Optical phase-space reconstruction of mirror position at the attometer level

We describe an experiment in which the quadratures of the position of an harmonically-bound mirror are observed at the attometer level. We have studied the Brownian motion of the mirror, both in the free regime and in the cold-damped regime when an external viscous force is applied by radiation pressure. We have also studied the thermal-noise squeezing when the external force is parametrically modulated. We have observed both the 50% theoretical limit of squeezing at low gain and the parametric oscillation of the mirror for a large gain.Comment: 10 pages, 11 figure

Nonlinear mechanics with photonic crystal nanomembranes

Optomechanical systems close to their quantum ground state and nonlinear nanoelectromechanical systems are two hot topics of current physics research. As high-reflectivity and low mass are crucial features to improve optomechanical coupling towards the ground state, we have designed, fabricated and characterized photonic crystal nanomembranes, at the crossroad of both topics. Here we demonstrate a number of nonlinear effects with these membranes. We first characterize the nonlinear behavior of a single mechanical mode and we demonstrate its nonlocal character by monitoring the subsequent actuation-related frequency shift of a different mode. We then proceed to study the underlying nonlinear dynamics, both by monitoring the phase-space trajectory of the free resonator and by characterizing the mechanical response in presence of a strong pump excitation. We observe in particular the frequency evolution during a ring-down oscillation decay, and the emergence of a phase conjugate mechanical response to a weaker probe actuation. Our results are crucial to understand the full nonlinear features of the PhC membranes, and possibly to look for nonlinear signatures of the quantum dynamics

Probing optomechanical correlations between two optical beams down to the quantum level

Quantum effects of radiation pressure are expected to limit the sensitivity of second-generation gravitational-wave interferometers. Though ubiquitous, such effects are so weak that they haven't been experimentally demonstrated yet. Using a high-finesse optical cavity and a classical intensity noise, we have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be extended down to the quantum level and has applications both in high-sensitivity measurements and in quantum optics

Scheme for teleportation of quantum states onto a mechanical resonator

We propose an experimentally feasible scheme to teleport an unkown quantum state onto the vibrational degree of freedom of a macroscopic mirror. The quantum channel between the two parties is established by exploiting radiation pressure effects.Comment: 5 pages, 2 figures, in press on PR

A micropillar for cavity optomechanics

We present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillar geometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high quality factor. We have coated a 60-$\mu$m diameter low-loss dielectric mirror on top of the pillar and are planning to use this micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantum ground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry

2D photonic-crystal optomechanical nanoresonator

We present the optical optimization of an optomechanical device based on a suspended InP membrane patterned with a 2D near-wavelength grating (NWG) based on a 2D photonic-crystal geometry. We first identify by numerical simulation a set of geometrical parameters providing a reflectivity higher than 99.8 % over a 50-nm span. We then study the limitations induced by the finite value of the optical waist and lateral size of the NWG pattern using different numerical approaches. The NWG grating, pierced in a suspended InP 265 nm-thick membrane, is used to form a compact microcavity involving the suspended nano-membrane as end mirror. The resulting cavity has a waist size smaller than 10 $\mu$m and a finesse in the 200 range. It is used to probe the Brownian motion of the mechanical modes of the nanomembrane

High-sensitivity optical monitoring of a micro-mechanical resonator with a quantum-limited optomechanical sensor

We experimentally demonstrate the high-sensitivity optical monitoring of a micro-mechanical resonator and its cooling by active control. Coating a low-loss mirror upon the resonator, we have built an optomechanical sensor based on a very high-finesse cavity (30000). We have measured the thermal noise of the resonator with a quantum-limited sensitivity at the 10^-19 m/rootHz level, and cooled the resonator down to 5K by a cold-damping technique. Applications of our setup range from quantum optics experiments to the experimental demonstration of the quantum ground state of a macroscopic mechanical resonator.Comment: 4 pages, 5 figure

Optomechanical characterization of acoustic modes in a mirror

We present an experimental study of the internal mechanical vibration modes of a mirror. We determine the frequency repartition of acoustic resonances via a spectral analysis of the Brownian motion of the mirror, and the spatial profile of the acoustic modes by monitoring their mechanical response to a resonant radiation pressure force swept across the mirror surface. We have applied this technique to mirrors with cylindrical and plano-convex geometries, and compared the experimental results to theoretical predictions. We have in particular observed the gaussian modes predicted for plano-convex mirrors.Comment: 8 pages, 8 figures, RevTe

A filtered multilevel Monte Carlo method for estimating the expectation of discretized random fields

We investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of the numerical simulators have inconsistent dimensions across the multilevel hierarchy. This requires the introduction of grid transfer operators borrowed from multigrid methods. Starting from a simple 1D illustration, we demonstrate numerically that the resulting MLMC estimator deteriorates the estimation of high-frequency components of the discretized expectation field compared to a Monte Carlo (MC) estimator. By adapting mathematical tools initially developed for multigrid methods, we perform a theoretical spectral analysis of the MLMC estimator of the expectation of discretized random fields, in the specific case of linear, symmetric and circulant simulators. This analysis provides a spectral decomposition of the variance into contributions associated with each scale component of the discretized field. We then propose improved MLMC estimators using a filtering mechanism similar to the smoothing process of multigrid methods. The filtering operators improve the estimation of both the small- and large-scale components of the variance, resulting in a reduction of the total variance of the estimator. These improvements are quantified for the specific class of simulators considered in our spectral analysis. The resulting filtered MLMC (F-MLMC) estimator is applied to the problem of estimating the discretized variance field of a diffusion-based covariance operator, which amounts to estimating the expectation of a discretized random field. The numerical experiments support the conclusions of the theoretical analysis even with non-linear simulators, and demonstrate the improvements brought by the proposed F-MLMC estimator compared to both a crude MC and an unfiltered MLMC estimator