  The first detection of gravitational waves by the Laser Interferometer
Gravitational-wave Observatory (LIGO) in 2015 launched the era of gravitational
wave astronomy. The quest for gravitational wave signals from objects that are
fainter or farther away impels technological advances to realize ever more
sensitive detectors. Since 2019, one advanced technique, the injection of
squeezed states of light is being used to improve the shot noise limit to the
sensitivity of the Advanced LIGO detectors, at frequencies above $\sim 50$ Hz.
Below this frequency, quantum back action, in the form of radiation pressure
induced motion of the mirrors, degrades the sensitivity. To simultaneously
reduce shot noise at high frequencies and quantum radiation pressure noise at
low frequencies requires a quantum noise filter cavity with low optical losses
to rotate the squeezed quadrature as a function of frequency. We report on the
observation of frequency-dependent squeezed quadrature rotation with rotation
frequency of 30Hz, using a 16m long filter cavity. A novel control scheme is
developed for this frequency-dependent squeezed vacuum source, and the results
presented here demonstrate that a low-loss filter cavity can achieve the
squeezed quadrature rotation necessary for the next planned upgrade to Advanced
LIGO, known as "A+."
