A General Approach to Optomechanical Parametric Instabilities

We present a simple feedback description of parametric instabilities which can be applied to a variety of optical systems. Parametric instabilities are of particular interest to the field of gravitational-wave interferometry where high mechanical quality factors and a large amount of stored optical power have the potential for instability. In our use of Advanced LIGO as an example application, we find that parametric instabilities, if left unaddressed, present a potential threat to the stability of high-power operation

Design of microresonators to minimize thermal noise below the standard quantum limit

Microfabricated resonators play a crucial role in the development of quantum measurement, including future gravitational wave detectors. We use a micro-genetic algorithm and a finite element method to design a microresonator whose geometry is optimized to maximize the sub-Standard Quantum Limit (SQL) performance including lower thermal noise (TN) below the SQL, a broader sub-SQL region, and a sub-SQL region at lower frequencies. For the proposed design, we study the effects of different geometries of the mirror pad and cantilever microresonator on sub-SQL performance. We find that the maximum ratio of SQL to TN is increased, its frequency is decreased, and the sub-SQL range is increased by increasing the length of the microresonator cantilever, increasing the radius of the mirror pad, decreasing the width of the microresonator cantilever, and shifting the laser beam location from the mirror center. We also find that there exists a trade-off between the maximum ratio of SQL to TN and the sub-SQL bandwidth. The performance of this designed microresonator will allow it to serve as a test-bed for quantum non-demolition measurements and to open new regimes of precision measurement that are relevant for many practical sensing applications, including advanced gravitational wave detectors

Optical cavities as amplitude filters for squeezed fields

We explore the use of Fabry-P\'erot cavities as high-pass filters for squeezed light, and show that they can increase the sensitivity of interferometric gravitational-wave detectors without the need for long (kilometer scale) filter cavities. We derive the parameters for the filters, and analyze the performance of several possible cavity configurations in the context of a future gravitational-wave interferometer with squeezed light (vacuum) injected into the output port.Comment: 9 pages, 6 figure

A picogram and nanometer scale photonic crystal opto-mechanical cavity

We describe the design, fabrication, and measurement of a cavity opto-mechanical system consisting of two nanobeams of silicon nitride in the near-field of each other, forming a so-called "zipper" cavity. A photonic crystal patterning is applied to the nanobeams to localize optical and mechanical energy to the same cubic-micron-scale volume. The picrogram-scale mass of the structure, along with the strong per-photon optical gradient force, results in a giant optical spring effect. In addition, a novel damping regime is explored in which the small heat capacity of the zipper cavity results in blue-detuned opto-mechanical damping.Comment: 15 pages, 4 figure

A microchip optomechanical accelerometer

The monitoring of accelerations is essential for a variety of applications ranging from inertial navigation to consumer electronics. The basic operation principle of an accelerometer is to measure the displacement of a flexibly mounted test mass; sensitive displacement measurement can be realized using capacitive, piezo-electric, tunnel-current, or optical methods. While optical readout provides superior displacement resolution and resilience to electromagnetic interference, current optical accelerometers either do not allow for chip-scale integration or require bulky test masses. Here we demonstrate an optomechanical accelerometer that employs ultra-sensitive all-optical displacement read-out using a planar photonic crystal cavity monolithically integrated with a nano-tethered test mass of high mechanical Q-factor. This device architecture allows for full on-chip integration and achieves a broadband acceleration resolution of 10 \mu g/rt-Hz, a bandwidth greater than 20 kHz, and a dynamic range of 50 dB with sub-milliwatt optical power requirements. Moreover, the nano-gram test masses used here allow for optomechanical back-action in the form of cooling or the optical spring effect, setting the stage for a new class of motional sensors.Comment: 16 pages, 9 figure

Dynamical Coupling between a Bose-Einstein Condensate and a Cavity Optical Lattice

A Bose-Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe bistability already below the single photon level and strong back-action dynamics which tunes the system periodically out of resonance.Comment: 5 pages, 4 figure

Resolved Sideband Cooling of a Micromechanical Oscillator

Micro- and nanoscale opto-mechanical systems provide radiation pressure coupling of optical and mechanical degree of freedom and are actively pursued for their ability to explore quantum mechanical phenomena of macroscopic objects. Many of these investigations require preparation of the mechanical system in or close to its quantum ground state. Remarkable progress in ground state cooling has been achieved for trapped ions and atoms confined in optical lattices. Imperative to this progress has been the technique of resolved sideband cooling, which allows overcoming the inherent temperature limit of Doppler cooling and necessitates a harmonic trapping frequency which exceeds the atomic species' transition rate. The recent advent of cavity back-action cooling of mechanical oscillators by radiation pressure has followed a similar path with Doppler-type cooling being demonstrated, but lacking inherently the ability to attain ground state cooling as recently predicted. Here we demonstrate for the first time resolved sideband cooling of a mechanical oscillator. By pumping the first lower sideband of an optical microcavity, whose decay rate is more than twenty times smaller than the eigen-frequency of the associated mechanical oscillator, cooling rates above 1.5 MHz are attained. Direct spectroscopy of the motional sidebands reveals 40-fold suppression of motional increasing processes, which could enable reaching phonon occupancies well below unity (<0.03). Elemental demonstration of resolved sideband cooling as reported here should find widespread use in opto-mechanical cooling experiments. Apart from ground state cooling, this regime allows realization of motion measurement with an accuracy exceeding the standard quantum limit.Comment: 13 pages, 5 figure