Paper MN-MoM9
Noise Temperature and Thermodynamic Temperature of Ultrasensitive Cantilevers Below 1 K

Monday, October 15, 2007, 10:40 am, Room 615

Micromechanical systems can be fabricated with the sensitivity necessary for detecting ultra-small forces arising from quantum mechanical effects. We use cantilevers as torsional magnetometers to study the magnetic properties of systems mounted directly on a cantilever. Our goal is to study persistent currents in normal metal rings. The properties of these currents remain an outstanding controversy in mesoscopic physics. As with all sample-on-cantilever arrangements, there are two distinct temperatures that determine the performance of the experiment: the cantilever’s Brownian motion temperature (T_n) and the temperature of the sample mounted on the cantilever (T_s). T_n is associated with a single macroscopic degree of freedom extended over the length of the cantilever. T_s on the other hand is associated with the very large number of microscopic degrees of freedom in the sample. For a high-Q cantilever, T_n, which sets the cantilever’s ultimate force sensitivity, is in weak contact with the thermal bath at temperature T_b. T_s is in contact with the bath via phonon conduction through the cantilever. This contact can also be weak for a small, electrically insulating cantilever at low temperatures. It is thus a priori uclear whether in a practical experiment T_s and T_n will equilibrate with each other or even with T_b. It is also unclear how they will respond to a localized heat source, e.g. a laser used to monitor the cantilever’s motion. We have used our sample-on-cantilever system to realize two primary thermometers to measure both T_n and T_s. We infer T_n by monitoring the cantilever’s Brownian motion and T_s from the critical magnetic field of a superconducting sample mounted on the cantilever. We find that for modest laser powers incident on the sample, these two temperatures stay equilibrated to each other and to T_b down to 300mK. For higher laser powers T_s and T_n remain equal to each other but are hotter than T_b. The temperature difference is well-described by a simple model of phonon transport along the cantilever beam. We have also fabricated single crystal silicon cantilevers with integrated micron-scale metal rings. We have demonstrated attonewton force sensitivity with these devices and will present measurements of the rings’ susceptibility in the normal and superconducting states.