Related papers: Detection of weak stochastic force in a parametric…
In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand…
We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general…
Noise usually has an unwelcome influence on system performance. For instance, noise inevitably affects the low-frequency mechanical freedom in optomechanical experiments. However, we investigate here the beneficial effects of thermal noise…
A common use for atomic force microscopy is to quantify local forces through tip-sample interactions between the probe tip and a sample surface. The accuracy of these measurements depends on the accuracy to which the cantilever spring…
Atomic force spectroscopy and microscopy (AFM) are invaluable tools to characterize nanostructures and biological systems. Most experiments, including state-of-the-art images of molecular bonds, are achieved by driving probes at their…
Achieving optimal force sensitivity with nanomechanical resonators requires the ability to resolve their thermal vibrations. In two-dimensional resonators, this can be done by measuring the energy they absorb while vibrating in an optical…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
The description of complex systems requires a progressively larger number of parameters. However, in practice, it often happens that a small subset of parameters suffices to describe the dynamics of the system itself: these combinations are…
We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired {\em steady state} corresponding to reduced thermal noise. Among the…
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future…
The use of Allan variance to characterize the stability of optical signals affected by stochastic polarization fluctuations and the identification of the underlying power law noise processes is explored. Allan variance can ease the…
We provide a full quantum mechanical analysis of a weak energy measurement of a driven mechanical resonator. We demonstrate that measurements too weak to resolve individual mechanical Fock states can nonetheless be used to unambiguously…
Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3dB of squeezing…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
Quantum enhanced sensing is a powerful technique in which nonclassical states are used to improve the sensitivity of a measurement. For enhanced mechanical displacement sensing, squeezed states of light have been shown to reduce the photon…
A preselection-free fiber-optic weak measurement sensing framework is proposed and experimentally verified in this paper. In view of the limitation that fiber-optic weak measurement require specific preselection, this scheme innovates…
Systems in nature are stochastic as well as nonlinear. In traditional applications, engineered filters aim to minimize the stochastic effects caused by process and measurement noise. Conversely, a previous study showed that the process…
Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to…
The method of location and spectral estimation of weak signals on a noise background is being considered. The method is based on the optimized on order and noise dispersion autoregressive model of a sought signal. A new approach of model…
Optically levitated micro- and nanoparticles are an ideal optomechanical platform for precision measurements, particularly enabling the detection of ultraweak forces. Nevertheless, quantum backaction and inherent instabilities induced by…