Drude model.Comment: 9 pages, 6 figures, version 2 includes corrections to the text and added references. Version 3 contains modified figures and text. Version 4 contains modified figures and tex

In this paper, we explore the spatio-temporal dynamics of spontaneous and stimulated forward Brillouin scattering. This general treatment incorporates the optomechanical coupling produced by boundary-induced radiation pressures (boundary motion) and material-induced electrostrictive forces (photo-elastic effects), permitting straightforward application to a range of emerging micro- and nano-scale optomechanical systems. Through a self-consistent fully coupled nonlinear treatment, developed within a general Hamiltonian framework, we establish the connection between the power spectral density of spontaneously scattered light in forward Brillouin interactions and the nonlinear coupling strength. We show that, in sharp contrast to backward Brillouin scattering, noise-initiated stimulated forward Brillouin scattering is forbidden in the majority of experimental systems. In fact, the single-pass gain, which characterizes the threshold for energy transfer in back-scattering processes, is negative for a large class of forward Brillouin devices. Beyond this frequent experimental case, we explore mechanisms for dispersive symmetry breaking that lead to amplification and dynamics reminiscent of backward Brillouin scattering.Comment: 12 pages, 3 figure

Brillouin processes couple light and sound through optomechanical three-wave interactions. Within bulk solids, this coupling is mediated by the intrinsic photo-elastic material response yielding coherent emission of high frequency (GHz) acoustic phonons. This same interaction produces strong optical nonlinearities that overtake both Raman or Kerr nonlinearities in practically all solids. In this paper, we show that the strength and character of Brillouin interactions are radically altered at low temperatures when the phonon coherence length surpasses the system size. In this limit, the solid becomes a coherent optomechanical system with macroscopic (cm-scale) phonon modes possessing large (60 µg) motional masses. These phonon modes, which are formed by shaping the surfaces of the crystal into a confocal phononic resonator, yield appreciable optomechanical coupling rates (∼100 Hz), providing access to ultra-high Q-factor (4.2×10 7 ) phonon modes at high (12 GHz) carrier frequencies. The single-pass nonlinear optical susceptibility is enhanced from its room temperature value by more than four orders of magnitude. Through use of bulk properties, rather than nano-structural control, this comparatively simple approach is enticing for the ability to engineer optomechanical coupling at high frequencies and with high power handling. In contrast to cavity optomechanics, we show that this system yields a unique form of dispersive symmetry breaking that enables selective phonon heating or cooling without an optical cavity (i.e., cavityless optomechanics). Extending these results, practically any transparent crystalline material can be shaped into an optomechanical system as the basis for materials spectroscopy, new regimes of laser physics, precision metrology, quantum information processing, and for studies of macroscopic quantum coherence. * william.renninger@yale.edu † These authors contributed equally to this work.

In recent years, material-induced noise arising from defects has emerged as an impediment to quantum-limited measurement in systems ranging from microwave qubits to gravity wave interferometers. As experimental systems push to ever smaller dimensions, extrinsic system properties can affect its internal material dynamics. In this paper, we identify surprising new regimes of material physics (defect-phonon and defect-defect dynamics) that are produced by dimensional confinement. Our models show that a range of tell-tale signatures, encoded in the characteristics of defect-induced noise, dissipation, and nonlinearity, are profoundly altered by geometry. Building on this insight, we demonstrate that the magnitude and character of this material-induced noise is transformed in microscale systems, providing an opportunity to improve the fidelity of quantum measurements. Moreover, we show that many emerging nano-electromechanical, cavity optomechanical and superconducting resonator systems are poised to probe these new regimes of dynamics, in both high and low field limits, providing a new way to explore the fundamental tenets of glass physics.

High quality-factor (Q) optical resonators are a key component for ultra-narrow linewidth lasers, frequency stabilization, precision spectroscopy and quantum applications. Integration in a photonic waveguide platform is key to reducing cost, size, power and sensitivity to environmental disturbances. However, to date, the Q of all-waveguide resonators has been relegated to below 260 Million. Here, we report a Si3N4 resonator with 422 Million intrinsic and 3.4 Billion absorption-limited Qs. The resonator has 453 kHz intrinsic, 906 kHz loaded, and 57 kHz absorption-limited linewidths and the corresponding 0.060 dB m−1 loss is the lowest reported to date for waveguides with deposited oxide upper cladding. These results are achieved through a careful reduction of scattering and absorption losses that we simulate, quantify and correlate to measurements. This advancement in waveguide resonator technology paves the way to all-waveguide Billion Q cavities for applications including nonlinear optics, atomic clocks, quantum photonics and high-capacity fiber communications.