Vacuum Optomechanical Coupling Rate Research Articles

Optomechanics with one-dimensional gallium phosphide photonic crystal cavities

Gallium phosphide offers an attractive combination of a high refractive index ($n>3$ for vacuum wavelengths up to 4 {\mu}m) and a wide electronic bandgap (2.26 eV), enabling optical cavities with small mode volumes and low two-photon absorption at telecommunication wavelengths. Heating due to strongly confined light fields is therefore greatly reduced. Here, we investigate the benefits of these properties for cavity optomechanics. Utilizing a recently developed fabrication scheme based on direct wafer bonding, we realize integrated one-dimensional photonic crystal cavities made of gallium phosphide with optical quality factors as high as $1.1\times10^5$. We optimize their design to couple the optical eigenmode at $\approx 200$ THz via radiation pressure to a co-localized mechanical mode with a frequency of 3 GHz, yielding sideband-resolved devices. The high vacuum optomechanical coupling rate ($g_0=2\pi\times 400$ kHz) permits amplification of the mechanical mode into the so-called mechanical lasing regime with input power as low as $\approx 20$ {\mu}W. The observation of mechanical lasing implies a multiphoton cooperativity of $C>1$, an important threshold for the realization of quantum state transfer protocols. Because of the reduced thermo-optic resonance shift, optomechanically induced transparency can be detected at room temperature in addition to the normally observed optomechanically induced absorption.

Anderson Photon-Phonon Colocalization in Certain Random Superlattices.

Fundamental observations in physics ranging from gravitational wave detection to laser cooling of a nanomechanical oscillator into its quantum ground state rely on the interaction between the optical and the mechanical degrees of freedom. A key parameter to engineer this interaction is the spatial overlap between the two fields, optimized in carefully designed resonators on a case-by-case basis. Disorder is an alternative strategy to confine light and sound at the nanoscale. However, it lacks an apriori mechanism guaranteeing a high degree of colocalization due to the inherently complex nature of the underlying interference processes. Here, we propose a way to address this challenge by using GaAs/AlAs vertical distributed Bragg reflectors with embedded geometrical disorder. Because of a remarkable coincidence in the physical parameters governing light and motion propagation in these two materials, the equations for both longitudinal acoustic waves and normal-incidence light become practically equivalent for excitations of the same wavelength. This guarantees spatial overlap between the electromagnetic and displacement fields of specific photon-phonon pairs, leading to strong light-matter interaction. In particular, a statistical enhancement in the vacuum optomechanical coupling rate, g_{o}, is found, making this system a promising candidate to explore Anderson localization of high frequency (∼20 GHz) phonons enabled by cavity optomechanics. The colocalization effect shown here unlocks the access to unexplored localization phenomena and the engineering of light-matter interactions mediated by Anderson-localized states.

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 Qi = (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.

Molecular cavity optomechanics as a theory of plasmon-enhanced Raman scattering

The exceptional enhancement of Raman scattering by localized plasmonic resonances in the near field of metallic nanoparticles, surfaces or tips (SERS, TERS) has enabled spectroscopic fingerprinting down to the single molecule level. The conventional explanation attributes the enhancement to the subwavelength confinement of the electromagnetic field near nanoantennas. Here, we introduce a new model that also accounts for the dynamical nature of the plasmon-molecule interaction. We thereby reveal an enhancement mechanism not considered before: dynamical backaction amplification of molecular vibrations. We first map the system onto the canonical Hamiltonian of cavity optomechanics, in which the molecular vibration and the plasmon are parametrically coupled. We express the vacuum optomechanical coupling rate for individual molecules in plasmonic 'hot-spots' in terms of the vibrational mode's Raman activity and find it to be orders of magnitude larger than for microfabricated optomechanical systems. Remarkably, the frequency of commonly studied molecular vibrations can be comparable to or larger than the plasmon's decay rate. Together, these considerations predict that an excitation laser blue-detuned from the plasmon resonance can parametrically amplify the molecular vibration, leading to a nonlinear enhancement of Raman emission that is not predicted by the conventional theory. Our optomechanical approach recovers known results, provides a quantitative framework for the calculation of cross-sections, and enables the design of novel systems that leverage dynamical backaction to achieve additional, mode-selective enhancements. It also provides a quantum mechanical framework to analyse plasmon-vibrational interactions in terms of molecular quantum optomechanics.

