Study of thermal noise in solids out of thermodynamic equilibrium

Mechanical systems show thermal noise as vibrations due to the thermal energy associated to each degree of freedom as predicted by the equipartition theorem. This noise source sets limits to the sensitivity of certain high precision experiments, such as gravitational wave detectors, so that its understanding is essential for the proper design of the apparatus. While thermal noise in equilibrium states has been well studied and understood, in non-equilibrium ones it is still a marginally investigated phenomenon. However for many experiments, like for example cryogenic gravitational-wave interferometers, thermal equilibrium cannot be assumed, and it is important to gain a better understanding of the behavior of thermal noise in these conditions. Our test system is a monolithic aluminum oscillator consisting of a suspended rod with a cubic mass at one end, and we study the longitudinal and transverse modes of vibration excited by thermal noise; the system allows for establishing thermal gradients across the rod to study non-equilibrium conditions. The oscillations have rms amplitudes of the order of 10 fm, and frequencies around 1400 Hz and 300 Hz. We detect the oscillator’s motion with a polarization-multiplexed interferometer. This technique exploits two superimposed interferometers, operating in two orthogonal polarizations and shifted one with respect to the other by 90 degrees; in this way it is possible to continuously follow the interference phase and be able to reconstruct displacements longer than a quarter-wavelength of the laser, induced by thermal expansion, while maintaining a sensitivity comparable to a classical michelson interferometer. The aim of the thesis is to optimize the experimental apparatus, assess its performance and take measurements of the oscillator thermal noise. Particular focus is put on verifying the correctness of the calibration, which is a critical aspect of the experiment.