Nano-Kelvin thermometry and temperature control: beyond the thermal noise limit.

We demonstrate thermometry with a resolution of 80  nK/Hz using an isotropic crystalline whispering-gallery mode resonator based on a dichroic dual-mode technique. We simultaneously excite two modes that have a mode frequency ratio that is very close to two (±0.3  ppm). The wavelength and temperature dependence of the refractive index means that the frequency difference between these modes is an ultrasensitive proxy of the resonator temperature. This approach to temperature sensing automatically suppresses sensitivity to thermal expansion and vibrationally induced changes of the resonator. We also demonstrate active suppression of temperature fluctuations in the resonator by controlling the intensity of the driving laser. The residual temperature fluctuations are shown to be below the limits set by fundamental thermodynamic fluctuations of the resonator material.