Low-vibration cryogenic test facility for next generation of ground-based gravitational-wave observatories

We present the design and commissioning of a cryogenic low-vibration test facility that measures displacement noise from a gram-scale silicon cantilever at the level of 10$^{-16}\, \mathrm{m/\sqrt{Hz}}$ at 1kHz. A volume of $\sim$36 litres is enclosed by radiation shields cooling an optical test cavity that is suspended from a multi-stage pendulum chain providing isolation from acoustic and environmental noise. This 3kg test cavity housing a crystalline silicon cantilever is radiatively cooled to 123K in 41 hours and held at that temperature over many months with a relative temperature stability of $\pm$1mK. The facility is capable of interferometrically measuring temperature-dependent broadband displacement noise between 50Hz and 10kHz where current and future ground-based gravitational wave observatories are most sensitive. With suitable cantilever design, the cryogenic facility we describe here will allow for the measurement of broadband thermal noise in crystalline silicon at 123K. This will guide the design of suspensions in planned future cryogenic ground-based gravitational-wave detectors such as LIGO Voyager and the Einstein Telescope. This facility is also suitable for the testing of new mirror coatings at cryogenic temperatures.