Synthesis of optical spring potentials in optomechanical systems

We propose a method to tailor the potential experienced by a moveable end mirror in a cavity optomechanical system by specifying the spectral properties of the input field. We show that by engineering the power spectral density of the cavity input field a desired force function can be approximated, with the accuracy of the approximation limited only by the linewidth of the cavity. The very general technique presented here could have applications in many kinds of optomechanical systems, particularly those used for sensing and metrology. We demonstrate the method by applying it to improve the sensitivity of a particular gravity measurement.