Photonic chip-based low-noise microwave oscillator.

Numerous modern technologies are reliant on the low-phase noise and exquisite timing stability of microwave signals. Substantial progress has been made in the field of microwave photonics, whereby low-noise microwave signals are generated by the down-conversion of ultrastable optical references using a frequency comb1-3. Such systems, however, are constructed with bulk or fibre optics and are difficult to further reduce in size and power consumption. In this work we address this challenge by leveraging advances in integrated photonics to demonstrate low-noise microwave generation via two-point optical frequency division4,5. Narrow-linewidth self-injection-locked integrated lasers6,7 are stabilized to a miniature Fabry-Pérot cavity8, and the frequency gap between the lasers is divided with an efficient dark soliton frequency comb9. The stabilized output of the microcomb is photodetected to produce a microwave signal at 20 GHz with phase noise of -96 dBc Hz-1 at 100 Hz offset frequency that decreases to -135 dBc Hz-1 at 10 kHz offset-values that are unprecedented for an integrated photonic system. All photonic components can be heterogeneously integrated on a single chip, providing a significant advance for the application of photonics to high-precision navigation, communication and timing systems.

Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator.

Quantum states of mechanical motion can be important resources for quantum information, metrology and studies of fundamental physics. Recent demonstrations of superconducting qubits coupled to acoustic resonators have opened up the possibility of performing quantum operations on macroscale motional modes1-3, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test decoherence mechanisms in macroscale objects and other modifications to standard quantum theory4,5. Many of these applications call for the ability to create and characterize complex quantum states, such as states with a well defined phonon number, also known as phonon Fock states. Such capabilities require fast quantum operations and long coherence times of the mechanical mode. Here we demonstrate the controlled generation of multi-phonon Fock states in a macroscale bulk acoustic-wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states6. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple a superconducting qubit to individual phonon modes. Our work shows that circuit quantum acoustodynamics7 enables sophisticated quantum control of macroscale mechanical objects and opens up the possibility of using acoustic modes as quantum resources.

Ultralow 0.034†dB/m loss wafer-scale integrated photonics realizing 720 million Q and 380 µW threshold Brillouin lasing.

We demonstrate 0.034 dB/m loss waveguides in a 200-mm wafer-scale, silicon nitride (Si3N4) CMOS-foundry-compatible integration platform. We fabricate resonators that measure up to a 720 million intrinsic Q resonator at 1615 nm wavelength with a 258 kHz intrinsic linewidth. This resonator is used to realize a Brillouin laser with an energy-efficient 380 µW threshold power. The performance is achieved by reducing scattering losses through a combination of single-mode TM waveguide design and an etched blanket-layer low-pressure chemical vapor deposition (LPCVD) 80 nm Si3N4 waveguide core combined with thermal oxide lower and tetraethoxysilane plasma-enhanced chemical vapor deposition (TEOS-PECVD) upper oxide cladding. This level of performance will enable photon preservation and energy-efficient generation of the spectrally pure light needed for photonic integration of a wide range of future precision scientific applications, including quantum, precision metrology, and optical atomic clocks.

Nonreciprocal Frequency Domain Beam Splitter.

The canonical beam splitter-a fundamental building block of quantum optical systems-is a reciprocal element. It operates on forward- and backward-propagating modes in the same way, regardless of direction. The concept of nonreciprocal quantum photonic operations, by contrast, could be used to transform quantum states in a momentum- and direction-selective fashion. Here we demonstrate the basis for such a nonreciprocal transformation in the frequency domain through intermodal Bragg scattering four-wave mixing (BSFWM). Since the total number of idler and signal photons is conserved, the process can preserve coherence of quantum optical states, functioning as a nonreciprocal frequency beam splitter. We explore the origin of this nonreciprocity and find that the phase-matching requirements of intermodal BSFWM produce an enormous asymmetry (76×) in the conversion bandwidths for forward and backward configurations, yielding ∼25 dB of nonreciprocal contrast over several hundred GHz. We also outline how the demonstrated efficiencies (∼10^{-4}) may be scaled to near-unity values with readily accessible powers and pumping configurations for applications in integrated quantum photonics.

Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain.

We develop a general framework of evaluating the Stimulated Brillouin Scattering (SBS) gain coefficient in optical waveguides via the overlap integral between optical and elastic eigen-modes. This full-vectorial formulation of SBS coupling rigorously accounts for the effects of both radiation pressure and electrostriction within micro- and nano-scale waveguides. We show that both contributions play a critical role in SBS coupling as modal confinement approaches the sub-wavelength scale. Through analysis of each contribution to the optical force, we show that spatial symmetry of the optical force dictates the selection rules of the excitable elastic modes. By applying this method to a rectangular silicon waveguide, we demonstrate how the optical force distribution and elastic modal profiles jointly determine the magnitude and scaling of SBS gains in both forward and backward SBS processes. We further apply this method to the study of intra- and inter-modal SBS processes, and demonstrate that the coupling between distinct optical modes are necessary to excite elastic modes with all possible symmetries. For example, we show that strong inter-polarization coupling can be achieved between the fundamental TE- and TM-like modes of a suspended silicon waveguide.

Narrowband microwave-photonic notch filters using Brillouin-based signal transduction in silicon.

The growing demand for bandwidth makes photonic systems a leading candidate for future telecommunication and radar technologies. Integrated photonic systems offer ultra-wideband performance within a small footprint, which can naturally interface with fiber-optic networks for signal transmission. However, it remains challenging to realize narrowband (∼MHz) filters needed for high-performance communications systems using integrated photonics. In this paper, we demonstrate all-silicon microwave-photonic notch filters with 50× higher spectral resolution than previously realized in silicon photonics. This enhanced performance is achieved by utilizing optomechanical interactions to access long-lived phonons, greatly extending available coherence times in silicon. We use a multi-port Brillouin-based optomechanical system to demonstrate ultra-narrowband (2.7 MHz) notch filters with high rejection (57 dB) and frequency tunability over a wide spectral band (6 GHz) within a microwave-photonic link. We accomplish this with an all-silicon waveguide system, using CMOS-compatible fabrication techniques.

Chip-based laser with 1-hertz integrated linewidth.

Lasers with hertz linewidths at time scales of seconds are critical for metrology, timekeeping, and manipulation of quantum systems. Such frequency stability relies on bulk-optic lasers and reference cavities, where increased size is leveraged to reduce noise but with the trade-off of cost, hand assembly, and limited applications. Alternatively, planar waveguide-based lasers enjoy complementary metal-oxide semiconductor scalability yet are fundamentally limited from achieving hertz linewidths by stochastic noise and thermal sensitivity. In this work, we demonstrate a laser system with a 1-s linewidth of 1.1 Hz and fractional frequency instability below 10-14 to 1 s. This low-noise performance leverages integrated lasers together with an 8-ml vacuum-gap cavity using microfabricated mirrors. All critical components are lithographically defined on planar substrates, holding potential for high-volume manufacturing. Consequently, this work provides an important advance toward compact lasers with hertz linewidths for portable optical clocks, radio frequency photonic oscillators, and related communication and navigation systems.

Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion.

We show that eigenmodes of dielectric optical waveguides exert surface dilation forces on waveguide boundaries owing to radiation pressure, and we develop an exact scaling law relating modal dispersion of an arbitrary dielectric waveguide to the magnitude of optical forces generated by radiation pressure. This result points to highly dispersive waveguides as an optimal choice for the generation of large optical forces in nano-optomechanical systems. Exact agreement with ab initio calculations is demonstrated.

Visible light photonic integrated Brillouin laser.

