Twin-beam-enhanced displacement measurement of a membrane in a cavity

Ultrasensitive measurement of a small displacement is an essential goal in various applications of science and technology, ranging from large-scale laser interferometric gravitational wave detectors to micro-electro-mechanical-systems-based force microscopy. The least measurable displacement is ultimately limited by the quantum nature of light in a classical optical sensor. Here we use the bright quantum correlated light, i.e., twin beams, generated by a coherent atomic medium to surpass the shot-noise limit (SNL) of the displacement measurement of a membrane in an optical cavity. The sensitivity of 200 $am/\sqrt {Hz}$ is achieved, which is more than two orders of magnitude better than a standard Michelson interferometer. An improvement of 3 $dB$ in the signal-to-noise ratio (SNR) beyond the SNL is realized at an equivalent optical power, by using quantum correlated light with noise squeezed 7 $dB$ below the vacuum level. Moreover, the frequency correlation of twin beams is directly measured by using optical cavities, and this relation is utilized to reduce the excess classical noise. Additionally, the displacement measurement sensitivity is further substantially enhanced by the cavity mediated dispersion and the SNR is increased by one order of magnitude compared to the free space case. These results provide a novel strategy for the world of precision measurement as well as to control cavity optomechanical systems with non-classical light.