Dynamical behavior of trampoline membranes

Abstract

This thesis comprises several experiments involving silicon nitride trampoline membranes. These membranes are excellent mechanical resonators and can be fabricated with desirable optical properties. Their dynamical behavior, particularly the interaction of their mechanical motion with light, is of interest for optomechanics and sensing applications. In the first experiment, I study the dissipation of trampoline membranes due to coupling to the substrate modes. It is known that the clamping of the substrate can affect the dissipation of its resonators, and this experiment provides a systematic investigation into this effect. The results show a clear reduction of mechanical Q-factor (increase of dissipation) when a resonator is resonant with a substrate mode. This highlights the design of the substrate modes for high-Q mechanical resonators. In the second experiment, I study the appearance of mechanical frequency combs in trampoline membranes. The interaction of a standing wave light field with the silicon nitride membrane through the dielectrophoretic force is similar to an optical trap. If the mechanical motion is sufficiently large, the periodicity of that force creates perfect integer multiple copies of the original motion frequency, which form a frequency comb. This makes it possible to generate mechanical frequency combs using a simple setup with little technical requirements. In the third experiment, I study the behavior of ringdown measurements involving near-degenerate modes. When both modes are within the detection bandwidth of the setup, their signal interferes and the ringdown displays ’ringing’. It is possible to extract the linear and non-linear parameters of both near-degenerate modes, and extract their relative coherence in the Brownian motion regime. This provides a characterization method for systems with near-degenerate mechanical modes. In the fourth experiment, I study the interaction of two trampoline membranes with a single optical cavity mode. The optical field couples the mechanical motion of the two membranes, but with a time delay based on the cavity lifetime. The associated phase-shift of the mechanical responses causes destructive interference, which leads to mechanical noise cancellation. This could be used to improve sensors suffering from mechanical thermal noise, and is important when studying optomechanical multi-resonator interactions.