Narrow linewidth visible light lasers are critical for atomic, molecular and optical (AMO) physics including atomic clocks, quantum computing, atomic and molecular spectroscopy, and sensing. Stimulated Brillouin scattering (SBS) is a promising approach to realize highly coherent on-chip visible light laser emission. Here we report demonstration of a visible light photonic integrated Brillouin laser, with emission at 674 nm, a 14.7 mW optical threshold, corresponding to a threshold density of 4.92 mW µm-2, and a 269 Hz linewidth. Significant advances in visible light silicon nitride/silica all-waveguide resonators are achieved to overcome barriers to SBS in the visible, including 1 dB/meter waveguide losses, 55.4 million quality factor (Q), and measurement of the 25.110 GHz Stokes frequency shift and 290 MHz gain bandwidth. This advancement in integrated ultra-narrow linewidth visible wavelength SBS lasers opens the door to compact quantum and atomic systems and implementation of increasingly complex AMO based physics and experiments.

422 Million intrinsic quality factor planar integrated all-waveguide resonator with sub-MHz linewidth.

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.

Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces.

Radiation pressure is known to scale to large values in engineered micro and nanoscale photonic waveguide systems. In addition to radiation pressure, dielectric materials also exhibit strain-dependent refractive index changes, through which optical fields can induce electrostrictive forces. To date, little attention has been paid to the electrostrictive component of optical forces in high-index contrast waveguides. In this paper, we examine the magnitude, scaling, and spatial distribution of electrostrictive forces through analytical and numerical models, revealing that electrostrictive forces increase to large values in high index-contrast waveguides. Similar to radiation pressure, electrostrictive forces increase quadratically with the optical field. However, since electrostrictive forces are determined by the material photoelastic tensor , the sign of the electrostrictive force is highly material-dependent, resulting in cancellation with radiation pressure in some instances. Furthermore, our analysis reveals that the optical forces resulting from both radiation pressure and electrostriction can scale to remarkably high levels (i.e., greater than 10(4)(N/m(2))) for realistic guided powers. Additionally, even in simple rectangular waveguides, the magnitude and distribution of both forces can be engineered at the various boundaries of the waveguide system by choice of material system and geometry of the waveguide. This tailorability points towards novel and simple waveguide designs which enable selective excitation of elastic waves with desired symmetries through engineered stimulated Brillouin scattering processes in nanoscale waveguide systems.

A three-dimensional optical photonic crystal with designed point defects.

Photonic crystals offer unprecedented opportunities for miniaturization and integration of optical devices. They also exhibit a variety of new physical phenomena, including suppression or enhancement of spontaneous emission, low-threshold lasing, and quantum information processing. Various techniques for the fabrication of three-dimensional (3D) photonic crystals--such as silicon micromachining, wafer fusion bonding, holographic lithography, self-assembly, angled-etching, micromanipulation, glancing-angle deposition and auto-cloning--have been proposed and demonstrated with different levels of success. However, a critical step towards the fabrication of functional 3D devices, that is, the incorporation of microcavities or waveguides in a controllable way, has not been achieved at optical wavelengths. Here we present the fabrication of 3D photonic crystals that are particularly suited for optical device integration using a lithographic layer-by-layer approach. Point-defect microcavities are introduced during the fabrication process and optical measurements show they have resonant signatures around telecommunications wavelengths (1.3-1.5 microm). Measurements of reflectance and transmittance at near-infrared are in good agreement with numerical simulations.

General treatment of optical forces and potentials in mechanically variable photonic systems.

We present an analytical formalism for the treatment of the forces and potentials induced by light in mechanically variable photonic systems (or optomechanically variable systems) consisting of linear media. Through energy and photon-number conservation, we show that knowledge of the phase and the amplitude response of an optomechanically variable system, and its dependence on the mechanical coordinate of interest, is sufficient to compute the forces produced by light. This formalism not only offers a simple analytical alternative to computationally intensive Maxwell stress-tensor methods, but also greatly simplifies the analysis of mechanically variable photonic systems driven by multiple external laser sources. Furthermore, we show, through this formalism, that a scalar optical potential can be derived in terms of the phase and amplitude response of an arbitrary optomechanically variable one-port system and in generalized optomechanically variable multi-port systems, provided that their optical response is variable through a single mechanical degree of freedom. With these simplifications, well-established theories of optical filter synthesis could be extended to allow for the synthesis of complex optical force and potential profiles, independent of the construction of the underlying device or its field distribution.

High-frequency cavity optomechanics using bulk acoustic phonons.

