Bio-sensing using toroidal microresonators & theoretical cavity optomechanics

In this thesis we report on two matters, (i) time-resolved single particle bio-sensing using a cavity enhanced refractive index sensor with unmatched sensitivity, and (ii) the theoretical analysis of parametric normal mode splitting in cavity optomechanics, as well as the quantum limit of a displacement transducer that relies on multiple cavity modes. It is the unifying element of these studies that they rely on a high-Q optical cavity transducer and amount to a precision measurement of an optical frequency. In the first part, we describe an experiment where a high-Q toroidal microcavity is used as a refractive index sensor for single particle studies. The resonator supports whispering gallery modes (WGM) that feature an evanescent fraction, probing the environment close to the toroid's surface. When a particle with a refractive index, different from its environment, enters the evanescent field of the WGM, the resonance frequency shifts. Here, we monitor the shift with a frequency resolution of df/f=7.7e-11 at a time resolution of 100µs , which constitutes a x10 improvement of the sensitivity and a x100 improvement in time resolution, compared to the state of the art. This unprecedented sensitivity is the key to real-time resolution of single lipid vesicles with 25nm radius adsorbing onto the surface. Moreover -- for the first time within one distinct measurement -- a record number of up to 200 identifiable events was recorded, which provides the foundation for a meaningful statistical analysis. Strikingly, the large number of recorded events and the high precision revealed a disagreement with the theoretical model for the single particle frequency shift. A correction factor that fully accounts for the polarizability of the particle, and thus corrects the deviation, was introduced and establishes a quantitative understanding of the binding events. Directed towards biological application, we introduce an elegant method to cover the resonator surface with a single lipid bilayer, which creates a universal, biomimetic interface for specific functionalization with lipid bound receptors or membrane proteins. Quantitative binding of streptavidin to biotinylated lipids is demonstrated. Moving beyond the detection limit, we provide evidence that the presence of single IgG proteins (that cannot be resolved individually) manifests in the frequency noise spectrum. The theoretical analysis of the thermo-refractive noise floor yields a fundamental limit of the sensors resolution. The second part of the thesis deals with the theoretical analysis of the coupling between an optical cavity mode and a mechanical mode of much lower frequency. Despite the vastly different resonance frequencies, a regime of strong coupling between the mechanics and the light field can be achieved, which manifests as a hybridization of the modes and as a mode splitting in the spectrum of the quadrature fluctuations. The regime is a precondition for coherent energy exchange between the mechanical oscillator and the light field. Experimental observation of optomechanical mode splitting was reported shortly after publication of our results [cf. Groblacher et al., Nature 460, 724--727]. Dynamical backaction cooling of the mechanical mode can be achieved, when the optical mode is driven red-detuned from resonance. We use a perturbation and a covariance approach to calculate both, the power dependence of the mechanical occupation number and the influence of excess noise in the optical drive that is used for cooling. The result was one to one applied for data analysis in a seminal article on ground state cooling of a mechanical oscillator [cf. Teufel et al., Nature 475, 359--363]. In addition we investigate a setting, where multiple optical cavity modes are coupled to a single mechanical degree of freedom. Resonant build-up of the motional sidebands amplifies the mechanical displacement signal, such that the standard quantum limit for linear position detection can be reached at significantly lower input power.