Resolved-sideband cooling and measurement of a micromechanical oscillator close to the quantum limit

The observation of quantum phenomena in macroscopic mechanical oscillators has been a subject of interest since the inception of quantum mechanics. Prerequisite to this regime are both preparation of the mechanical oscillator at low phonon occupancy and a measurement sensitivity at the scale of the spread of the oscillator's ground state wavefunction. It has been widely perceived that the most promising approach to address these two challenges are electro nanomechanical systems. Here we approach for the first time the quantum regime with a mechanical oscillator of mesoscopic dimensions--discernible to the bare eye--and 1000-times more massive than the heaviest nano-mechanical oscillators used to date. Imperative to these advances are two key principles of cavity optomechanics: Optical interferometric measurement of mechanical displacement at the attometer level, and the ability to use measurement induced dynamic back-action to achieve resolved sideband laser cooling of the mechanical degree of freedom. Using only modest cryogenic pre-cooling to 1.65 K, preparation of a mechanical oscillator close to its quantum ground state (63+-20 phonons) is demonstrated. Simultaneously, a readout sensitivity that is within a factor of 5.5+-1.5 of the standard quantum limit is achieved. The reported experiments mark a paradigm shift in the approach to the quantum limit of mechanical oscillators using optical techniques and represent a first step into a new era of experimental investigation which probes the quantum nature of the most tangible harmonic oscillator: a mechanical vibration.Comment: 14 pages, 4 figure

Novel Cavity Optomechanical Systems at the Micro- and Nanoscale and Quantum Measurements of Nanomechanical Oscillators

This thesis reports on coupling optical microresonators to micro- and nanomechanical oscillators. The mutual optomechanical coupling based on radiation pressure between the microcavity and a mechanical degree of freedom modulating its spatial structure thereby allows both transduction and actuation of the motion of the mechanical degree of freedom by the light field launched into the microcavity. The first part of the thesis reports on a novel experimental approach based on cavity enhanced evanescent near-fields of toroid microresonators. It enables the extension of dispersive cavity optomechanical coupling to sub-wavelength scale nanomechanical oscillators which are at the heart of a variety of precision measurements. The optomechanical coupling present in the developed system is carefully analyzed experimentally and good agreement with theoretical expectations is found. The demonstrated platform allows transduction of nanomechanical motion with an exceptionally high sensitivity, outperforming the previous state-of-the-art transducers. Thereby, for the first time a measurement imprecision lower than the level of the standard quantum limit is achieved. In the present measurements, quantum backaction should already be the dominating contribution to the measurement sensitivity which is however masked by thermal noise. This may pave the way to the first experimental demonstration of radiation pressure quantum backaction on a solid-state mechanical oscillator. Moreover, the radiation pressure interaction between evanescent cavity field and nanomechanical oscillator is shown to enable actuating and controlling the motional state of the oscillator. Both amplification, leading to self-sustained mechanical oscillations, and cooling by radiation pressure dynamical backaction is reported. In addition, the capability of the near-field platform to implement resonant interaction of a mechanical mode with two optical modes is shown as well as the feasibility of quadratic coupling to the nanomechanical oscillators. In the second part of the thesis monolithic on-chip resonators that combine ultra-low optical and mechanical dissipation are designed. To this end, the intrinsic mechanical modes of toroid microresonators are analyzed in detail. High-sensitivity measurements enable the observation of a plethora of mechanical modes and good agreement with finite element modelling is found. In particular the dissipation mechanisms limiting their mechanical quality are studied. Clamping losses are identified as the dominant loss mechanism at room temperature. Using a novel geometric design, these are systematically minimized which leads to spoke-supported microresonators with intrinsic material-loss limited mechanical quality factors rivalling the best published values at similar frequencies

High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators

The inherent coupling of optical and mechanical modes in high finesse optical microresonators provide a natural, highly sensitive transduction mechanism for micromechanical vibrations. Using homodyne and polarization spectroscopy techniques, we achieve shot-noise limited displacement sensitivities of 10^(-19) m Hz^(-1/2). In an unprecedented manner, this enables the detection and study of a variety of mechanical modes, which are identified as radial breathing, flexural and torsional modes using 3-dimensional finite element modelling. Furthermore, a broadband equivalent displacement noise is measured and found to agree well with models for thermorefractive noise in silica dielectric cavities. Implications for ground-state cooling, displacement sensing and Kerr squeezing are discussed.Comment: 25 pages, 8 figure

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 \vcr 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.Comment: 11 pages, 2 figure

From Cavity Electromechanics to Cavity Optomechanics

We present an overview of experimental work to embed high-Q mesoscopic mechanical oscillators in microwave and optical cavities. Based upon recent progress, the prospect for a broad field of "cavity quantum mechanics" is very real. These systems introduce mesoscopic mechanical oscillators as a new quantum resource and also inherently couple their motion to photons throughout the electromagnetic spectrum.Comment: 8 pages, 6 figures, ICAP proceedings submissio

Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain

We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral formula which applies for arbitrary states of the system with a smooth distribution of Bethe roots, including the ground state and finite temperature Gibbs-states. In the cases K<=4 we perform the explicit factorization of the multiple integral. In the case of K=3 we obtain the recent result of Kormos et.al., whereas our formula for K=4 is new. Numerical results are presented as well.Comment: 23 pages, 2 figures, v2: minor modifications and references adde

Cryogenic properties of optomechanical silica microcavities

We present the optical and mechanical properties of high-Q fused silica microtoroidal resonators at cryogenic temperatures (down to 1.6 K). A thermally induced optical multistability is observed and theoretically described; it serves to characterize quantitatively the static heating induced by light absorption. Moreover the influence of structural defect states in glass on the toroid mechanical properties is observed and the resulting implications of cavity optomechanical systems on the study of mechanical dissipation discussed.Comment: 4 pages, 3 figure

Measuring nanomechanical motion with an imprecision far below the standard quantum limit

We demonstrate a transducer of nanomechanical motion based on cavity enhanced optical near-fields capable of achieving a shot-noise limited imprecision more than 10 dB below the standard quantum limit (SQL). Residual background due to fundamental thermodynamical frequency fluctuations allows a total imprecision 3 dB below the SQL at room temperature (corresponding to 600 am/Hz^(1/2) in absolute units) and is known to reduce to negligible values for moderate cryogenic temperatures. The transducer operates deeply in the quantum backaction dominated regime, prerequisite for exploring quantum backaction, measurement-induced squeezing and accessing sub-SQL sensitivity using backaction evading techniques

On optical forces in spherical whispering gallery mode resonators

In this paper we discuss the force exerted by the field of an optical cavity on a polarizable dipole. We show that the modification of the cavity modes due to interaction with the dipole significantly alters the properties of the force. In particular, all components of the force are found to be non-conservative, and cannot, therefore, be derived from a potential energy. We also suggest a simple generalization of the standard formulas for the optical force on the dipole, which reproduces the results of calculations based on the Maxwell stress tensor.Comment: To pe published in Optics Express Focus Issue: "Collective phenomena in photonic, plasmonic and hybrid structures