Noise Temperature and Thermodynamic Temperature of a Sample-on-Cantilever System Below 1K

Micromechanical systems such as cantilevers are frequently used to detect ultra-small forces and displacements. In a sample-on-cantilever geometry, operation at low temperature requires cooling the thermodynamic temperature of the sample T$_{S}$ and the noise temperature of the cantilever T$_{N}$. This can be challenging because for high-Q cantilevers, these temperatures are only weakly coupled. In addition, for insulating cantilevers monitored by a reflected laser beam, these temperatures may also be weakly coupled to the refrigerator temperature. We have made quantitative measurements of T$_{N}$ and T$_{S}$ for a sample-on-cantilever set-up as a function of incident laser power and refrigerator temperature below 1 Kelvin. We infer T$_{S}$ from measurements of the critical magnetic field of a superconducting sample mounted on the cantilever. T$_{N}$ is inferred from the cantilever's Brownian motion. We find that for this system both T$_{S}$ and T$_{N}$ remain quite close to the refrigerator temperature.