Optical interferometry now allows for extreme displacement sensitivity, often only limited by quantum noise: quantum shot noise and/or quantum radiation pressure noise (QRPN, a macroscopic version of quantum back-action), which utimately leads to the standard quantum limit (SQL), the smallest displacement observable for a mechanical resonator using standard laser sources (coherent states). The SQL has been predicted for over 35 years, originally in the context of gravitational-wave detection, but as radiation-pressure effects are extremeley weak for macroscopic mechanical resonators, it has long eluded experimental demonstration. The status of the SQL should drastically change over the next few years as the advanced gravitational-wave interferometers (Advanced LIGO and Advanced Virgo) should be operated at their design sensitivity within a couple of years. They should then be limited by QRPN at the lower side of their science frequency band (from 10 Hz to 50 Hz) and by QSN at the higher side (above 200 Hz and up to 10 kHz). The SQL is also of particular interest to the optomechanics field, which has experienced huge experimental progress over the last 15 years. This has recently culminated with experimental milestones such as the demonstration of a mechanical resonator cooled close to its quantum ground state, and the effect of QRPN over a mechanical membrane, experiment types closely related to the SQL. Optomechanics is obviously related to quantum measurement theory, but also to practical novel sensing devices such as atomic force microscopes (AFM) or optomechanical accelerometers. Therefore any sensitivity enhancement beyond the SQL will have important applications. The SQL can in principle be overcome using squeezed light, a research topic which has experienced considerable experimental progress as well. But combining optomechanical setups with squeezed light is still an experimental challenge. Our project is two-sided. We first plan to build, characterize and inject a squeezed bright beam into a dedicated table-top optomechanical system operated in a dilution fridge to investigate the SQL and how to further increase the displacement sensitivity beyond the SQL. This requires frequency-dependent squeezing, which we will obtain by injecting the squeezed beam into a rotation cavity. This proof-of-principle experiment will be performed at MHz frequencies to avoid many technical noise sources. As high-sensitivity measurements such as gravitational-wave interferometers in fundamental physics or AFM in applied physics are usually performed at lower frequencies, we will also investigate similar effects at lower frequency. We plan to rely on the experience gained from the high-frequency experiment to build and operate a squeezed vacuum source optimized in the audio band (10 Hz – 10 kHz). We will then take advantage of the 50-m long CALVA platform at LAL Orsay as a rotation cavity to demonstrate frequency-dependent squeezing with a corner frequency 1 kHz and below.