Design of a femtogram scale double-slot photonic crystal optomechanical cavity.

We present the design of a double-slot photonic crystal cavity as an optomechanical device which contains a nanomechanical resonator with an effective mass as small as 6.91 fg. The optical Q-factor is optimized to 2 × 10(5). Using phononic crystals, the mechanical vibration is confined in a small volume to form a mechanical mode of 4 GHz with a high mechanical Q-factor and a femtogram effective mass. The localized mechanical mode overlaps with the optical field and strengthens the optomechanical coupling with a vacuum optomechanical coupling rate g0/2π exceeding 600 kHz. Considering fabrication imperfections, structures with deviation from ideal design are studied. The symmetry breakage of the structures and the displacement fields makes the mechanical effective masses reduced and close to 4 fg. The devices can be used in ultrasensitive sensing of mass, force and displacement.

Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison

We present the design and experimental comparison of femtogram L3-nanobeam photonic crystal cavities for optomechanical studies. Two symmetric nanobeams are created by placing three air slots in a silicon photonic crystal slab where three holes are removed. The nanobeams' mechanical frequencies are higher than 600 MHz with ultrasmall effective modal masses at approximately 20 femtograms. The optical quality factor (Q) is optimized up to 53,000. The optical and mechanical modes are dispersively coupled with a vacuum optomechanical coupling rate g(0)/2π exceeding 200 kHz. The anchor-loss-limited mechanical Q of the differential beam mode is evaluated to be greater than 10,000 for structures with ideally symmetric beams. The influence of variations on the air slot width and position is also investigated. The devices can be used as ultrasensitive sensors of mass, force, and displacement.

Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities

We experimentally demonstrate an optomechanical cavity based on an air-slot photonic crystal cavity with optical quality factor Qo = 4.2 × 104 and a small modal volume of 0.05 cubic wavelengths. The optical mode is coupled with the in-plane mechanical modes with frequencies up to hundreds of MHz. The fundamental mechanical mode shows a frequency of 65 MHz and a mechanical quality factor of 376. The optical spring effect, optical damping, and amplification are observed with a large experimental optomechanical coupling rate gom/2π of 154 GHz/nm, corresponding to a vacuum optomechanical coupling rate g*/2π of 707 kHz. With sub-mW or less input power levels, the cavity exhibits strong parametric oscillations. The phase noise of the photonic crystal optomechanical oscillator is also measured.

Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling

Nanomechanical oscillators are at the heart of a variety of precision measurements. This article reports on dispersive radiation coupling of nanomechanical oscillators to the evanescent near-field of toroid optical microresonators. The optomechanical coupling coefficient which reaches values > 200 MHz/nm, corresponding to a vacuum optomechanical coupling rate > 4 kHz, is characterized in detail and good agreement between experimental, analytical and finite element simulation based values is found. It is shown that both the mode-structure and -patterns of nanomechanical oscillators can be characterized relying solely on Brownian motion. Moreover, it is demonstrated that the radiation pressure interaction can cause self-sustained coherent nanomechanical oscillations at nano-Watt power levels as well as cooling of the nanomechanical oscillator. Finally, the feasibility of coupling nanomechanical motion to two optical modes where the optical mode spacing exactly equals the mechanical resonance frequency is demonstrated for the first time. As shown here, this Raman-type scheme allows both amplification and cooling. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Wavelength-sized GaAs optomechanical resonators with gigahertz frequency

We report on wavelength-sized GaAs optomechanical disk resonators showing ultrastrong optomechanical interaction. We observe optical transduction of a disk mechanical breathing mode with 1.4 GHz frequency and effective mass of ∼2 pg. The measured vacuum optomechanical coupling rate reaches g0=0.8 MHz, with a related differential optomechanical coupling factor gom=485 GHz/nm. The disk Brownian motion is optically resolved with a sensitivity of 10−17 m/√Hz at room temperature and pressure.

Determination of the vacuum optomechanical coupling rate using frequency noise calibration

The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate g0 analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe field and knowledge of the mechanical oscillator's occupation. The method is experimentally verified for a micromechanical mode in a toroidal whispering-gallery-resonator and a nanomechanical oscillator coupled to a toroidal cavity via its near field.