Direct measurement of a spatially varying thermal bath using Brownian motion

Micromechanical resonator performance is fundamentally limited by the coupling to a thermal environment. The magnitude of this thermodynamical effect is typically considered in accordance with a physical temperature, assumed to be uniform across the resonator's physical span. However, in some circumstances, e.g., quantum optomechanics or interferometric gravitational wave detection, the temperature of the resonator may not be uniform, resulting in the resonator being thermally linked to a spatially varying thermal bath.