PhD Defense: Letizia Catalini

Over the last forty years, nanomechanical resonators have gained a central role in widespread fields in science and technology. More recently, the invention of techniques like dissipation dilution and soft clamping led to the fabrication of nanomechanical resonator with unprecedented high quality factors. The corresponding long coherence time together with the low effective mass and the high resonance frequency place these systems at the forefront in force sensing applications. Moreover, the possibility of interfacing these resonators with disparate systems such as electromagnetic cavities, and superconducting qubits, makes them promising building blocks for the next generation of quantum technologies.

 

We focus on several nonlinear phenomena arising in dissipation-diluted membrane resonators. The high quality factor featured by soft-clamped membranes allows us to enter the regime of large displacement amplitude for the out-of-plane modes, in which a linear description of the motion fails. In this regime, we observe both conservative and dissipative nonlinearities. We model these nonlinearities as geometric, and we derive formal expressions to predict them starting from a continuum elastic theory. We test our model by comparing the predicted nonlinear parameters with the measured ones on a vast selection of geometries. By further extending this model, we predict that the in-plane modes of the membrane couple to the out-of-plane ones. This coupling modulates the resonance frequency of out-of-plane modes, thus realizing a parametric modulation. We perform preliminary experimental investigations of this phenomenon.