To date, microscale and nanoscale optomechanical systems have enabled many proof-of-principle quantum operations through access to high-frequency (gigahertz) phonon modes that are readily cooled to their thermal ground state. However, minuscule amounts of absorbed light produce excessive heating that can jeopardize robust ground-state operation within these microstructures. In contrast, we demonstrate an alternative strategy for accessing high-frequency (13 GHz) phonons within macroscopic systems (centimeter scale) using phase-matched Brillouin interactions between two distinct optical cavity modes. Counterintuitively, we show that these macroscopic systems, with motional masses that are 1 million to 100 million times larger than those of microscale counterparts, offer a complementary path toward robust ground-state operation. We perform both optomechanically induced amplification/transparency measurements and demonstrate parametric instability of bulk phonon modes. This is an important step toward using these beam splitter and two-mode squeezing interactions within bulk acoustic systems for applications ranging from quantum memories and microwave-to-optical conversion to high-power laser oscillators.

A silicon Brillouin laser.

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.

On-chip inter-modal Brillouin scattering.

Brillouin nonlinearities-which result from coupling between photons and acoustic phonons-are exceedingly weak in conventional nanophotonic silicon waveguides. Only recently have Brillouin interactions been transformed into the strongest and most tailorable nonlinear interactions in silicon using a new class of optomechanical waveguides that control both light and sound. In this paper, we use a multi-mode optomechanical waveguide to create stimulated Brillouin scattering between light-fields guided in distinct spatial modes of an integrated waveguide for the first time. This interaction, termed stimulated inter-modal Brillouin scattering, decouples Stokes and anti-Stokes processes to enable single-sideband amplification and dynamics that permit near-unity power conversion. Using integrated mode multiplexers to address separate optical modes, we show that circulators and narrowband filters are not necessary to separate pump and signal waves. We also demonstrate net optical amplification and Brillouin energy transfer as the basis for flexible on-chip light sources, amplifiers, nonreciprocal devices and signal-processing technologies.

Quantum acoustics with superconducting qubits.

Mechanical objects have important practical applications in the fields of quantum information and metrology as quantum memories or transducers for measuring and connecting different types of quantum systems. The field of electromechanics is in pursuit of a robust and highly coherent device that couples motion to nonlinear quantum objects such as superconducting qubits. Here, we experimentally demonstrate a high-frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction with a cooperativity of 260. We measure qubit and mechanical coherence times on the order of 10 microseconds. Our device requires only simple fabrication methods and provides controllable access to a multitude of phonon modes. We demonstrate quantum control and measurement on gigahertz phonons at the single-quantum level.

Closed-form solutions and scaling laws for Kerr frequency combs.

A single closed-form analytical solution of the driven nonlinear Schrödinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavity solitons in certain limits. Moreover, these closed-form solutions represent the first step towards an analytical framework for wavetrain formation, and reveal new parameter regimes for enhanced Kerr-comb performance.

Control of coherent information via on-chip photonic-phononic emitter-receivers.

Rapid progress in integrated photonics has fostered numerous chip-scale sensing, computing and signal processing technologies. However, many crucial filtering and signal delay operations are difficult to perform with all-optical devices. Unlike photons propagating at luminal speeds, GHz-acoustic phonons moving at slower velocities allow information to be stored, filtered and delayed over comparatively smaller length-scales with remarkable fidelity. Hence, controllable and efficient coupling between coherent photons and phonons enables new signal processing technologies that greatly enhance the performance and potential impact of integrated photonics. Here we demonstrate a mechanism for coherent information processing based on travelling-wave photon-phonon transduction, which achieves a phonon emit-and-receive process between distinct nanophotonic waveguides. Using this device, physics--which supports GHz frequencies--we create wavelength-insensitive radiofrequency photonic filters with frequency selectivity, narrow-linewidth and high power-handling in silicon. More generally, this emit-receive concept is the impetus for enabling new signal processing schemes.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides.

Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic-phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized-with over 1,000 times larger nonlinearity than reported in previous systems-yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip.