Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap

High Q-Factor Diamond Optomechanical Resonators with Silicon Vacancy Centers at Millikelvin Temperatures

Phonons are envisioned as coherent intermediaries between different types of quantum systems. Engineered nanoscale devices, such as optomechanical crystals (OMCs), provide a platform to utilize phonons as quantum information carriers. Here we demonstrate OMCs in diamond designed for strong for interactions between phonons and a silicon vacancy (SiV) spin. Using optical measurements at millikelvin temperatures, we measure a line width of 13 kHz (Q-factor of ∼4.4 × 105) for a 6 GHz acoustic mode, a record for diamond in the GHz frequency range and within an order of magnitude of state-of-the-art line widths for OMCs in silicon. We investigate SiV optical and spin properties in these devices and outline a path toward a coherent spin-phonon interface.

Exploring regenerative coupling in phononic crystals for room temperature quantum optomechanics

Quantum technologies play a pivotal role in driving transformative advancements across diverse fields, surpassing classical approaches and empowering us to address complex challenges more effectively; however, the need for ultra-low temperatures limits the use of these technologies to particular fields. This work comes to alleviate this problem. We present a way of phononic bandgap engineering using FEM by which the radiative mechanical energy dissipation of a nanomechanical oscillator can be significantly suppressed through coupling with a complementary oscillating mode of a defect of the surrounding phononic crystal (PnC). Applied to an optomechanically coupled nanobeam resonator in the megahertz regime, we find a mechanical quality factor improvement of up to four orders of magnitude compared to conventional PnC designs. As this method is based on geometrical optimization of the PnC and frequency matching of the resonator and defect mode, it is applicable to a wide range of resonator types and frequency ranges. Taking advantage of the, hereinafter referred to as, "regenerative coupling" in phononic crystals, the presented device is capable of reaching f × Q products exceeding 10E16 Hz with only two rows of PnC shield. Thus, stable quantum states with mechanical decoherence times up to 700 μs at room temperature can be obtained, offering new opportunities for the optimization of mechanical resonator performance and advancing the room temperature quantum field across diverse applications.

Enhanced nonlinear optomechanics in a coupled-mode photonic crystal device

The nonlinear component of the optomechanical interaction between light and mechanical vibration promises many exciting classical and quantum mechanical applications, but is generally weak. Here we demonstrate enhancement of nonlinear optomechanical measurement of mechanical motion by using pairs of coupled optical and mechanical modes in a photonic crystal device. In the same device we show linear optomechanical measurement with a strongly reduced input power and reveal how both enhancements are related. Our design exploits anisotropic mechanical elasticity to create strong coupling between mechanical modes while not changing optical properties. Additional thermo-optic tuning of the optical modes is performed with an auxiliary laser and a thermally-optimised device design. We envision broad use of this enhancement scheme in multimode phonon lasing, two-phonon heralding and eventually nonlinear quantum optomechanics.

Partitioned gradient-index phononic crystals for full phase control

Gradient-index phononic crystals (GRIN-PC), characterized by layers with spatially changing refractive indices, have recently been investigated as part of the effort to realize flat lenses in acoustic and elastic regimes. Such gradient-index lens must be inversely designed from the corresponding refractive indices in order to manipulate the target wave. Unfortunately, estimating the index of this type of lens is not straightforward and requires substantial iterative computation in general, which greatly limits the applicability of GRIN-PC to flat lenses. In this work, we propose a novel design of a GRIN-PC in which neighboring layers are separated by partitions, thus preventing waves in each layer from interacting with other layers. This partitioned GRIN-PC design enables us readily to control the phase gradient accurately at the lens' end, resulting in direct calculation of indices for target wave manipulation. A detailed methodology for partitioned GRIN-PC based collimator and Bessel-beam generator is proposed and experimentally validated to confirm the versatile use of our design in wave engineering applications.

Efficient anchor loss suppression in coupled near-field optomechanical resonators

Elastic dissipation through radiation towards the substrate is a major loss channel in micro- and nanomechanical resonators. Engineering the coupling of these resonators with optical cavities further complicates and constrains the design of low-loss optomechanical devices. In this work we rely on the coherent cancellation of mechanical radiation to demonstrate material and surface absorption limited silicon near-field optomechanical resonators oscillating at tens of MHz. The effectiveness of our dissipation suppression scheme is investigated at room and cryogenic temperatures. While at room temperature we can reach a maximum quality factor of 7.61k (fQ-product of the order of 10¹¹ Hz), at 22 K the quality factor increases to 37k, resulting in a fQ-product of 2 × 10¹² Hz.

Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution

The small mass and high coherence of nanomechanical resonators render them the ultimate mechanical probe, with applications that range from protein mass spectrometry and magnetic resonance force microscopy to quantum optomechanics. A notorious challenge in these experiments is the thermomechanical noise related to the dissipation through internal or external loss channels. Here we introduce a novel approach to define the nanomechanical modes, which simultaneously provides a strong spatial confinement, full isolation from the substrate and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localizes the mode but does not impose the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables a mechanical Q > 108 at 1 MHz to yield the highest mechanical Qf products (>1014 Hz) yet reported at room temperature.The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 K predicts quanta per milliseconds heating rates, similar to those of trapped ions.

Ultrahigh-Q optomechanical crystal cavities fabricated in a CMOS foundry

Photonic crystals use periodic structures to create frequency regions where the optical wave propagation is forbidden, which allows the creation and integration of complex optical functionalities in small footprint devices. Such strategy has also been successfully applied to confine mechanical waves and to explore their interaction with light in the so-called optomechanical cavities. Because of their challenging design, these cavities are traditionally fabricated using dedicated high-resolution electron-beam lithography tools that are inherently slow, limiting this solution to small-scale or research applications. Here we show how to overcome this problem by using a deep-UV photolithography process to fabricate optomechanical crystals in a commercial CMOS foundry. We show that a careful design of the photonic crystals can withstand the limitations of the photolithography process, producing cavities with measured intrinsic optical quality factors as high as Q_i = (1.21 ± 0.02) × 10⁶. Optomechanical crystals are also created using phononic crystals to tightly confine the GHz sound waves within the optical cavity, resulting in a measured vacuum optomechanical coupling rate of g₀ = 2π × (91 ± 4) kHz. Efficient sideband cooling and amplification are also demonstrated since these cavities are in the resolved sideband regime. Further improvements in the design and fabrication process suggest that commercial foundry-based optomechanical cavities could be used for quantum ground-state cooling.

High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs

Light scattering by a two-dimensional photonic-crystal slab (PCS) can result in marked interference effects associated with Fano resonances. Such devices offer appealing alternatives to distributed Bragg reflectors and filters for various applications, such as optical wavelength and polarization filters, reflectors, semiconductor lasers, photodetectors, bio-sensors and non-linear optical components. Suspended PCS also have natural applications in the field of optomechanics, where the mechanical modes of a suspended slab interact via radiation pressure with the optical field of a high-finesse cavity. The reflectivity and transmission properties of a defect-free suspended PCS around normal incidence can be used to couple out-of-plane mechanical modes to an optical field by integrating it in a free-space cavity. Here we demonstrate the successful implementation of a PCS reflector on a high-tensile stress Si₃N₄ nanomembrane. We illustrate the physical process underlying the high reflectivity by measuring the photonic-crystal band diagram. Moreover, we introduce a clear theoretical description of the membrane scattering properties in the presence of optical losses. By embedding the PCS inside a high-finesse cavity, we fully characterize its optical properties. The spectrally, angular- and polarization-resolved measurements demonstrate the wide tunability of the membrane's reflectivity, from nearly 0 to 99.9470±0.0025%, and show that material absorption is not the main source of optical loss. Moreover, the cavity storage time demonstrated in this work exceeds the mechanical period of low-order mechanical drum modes. This so-called resolved-sideband condition is a prerequisite to achieve quantum control of the mechanical resonator with light.

Optomechanical oscillator pumped and probed by optically two isolated photonic crystal cavity systems

Optomechanical control of on-chip emitters is an important topic related to integrated all-optical circuits. However, there is neither a realization nor a suitable optomechanical structure for this control. The biggest obstacle is that the emission signal can hardly be distinguished from the pump light because of the several orders' power difference. In this study, we designed and experimentally verified an optomechanical oscillation system, in which a lumped mechanical oscillator connected two optically isolated pairs of coupled one-dimensional photonic crystal cavities. As a functional device, the two pairs of coupled cavities were respectively used as an optomechanical pump for the lumped oscillator (cavity pair II, wavelengths were designed to be within a 1.5 μm band) and a modulation target of the lumped oscillator (cavity pair I, wavelengths were designed to be within a 1.2 μm band). By conducting finite element method simulations, we found that the lumped-oscillator-supported configurations of both cavity pairs enhance the optomechanical interactions, especially for higher order optical modes, compared with their respective conventional side-clamped configurations. Besides the desired first-order in-plane antiphase mechanical mode, other mechanical modes of the lumped oscillator were investigated and found to possibly have optomechanical applications with a versatile degree of freedom. In experiments, the oscillator's RF spectra were probed using both cavity pairs I and II, and the results matched those of the simulations. Dynamic detuning of the optical spectrum of cavity pair I was then implemented with a pumped lumped oscillator. This was the first demonstration of an optomechanical lumped oscillator connecting two optically isolated pairs of coupled cavities, whose biggest advantage is that one cavity pair can be modulated with an lumped oscillator without interference from the pump light in the other cavity pair. Thus, the oscillator is a suitable platform for optomechanical control of integrated lasers, cavity quantum electrodynamics, and spontaneous emission. Furthermore, this device may open the door on the study of interactions between photons, phonons, and excitons in the quantum regime.

Strong optomechanical coupling in a slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio

We describe the design, fabrication, and characterization of a one-dimensional silicon photonic crystal cavity in which a central slot is used to enhance the overlap between highly localized optical and mechanical modes. The optical mode has an extremely small mode volume of 0.017(λ_vac / n)³, and an optomechanical vacuum coupling rate of 310 kHz is measured for a mechanical mode at 2.69 GHz. With optical quality factors up to 1.2 × 10⁵, fabricated devices are in the resolved-sideband regime. The electric field has its maximum at the slot wall and couples to the in-plane breathing motion of the slot. The optomechanical coupling is thus dominated by the moving-boundary effect, which we simulate to be six times greater than the photoelastic effect, in contrast to most structures, where the photoelastic effect is often the primary coupling mechanism.

Nonlinear Radiation Pressure Dynamics in an Optomechanical Crystal

Utilizing a silicon nanobeam optomechanical crystal, we investigate the attractor diagram arising from the radiation pressure interaction between a localized optical cavity at λ_{c}=1542  nm and a mechanical resonance at ω_{m}/2π=3.72  GHz. At a temperature of T_{b}≈10  K, highly nonlinear driving of mechanical motion is observed via continuous wave optical pumping. Introduction of a time-dependent (modulated) optical pump is used to steer the system towards an otherwise inaccessible dynamically stable attractor in which mechanical self-oscillation occurs for an optical pump red detuned from the cavity resonance. An analytical model incorporating thermo-optic effects due to optical absorption heating is developed and found to accurately predict the measured device behavior.

Remote sensing in hybridized arrays of nanostrings

We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas isolated individual resonators exhibit sinusoidal vibrational modes with an almost perfectly harmonic spectrum, the modes of the interacting strings are substantially hybridized. Even far-separated strings can show significantly correlated displacement. This remote coupling property is exploited to quantify the deposition of femtogram-scale masses with string-by-string positional discrimination based on measurements of one string only.

Two-dimensional phononic-photonic band gap optomechanical crystal cavity

We present the fabrication and characterization of an artificial crystal structure formed from a thin film of silicon that has a full phononic band gap for microwave X-band phonons and a two-dimensional pseudo-band gap for near-infrared photons. An engineered defect in the crystal structure is used to localize optical and mechanical resonances in the band gap of the planar crystal. Two-tone optical spectroscopy is used to characterize the cavity system, showing a large coupling (g0/2π≈220  kHz) between the fundamental optical cavity resonance at ωo/2π=195  THz and colocalized mechanical resonances at frequency ωm/2π≈9.3  GHz.

Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics

Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane's silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane's frame so that it assumes the form of a cm-sized bridge featuring a 1-dimensional periodic pattern, whose phononic density of states is tailored to exhibit one, or several, full band gaps around the membrane's high-Q modes in the MHz-range. We quantify the effectiveness of this phononic bandgap shield by optical interferometry measuring both the suppressed transmission of vibrations, as well as the influence of frame clamping conditions on the membrane modes. We find suppressions up to 40 dB and, for three different realized phononic structures, consistently observe significant suppression of the dependence of the membrane's modes on sample clamping-if the mode's frequency lies in the bandgap. As a result, we achieve membrane mode quality factors of 5 × 10(6) with samples that are tightly bolted to the 8 K-cold finger of a cryostat. Q × f -products of 6 × 10(12) Hz at 300 K and 14 × 10(12) Hz at 8 K are observed, satisfying one of the main requirements for optical cooling of mechanical vibrations to their quantum ground-state.

Mode control and mode conversion in nonlinear aluminum nitride waveguides

While single-mode waveguides are commonly used in integrated photonic circuits, emerging applications in nonlinear and quantum optics rely fundamentally on interactions between modes of different order. Here we propose several methods to evaluate the modal composition of both externally and device-internally excited guided waves and discuss a technique for efficient excitation of arbitrary modes. The applicability of these methods is verified in photonic circuits based on aluminum nitride. We control modal excitation through suitably engineered grating couplers and are able to perform a detailed study of waveguide-internal second harmonic generation. Efficient and broadband power conversion between orthogonal polarizations is realized within an asymmetric directional coupler to demonstrate selective excitation of arbitrary higher-order modes. Our approach holds promise for applications in nonlinear optics and frequency up/down-mixing in a chipscale framework.

Cooling by heating: very hot thermal light can significantly cool quantum systems

We introduce the idea of actually cooling quantum systems by means of incoherent thermal light, hence giving rise to a counterintuitive mechanism of "cooling by heating." In this effect, the mere incoherent occupation of a quantum mechanical mode serves as a trigger to enhance the coupling between other modes. This notion of effectively rendering states more coherent by driving with incoherent thermal quantum noise is applied here to the optomechanical setting, where this effect occurs most naturally. We discuss two ways of describing this situation, one of them making use of stochastic sampling of gaussian quantum states with respect to stationary classical stochastic processes. The potential of experimentally demonstrating this counterintuitive effect in optomechanical systems with present technology is sketched.

Laser cooling of a nanomechanical oscillator into its quantum ground state

The simple mechanical oscillator, canonically consisting of a coupled mass-spring system, is used in a wide variety of sensitive measurements, including the detection of weak forces and small masses. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion. On the macroscopic scale of our everyday experience, owing to interactions with its highly fluctuating thermal environment a mechanical oscillator is filled with many energy quanta and its quantum nature is all but hidden. Recently, in experiments performed at temperatures of a few hundredths of a kelvin, engineered nanomechanical resonators coupled to electrical circuits have been measured to be oscillating in their quantum ground state. These experiments, in addition to providing a glimpse into the underlying quantum behaviour of mesoscopic systems consisting of billions of atoms, represent the initial steps towards the use of mechanical devices as tools for quantum metrology or as a means of coupling hybrid quantum systems. Here we report the development of a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip, in which radiation pressure from a laser is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of 0.85 ± 0.08). This cooling is realized at an environmental temperature of 20 K, roughly one thousand times larger than in previous experiments and paves the way for optical control of mesoscale mechanical oscillators in the quantum regime.

An Introduction to Quantum Optomechanics

We provide an introduction to the description of mechanical systems in the quantum regime, and provide a review of the various types of micro-scale and nano-scale optomechanical and electromechanical systems. The aim is to achieve quantum control of micromechanical and nanomechanical resonators using the electromagnetic field. Such control requires the demonstration of state preparation (in particular, cooling to the ground state), coherent control and quantum-limited measurement. These problems are discussed in turn. Some particular problems in force detection, metrology, nonlinear optomechanics and many-body optomechanics are also discussed.