Sub-Kelvin Cooling of a Macroscopic Oscillator and femto-Newton Force Measurement

Measuring very small forces, particularly those of a gravitational nature, has always been of great interest, as fundamental tests of our understanding of the physical laws. Ultra-long period mechanical oscillators, typically used in such measurements, will have kT/2 of thermal energy associated with each degree of freedom, owing to the equal-partition of energy. Moreover, additional seismic fluctuations in the low frequency band can raise this equivalent temperature significantly to 10^5 K. Recently, various methods using opto-mechanical forces have been reported to decrease this thermal energy for MHz, micro-cantilever oscillators, effectively cooling them. Here we show the direct, dynamical cooling of a gram-size, macroscopic oscillator to 300 mK in equivalent temperature - noise reduction by a factor of 10^6. By precisely measuring the torsional oscillator's position, we dynamically provide an external 'viscous' damping force. Such an added, dissipative force is essentially free of noise, resulting in rapid cooling of the oscillator. Additionally, we observe the time-dependent cooling process, at various cooling force parameters. This parameter dependence agrees well with a simple physical model which we provide. We further show that the device is sensitive to forces as small as <100 fN - a force only a few percent of that typically exerted by a single biological molecule or that observed in a typical gravity experiment. We also demonstrate the dynamic control of the oscillator's natural frequency, over a span of nearly two decades. The method may find important applications in precision measurements of very weak forces.