Jasper Chan

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 ). 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.

A picogram- and nanometre-scale photonic-crystal optomechanical cavity

The dynamic back-action caused by electromagnetic forces (radiation pressure) in optical and microwave cavities is of growing interest. Back-action cooling, for example, is being pursued as a means of achieving the quantum ground state of macroscopic mechanical oscillators. Work in the optical domain has revolved around millimetre- or micrometre-scale structures using the radiation pressure force. By comparison, in microwave devices, low-loss superconducting structures have been used for gradient-force-mediated coupling to a nanomechanical oscillator of picogram mass. Here we describe measurements of an optical system consisting of a pair of specially patterned nanoscale beams in which optical and mechanical energies are simultaneously localized to a cubic-micron-scale volume, and for which large per-photon optical gradient forces are realized. The resulting scale of the per-photon force and the mass of the structure enable the exploration of cavity optomechanical regimes in which, for example, the mechanical rigidity of the structure is dominantly provided by the internal light field itself. In addition to precision measurement and sensitive force detection, nano-optomechanics may find application in reconfigurable and tunable photonic systems, light-based radio-frequency communication and the generation of giant optical nonlinearities for wavelength conversion and optical buffering.

Electromagnetically induced transparency and slow light with optomechanics

Controlling the interaction between localized optical and mechanical excitations has recently become possible following advances in micro- and nanofabrication techniques. So far, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. Conversely, the optical response of these systems is also modified in the presence of mechanical interactions, leading to effects such as electromagnetically induced transparency (EIT) and parametric normal-mode splitting. In atomic systems, studies of slow and stopped light (applicable to modern optical networks and future quantum networks) have thrust EIT to the forefront of experimental study during the past two decades. Here we demonstrate EIT and tunable optical delays in a nanoscale optomechanical crystal, using the optomechanical nonlinearity to control the velocity of light by way of engineered photon–phonon interactions. Our device is fabricated by simply etching holes into a thin film of silicon. At low temperature (8.7 kelvin), we report an optically tunable delay of 50 nanoseconds with near-unity optical transparency, and superluminal light with a 1.4 microsecond signal advance. These results, while indicating significant progress towards an integrated quantum optomechanical memory, are also relevant to classical signal processing applications. Measurements at room temperature in the analogous regime of electromagnetically induced absorption show the utility of these chip-scale optomechanical systems for optical buffering, amplification, and filtering of microwave-over-optical signals.

Optimized optomechanical crystal cavity with acoustic radiation shield

We present the design of an optomechanical crystal nanobeam cavity that combines finite-element simulation with numerical optimization, and considers the optomechanical coupling arising from both moving dielectric boundaries and the photo-elastic effect. Applying this methodology results in a nanobeam with an experimentally realized intrinsic optical Q-factor of 1.2×10^6, a mechanical frequency of 5.1 GHz, a mechanical Q-factor of 6.8×10^5 (at T = 10 K), and a zero-point-motion optomechanical coupling rate of g = 1.1 MHz.

Optical and mechanical design of a "zipper" photonic crystal optomechanical cavity.

Design of a simple doubly clamped cantilever structure capable of localizing mechanical and optical energy at the nanoscale is presented. The optical design is based upon photonic crystal concepts in which simple nanoscale patterning of a sub-micron cross-section cantilever can result in strong optical localization to an effective optical mode volume of 4 cubic wavelengths in the material (4(λ=n)³). By placing two identical cantilevers within the near field of each other, strong optomechanical coupling can be realized for differential motion between the cantilevers. Current designs for thin film silicon nitride cantilevers indicate that such structures can simultaneously realize an optical Q-factor greater than 10⁶, motional mass m<inf>x</inf> ∼ 5 picograms, mechanical mode frequency Ω<inf>M</inf> ∼100 MHz, and an optomechanical coupling factor (g<inf>OM</inf> ≡ dω=dx = ω<inf>0</inf>/L<inf>OM</inf>) with effective length L<inf>OM</inf> ∼ 1 µm.

Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals.

Periodically structured materials can sustain both optical and mechanical excitations which are tailored by the geometry. Here we analyze the properties of dispersively coupled planar photonic and phononic crystals: optomechanical crystals. In particular, the properties of co-resonant optical and mechanical cavities in quasi-1D (patterned nanobeam) and quasi-2D (patterned membrane) geometries are studied. It is shown that the mechanical Q and optomechanical coupling in these structures can vary by many orders of magnitude with modest changes in geometry. An intuitive picture is developed based upon a perturbation theory for shifting material boundaries that allows the optomechanical properties to be designed and optimized. Several designs are presented with mechanical frequency approximately 1-10 GHz, optical Q-factor Qo > 107, motional masses meff approximately 100 femtograms, optomechanical coupling length LOM < 5 microm, and clampinig losses that are exponentially suppressed with increasing number of phononic crystal periods (radiation-limited mechanical Q-factor Qm > 107 for total device size less than 30 microm).

Slot-mode-coupled optomechanical crystals

We present a design methodology and analysis of a cavity optomechanical system in which a localized GHz frequency mechanical mode of a nanobeam resonator is evanescently coupled to a high quality factor (Q > 10(6)) optical mode of a separate nanobeam optical cavity. Using separate nanobeams provides flexibility, enabling the independent design and optimization of the optics and mechanics of the system. In addition, the small gap (≈ 25 nm) between the two resonators gives rise to a slot mode effect that enables a large zero-point optomechanical coupling strength to be achieved, with g/2 π > 300 kHz in a Si(3)N(4) system at 980 nm and g/2 π ≈ 900 kHz in a Si system at 1550 nm. The fact that large coupling strengths to GHz mechanical oscillators can be achieved in Si(3)N(4) is important, as this material has a broad optical transparency window, which allows operation throughout the visible and near-infrared. As an application of this platform, we consider wide-band optical frequency conversion between 1300 nm and 980 nm, using two optical nanobeam cavities coupled on either side to the breathing mode of a mechanical nanobeam resonator.

Laser noise in cavity-optomechanical cooling and thermometry

We review and study the roles of quantum and classical fluctuations in recent cavity-optomechanical experiments which have now reached the quantum regime (mechanical phonon occupancy ?1) using resolved sideband laser cooling. In particular, both the laser noise heating of the mechanical resonator and the form of the optically transduced mechanical spectra, modified by quantum and classical laser noise squashing, are derived under various measurement conditions. Using this theory, we analyze recent ground-state laser cooling and motional sideband asymmetry experiments with nanoscale optomechanical crystal resonators.

Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity

Optical forces in guided-wave nanostructures have recently been proposed as an effective means of mechanically actuating and tuning optical components. In this work, we study the properties of a photonic crystal optomechanical cavity consisting of a pair of patterned Si3N4 nanobeams. Internal stresses in the stoichiometric Si3N4 thin-film are used to produce inter-beam slot-gaps ranging from 560-40 nm. A general pump-probe measurement scheme is described which determines, self-consistently, the contributions of thermo-mechanical, thermo-optic, and radiation pressure effects. For devices with 40 nm slot-gap, the optical gradient force is measured to be 134 fN per cavity photon for the strongly coupled symmetric cavity supermode, producing a static cavity tuning greater than five times that of either the parasitic thermo-mechanical or thermo-optic effects.

Si 3 N 4 nanobeam optomechanical crystals

We demonstrate sideband-resolved Si₃N₄ optomechanical crystals supporting 10⁵ quality factor optical modes at 980 nm, coupled to GHz frequency mechanical modes. We also develop slot-mode-based geometries for enhanced optomechanical coupling and multimode applications.