Mechanical resonators that possess coupled modes with harmonic frequency relations have recently sparked interest due to their suitability for controllable energy transfer and non-Hermitian dynamics. Here we show coupling between high-𝑄-factor (greater than 104) resonances with a nearly 1:1 frequency relation in spatially symmetric microresonators. We develop and demonstrate a method to analyze their dynamical behavior based on the simultaneous and resonant detection of both spectral peaks, and validate this with experimental results. The frequency difference between the peaks modulates their ringdown, and creates a beat pattern in the linear decay. This method applies to both the externally driven regime and the Brownian-motion (thermal) regime, and allows characterization of both linear and nonlinear parameters. The mechanism behind this method renders it broadly applicable to both optical and electrical readout, as well as to different mechanical systems. This will aid studies using near-degenerate mechanical modes, for example, optomechanical energy transfer, synchronization, and gyroscopic sensors.@en

Mechanical frequency combs are poised to bring the applications and utility of optical frequency combs into the mechanical domain. So far, their main challenge has been strict requirements on drive frequencies and power, which complicate operation. We demonstrate a straightforward mechanism to create a frequency comb consisting of mechanical overtones (integer multiples) of a single eigenfrequency, by monolithically integrating a suspended dielectric membrane with a counter-propagating optical trap. The periodic optical field modulates the dielectrophoretic force on the membrane at the overtones of a membrane’s motion. These overtones share a fixed frequency and phase relation, and constitute a mechanical frequency comb. The periodic optical field also creates an optothermal parametric drive that requires no additional power or external frequency reference. This combination of effects results in an easy-to-use mechanical frequency comb platform that requires no precise alignment, no additional feedback or control electronics, and only uses a single, mW continuous wave laser beam. This highlights the overtone frequency comb as the straightforward future for applications in sensing, metrology and quantum acoustics.

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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.@en

State-of-the-art nanomechanical resonators are heralded as a central component for next-generation clocks, filters, resonant sensors, and quantum technologies. To practically build these technologies will require monolithic integration of microchips, resonators, and readout systems. While it is widely seen that mounting microchip substrates into a system can greatly impact the performance of high-Q resonators, a systematic study has remained elusive, owing to the variety of physical processes and factors that influence the dissipation. Here, we analytically analyze a mechanism by which substrates couple to resonators manufactured on them and experimentally demonstrate that this coupling can increase the mechanical dissipation of nanomechanical resonators when resonance frequencies of resonator and substrate coincide. More generally, we then show that a similar coupling mechanism can exist between two adjacent resonators. Since the substrate–mode coupling mechanism strongly depends on both the resonator position on the substrate and the mounting of the substrate, this work provides key design guidelines for high-precision nanomechanical technologies.@en

Studying the interplay between multiple coupled mechanical resonators is a promising new direction in the field of optomechanics. Understanding the dynamics of the interaction can lead to rich new effects, such as enhanced coupling and multi-body physics. In particular, multi-resonator optomechanical systems allow for distinct dynamical effects due to the optical cavity coherently coupling mechanical resonators. Here, we study the mechanical response of two SiN membranes and a single optical mode, and find that the cavity induces a time delay between the local and cavity-transduced thermal noises experienced by the resonators. This results in an optomechanical phase lag that causes destructive interference, cancelling the mechanical thermal noise by up to 20 dB in a controllable fashion and matching our theoretical expectation. Based on the effective coupling between membranes, we further propose, derive, and measure a collective effect, cooperativity competition on mechanical dissipation, whereby the linewidth of one resonator depends on the coupling efficiency (cooperativity) of the other resonator.

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From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel “torsional soft-clamping” mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

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