In the past decade, there has been a surge in research at the boundary between photonics and phononics 1 . Most efforts centered on coupling light to motion in a high-quality optical cavity 2 , typically geared towards observing the quantum state of a mechanical oscillator 3 . It was recently predicted that the strength of the light-sound interaction would increase drastically in nanoscale silicon photonic wires 4 . Here we demonstrate, for the first time, such a giant overlap between nearinfrared light and gigahertz sound co-localized in a small-core silicon wire. The wire is supported by a tiny pillar to block the path for external phonon leakage, trapping 10 GHz phonons in an area below 0.1 µm 2 . Since our geometry can be coiled up to form a ring cavity, it paves the way for complete fusion between the worlds of cavity optomechanics and Brillouin scattering. The result bodes well for the realization of low-footprint optically-pumped lasers/sasers 5 and delay lines 6 on a densely integrated silicon chip.The diffraction of light by sound was first studied by Léon Brillouin in the early 1920s. Therefore such inelastic scattering has long been called Brillouin scattering 7 . On the quantum level, the process annihilates pump photons while creating acoustic phonons and redshifted Stokes photons. The effect is known as stimulated Brillouin scattering (SBS) when the sound is generated by a strong modulated light field. This sets the stage for a self-sustaining feedback loop: the beat note between two optical waves (called the pump and the Stokes) generates sound that reinforces the initial beat note.In a seminal experimental study 8 , Brillouin scattering was viewed as a source of intense coherent sound. Later, the effect became better known as a noise source in quantum optics 9 and for applications such as spectrally pure lasing 10-12 , microwave signal processing 13,14 , slow light 15 , information storage 6 and phononic band structure mapping 16 .Traditionally 5-20 , the photon-phonon interaction was mediated by the material nonlinearity. Electrostriction drove the phonon creation, and phonon-induced permittivity changes lead to photon scattering. This conventional image of SBS as a bulk effect, without reference to geometry, breaks down in nanoscale waveguides. The impressive progress in engineering radiation pressure in micro-and nanoscale systems [21][22][23][24][25] recently inspired the * raphael.vanlaer@intec.ugent.be theoretical prediction of enormously enhanced photonphonon coupling 4,26-28 in silicon nanowires. In such waveguides, boundary effects can no longer be neglected. Thus both electrostriction and radiation pressure create phonons. Equivalently, the new theory takes into account not only bulk permittivity changes but also the shifting material boundaries. The strong photon confinement offered by these waveguides boosts both types of optical forces. However, destructive interference between the two contributions may still completely cancel the photon-phonon coupling. The giant light-sound overlap...

Radio-frequency communication systems have long used bulk-and surface-acoustic-wave devices supporting ultrasonic mechanical waves to manipulate and sense signals. These devices have greatly improved our ability to process microwaves by interfacing them to orders-ofmagnitude slower and lower loss mechanical fields. In parallel, long-distance communications have been dominated by low-loss infrared optical photons. As electrical signal processing and transmission approaches physical limits imposed by energy dissipation, optical links are now being actively considered for mobile and cloud technologies. Thus there is a strong driver for wavelength-scale mechanical wave or "phononic" circuitry fabricated by scalable semiconductor processes. With the advent of these circuits, new micro-and nanostructures that combine electrical, optical and mechanical elements have emerged. In these devices, such as optomechanical waveguides and resonators, optical photons and gigahertz phonons are ideally matched to one another as both have wavelengths on the order of micrometers. The development of phononic circuits has thus emerged as a vibrant field of research pursued for optical signal processing and sensing applications as well as emerging quantum technologies. In this review, we discuss the key physics and figures of merit underpinning this field. We also summarize the state of the art in nanoscale electro-and optomechanical systems with a focus on scalable platforms such as silicon. Finally, we give perspectives on what these new systems may bring and what challenges they face in the coming years. In particular, we believe hybrid electro-and optomechanical devices incorporating highly coherent and compact mechanical elements on a chip have significant untapped potential for electro-optic modulation, quantum microwave-tooptical photon conversion, sensing and microwave signal processing.

Efficient interconversion of both classical and quantum information between microwave and optical frequency is an important engineering challenge. The optomechanical approach with gigahertzfrequency mechanical devices has the potential to be extremely efficient due to the large optomechanical response of common materials, and the ability to localize mechanical energy into a micron-scale volume. However, existing demonstrations suffer from some combination of low optical quality factor, low electrical-to-mechanical transduction efficiency, and low optomechanical interaction rate.Here we demonstrate an on-chip piezo-optomechanical transducer that systematically addresses all these challenges to achieve nearly three orders of magnitude improvement in conversion efficiency over previous work. Our modulator demonstrates acousto-optic modulation with Vπ = 0.02 V. We show bidirectional conversion efficiency of 10 −5 with 3.3 µW red-detuned optical pump, and 5.5% with 323 µW blue-detuned pump. Further study of quantum transduction at millikelvin temperatures is required to understand how the efficiency and added noise are affected by reduced mechanical dissipation, thermal conductivity, and thermal capacity. arXiv:1909.04627v1 [quant-ph]

The quantum nature of an oscillating mechanical object is anything but apparent. The coherent states that describe the classical motion of a mechanical oscillator do not have well-defined energy, but are rather quantum superpositions of equally-spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures the mechanical energy with a precision greater than the energy of a single phonon, ω m . One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish different phonon number states by resolvable differences in the atom's transition frequency. For photons, such dispersive measurements have been studied in cavity [1,2] and circuit quantum electrodynamics [3] where experiments using real and artificial atoms have resolved the photon number states of cavities. Here, we report an experiment where an artificial atom senses the motional energy of a driven nanomechanical oscillator with sufficient sensitivity to resolve the quantization of its energy. To realize this, we build a hybrid platform that integrates nanomechanical piezoelectric resonators with a microwave superconducting qubit on the same chip. We excite phonons with resonant pulses of varying amplitude and probe the resulting excitation spectrum of the qubit to observe phonon-number-dependent frequency shifts ≈ 5 times larger than the qubit linewidth. Our result demonstrates a fully integrated platform for quantum acoustics that combines large couplings, considerable coherence times, and excellent control over the mechanical mode structure. With modest experimental improvements, we expect our approach will make quantum nondemolition measurements of phonons [4] an experimental reality, leading the way to new quantum sensors and information processing approaches [5] that use chip-scale nanomechanical devices.In the last decade, mechanical devices have been brought squarely into the domain of quantum science through a series of remarkable experiments exploring * These authors contributed equally to this workPhonon number splitting outline. The state of a mechanical oscillator is described in quantum mechanics by a linear superposition of equally-spaced energy eigenstates |n , each representing a state of n phonons in the system. This quantized structure is normally not resolvable since the transitions between the energy levels all occur at the same frequency ωm. By coupling the resonator to a qubit of transition frequency ωge with a rate g, we cause a splitting in the qubit spectrum parameterized by a dispersive coupling rate χ. This allows us to distinguish between the different phonon number states that are present in the oscillator.the physics of measurement, transduction, and sensing [6][7][8][9][10][11][12][13]. Two paradigms for obtaining quantum control over these systems are those of cavity optomechanics (COM), where the positionx parametrically couple...

Demonstrating a device that efficiently connects light, motion, and microwaves is an outstanding challenge in classical and quantum photonics. We make significant progress in this direction by demonstrating a photonic crystal resonator on thin-film lithium niobate (LN) that simultaneously supports high-Q optical and mechanical modes, and where the mechanical modes are coupled piezoelectrically to microwaves. For optomechanical coupling, we leverage the photoelastic effect in LN by optimizing the device parameters to realize coupling rates g 0 /2π ≈ 120 kHz. An optomechanical cooperativity C > 1 is achieved leading to phonon lasing. Electrodes on the nanoresonator piezoelectrically drive mechanical waves on the beam that are then read out optically allowing direct observation of the phononic bandgap. Quantum coupling efficiency of η ≈ 10 −8 from the input microwave port to the localized mechanical resonance is measured. Improvements of the microwave circuit and electrode geometry can increase this efficiency and bring integrated ultra-low-power modulators and quantum microwave-to-optical converters closer to reality.

So far, Brillouin scattering and cavity optomechanics were mostly disconnected branches of research -- although both deal with photon-phonon coupling. This begs for the development of a broader theory that contains both fields. Here, we derive the dynamics of optomechanical cavities from that of Brillouin-active waveguides. This explicit transition elucidates the link between phenomena such as Brillouin amplification and electromagnetically induced transparency. It proves that effects familiar from cavity optomechanics all have traveling-wave partners, but not vice versa. We reveal a close connection between two parameters of central importance in these fields: the Brillouin gain coefficient and the zero-point optomechanical coupling rate. This enables comparisons between systems as diverse as ultracold atom clouds, plasmonic Raman cavities and nanoscale silicon waveguides. In addition, back-of-the-envelope calculations show that unobserved effects, such as photon-assisted amplification of traveling phonons, are now accessible in existing systems. Finally, we formulate both circuit- and cavity-oriented optomechanics in terms of vacuum coupling rates, cooperativities and gain coefficients, thus reflecting the similarities in the underlying physics.Comment: published manuscript, minor change

Quantum networks are likely to have a profound impact on the way we compute and communicate in the future. In order to wire together superconducting quantum processors over kilometerscale distances, we need transducers that can generate entanglement between the microwave and optical domains with high fidelity. We present an integrated electro-optic transducer that combines low-loss lithium niobate photonics with superconducting microwave resonators on a sapphire substrate. Our triply-resonant device operates in a dilution refrigerator and converts microwave photons to optical photons with an on-chip efficiency of 6.6 × 10 −6 and a conversion bandwidth of 20 MHz. We discuss design trade-offs in this device, including strategies to manage acoustic loss, and outline ways to increase the conversion efficiency in the future.

The century-old study of photon-phonon coupling has seen a remarkable revival in the past decade. Driven by early observations of dynamical back-action, the field progressed to ground-state cooling and the counting of individual phonons. A recent branch investigates the potential of traveling-wave, optically broadband photon-phonon interaction in silicon circuits. Here, we report continuous-wave Brillouin gain exceeding the optical losses in a series of suspended silicon beams, a step towards selective on-chip amplifiers. We obtain efficiencies up to 10 W m , 4 1 1 -the highest to date in the phononic gigahertz range. We also find indications that geometric disorder poses a significant challenge towards nanoscale phonon-based technologies.