Stimulated Brillouin scattering (SBS) is traditionally viewed as a process whose strength is dictated by intrinsic material nonlinearities with little dependence on waveguide geometry. We show that this paradigm breaks down at the nanoscale, as tremendous radiation pressures produce new forms of SBS nonlinearities. A coherent combination of radiation pressure and electrostrictive forces is seen to enhance both forward and backward SBS processes by orders of magnitude, creating new geometric degrees of freedom through which photon-phonon coupling becomes highly tailorable. At nanoscales, the backward-SBS gain is seen to be 10 4 times greater than in conventional silica fibers with 100 times greater values than predicted by conventional SBS treatments. Furthermore, radically enhanced forward-SBS processes are 10 5 times larger than any known waveguide system. In addition, when nanoscale silicon waveguides are cooled to low temperatures, a further 10-100 times increase in SBS gain is seen as phonon losses are reduced. As a result, a 100-m segment of the waveguide has equivalent nonlinearity to a kilometer of fiber. Couplings of this magnitude would enable efficient chip-scale stimulated Brillouin scattering in silicon waveguides for the first time. More generally, we develop a new full-vectorial theoretical formulation of stimulated Brillouin scattering that accurately incorporates the effects of boundary-induced nonlinearities and radiation pressure, both of which are seen to have tremendous impact on photonphonon coupling at subwavelength scales. This formalism, which treats both intermode and intramode coupling within periodic and translationally invariant waveguide systems, reveals a rich landscape of new stimulated Brillouin processes when applied to nanoscale systems.

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.

The ability to engineer and manipulate different varieties of quantum mechanical objects allows us to take advantage of their unique properties and create useful hybrid technologies 1 .Thus far, complex quantum states and exquisite quantum control have been demonstrated in systems ranging from trapped ions 2, 3 and solid state qubits 4,5 to superconducting microwave resonators 6,7 . Recently, there have been many efforts 8,9 to extend these demonstrations to the motion of complex, macroscopic objects. These 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. In pursuit of such macroscopic quantum phenomena, mechanical oscillators have been interfaced with quantum devices such as optical cavities and superconducting circuits [10][11][12] . In particular, there have been a few experiments that couple motion to nonlinear quantum objects [13][14][15] such as superconducting qubits. Importantly, this opens up the possibility of creating, storing, and manipulating non-Gaussian quantum states in mechanical degrees of freedom. However, before sophisticated quantum control of mechanical motion can be achieved, we must overcome the challenge of realizing systems with long coherence times while maintaining a 1 arXiv:1703.00342v1 [quant-ph] 1 Mar 2017 sufficient interaction strength. These systems should be implemented in a simple and robust manner that allows for increasing complexity and scalability in the future. Here we experimentally demonstrate a high frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction. In contrast to previous experiments with qubit-mechanical systems [13][14][15] , our device requires only simple fabrication methods, extends coherence times to many microseconds, and provides controllable access to a multitude of phonon modes. We use this system to demonstrate basic quantum operations on the coupled qubit-phonon system. Straightforward improvements to the current device will allow for advanced protocols analogous to what has been shown in optical and microwave resonators, resulting in a novel resource for implementing hybrid quantum technologies.Measuring and controlling the motion of massive objects in the quantum regime is of great interest for both technological applications and for furthering our understanding of quantum mechanics in complex systems. In some respects, the physics of phonons inside a crystal is similar to that of photons inside an electromagnetic resonator, which are routinely treated as quantum mechanical objects. However, such mechanical excitations involve the collective motion of a large number of atoms in the complex environment of a macroscopic object. Nevertheless, there has only been one demonstration of a nonlinear electromechanical system in the strong coupling limit 13 . The outstanding question is how to simultaneously achieve coherences 3 and c...

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.

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.

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 macroscopic motional modes 1-3 , which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test for novel decoherence mechanisms in macroscopic objects and other modifications to standard quantum theory 4, 5 .Many of these applications call for the ability to create and characterize complex quantum states, putting demanding requirements on the speed of quantum operations and the coherence of the mechanical mode. In this work, we demonstrate the controlled generation of multi-phonon Fock states in a macroscopic bulk-acoustic wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states 6 . These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple to individual phonon modes. Our work shows that circuit quantum acousto-dynamics (circuit QAD) 7 enables sophisticated 1 arXiv:1804.07426v2 [quant-ph]

A promising path for introducing rapid modulation into fibres would be through the piezoelectric effect [10][11] . Embedding piezoelectric domains would allow fibres to be electrically actuated over broad frequencies on the one hand, and to function as sensitive broadband microphones on the other. However, fibres for the most part have been made of materials in the disordered glassy state precluding the crystalline symmetry requirements necessary for piezoelectricity.Recent progress in drawing of fibres made of a multiplicity of materials 12 present new opportunities for re-examining this challenge. With this approach, fibre materials are drawn from 3 preforms in a regime dominated by viscous forces allowing for internal low viscosity domains to be arranged in non-equilibrium cross sections confined by viscous glassy boundary layers. In fact constructing a piezoelectric fibre could be accomplished in a straightforward manner by assembling a preform made of a piezoelectric material poly(vinylidene fluoride) (PVDF) 13-14 , with metal electrodes and an insulating polymer, which would be followed by a thermal draw.The stress present during the fibre draw should in principle induce the non-polar α to the ferroelectric β phase transition in the PVDF layer 13,[15][16] . The process should yield many metres of fibre with built-in internal electrodes which could be utilized to establish the large electric field necessary for poling the PVDF layer. However, upon detailed examination a number of significant challenges and seemingly conflicting requirements arise. The necessity to utilize crystalline materials both for the piezoelectric layer and the electrical conductors leads to the formation of multiple adjacent low viscosity and high aspect ratio domains. These domains undergoing a reduction in cross sectional dimensions are susceptible to capillary breakup and mixing during fibre drawing due to flow instabilities. Layer thickness non-uniformity either in the lateral or in the longitudinal directions [17][18] precludes the formation of the coercive field needed for poling. Moreover, even if capillary breakup were kinetically averted and uniform sections of fibres were to emerge they would not exhibit piezoelectricity because the stress and strain conditions necessary to induce the thermodynamic phase transition in PVDF cannot be sustained in the fibre draw process.To address these challenges we choose to focus our attention on the ability to maintain geometric coherence and layer thickness uniformity. A viscous and conductive carbon-loaded poly(carbonate) (CPC) is used to confine the low viscosity crystalline piezoelectric layer during 4 the draw process. The CPC layers exhibit high viscosity (10 5~1 0 6 Pa·s) at the draw temperature and adequate conductivity (1~10 4 ohm·m) over the frequency range from DC to tens of MHz, thus facilitating short range (hundreds of microns) charge transport on length scales associated with the fibre cross section. Then a piezoelectric polymer which crystallizes into the appropriate phase...

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