We demonstrate thermally limited force spectroscopy using a probe formed by a dielectric microsphere optically trapped in water near a dielectric surface. We achieve force resolution below 1 fN in 100 s, corresponding to a 2 Å rms displacement of the probe. Our measurement combines a calibrated evanescent wave particle tracking technique and a lock-in detection method. We demonstrate the accura...

A laser interferometer gravitational wave detector is, in essence, a device for monitoring a classical force (the gravitational wave) that acts on freely moving test masses (the interferometer's suspended mirrors). \Advanced" detectors, expected to operate in the LIGO/VIRGO interferometric network [1] in the middle or later part of the next decade, will be constrained by the standard quantum li...

Abstract: In this paper, we consider the stabilization problem of 1-d wave equation with input delay. Suppose that the wave system is fixed at one end whereas a control force is applied at other end. Here we consider the control force of the form αu(t) + βu(t − τ) where τ is the time delay. In this paper we find a feedback control law that stabilizes exponentially the system for any |α| ̸= |β| a...