The current generation of gravitational wave laser interferometer detectors operate at the sensitivity limit imposed by quantum uncertainty of photon amplitude and phase quadratures. Heisenberg's principle dictates that the product of amplitude and phase uncertainty must be above a certain value, but apart from that we can still manipulate either quadrature to achieve quantum noise reduction, since the effect of amplitude and phase uncertainty is frequency dependent in gravitational wave detectors. This is the crux of the frequency dependent squeezing technique, which reduces quantum amplitude uncertainty at low frequency and quantum phase uncertainty at high frequency, where these respective quadratures each dominate. Thus, we can reduce quantum noise across the entire detection band. However, this technique is extremely sensitive to optical losses at all parts of the squeezing generation chain, and so far only a low degree of broadband squeezing has been observed. This proceeding outlines the current status of squeezing research at the former TAMA300 gravitational wave detector at the National Astronomical Observatory of Japan, where we aim to improve the level of achievable broadband squeezing. An update is also given regarding design and noise of squeezed injection for the underground gravitational wave detector KAGRA located in Gifu, Japan.