Thermoelastic effects at low temperatures and quantum limits in displacement measurements

The displacement fluctuations of mirrors in optomechanical devices, induced via thermal expansion by temperature fluctuations due either to thermodynamic fluctuations or to fluctuations in the photon absorption, can be made smaller than quantum fluctuations, at the low temperatures, high reflectivities, and high light powers needed to readout displacements at the standard quantum limit. The result is relevant for the design of quantum-limited gravitational-wave detectors, both ``interferometers'' and ``bars,'' and for experiments to study directly mechanical motion in the quantum regime.