Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators

Area of Science:

• Nonlinear Dynamics and Complex Systems
• Mechanical Engineering
• Quantum Optics

Background:

• Nonlinear systems exhibit amplitude-dependent frequencies and strong interactions at internal resonances, leading to complex dynamics like nonergodicity.
• Existing models struggle to universally explain diverse experimental observations in micro- and nanomechanical resonators.
• Fast energy exchange at internal resonances is key to understanding phenomena like time-varying relaxation rates.

Purpose of the Study:

• To experimentally reveal persistent nonlinear phase-locked states in coupled nonlinear systems.
• To demonstrate the essential role of these phase-locked states in transient dynamics.
• To provide a universal physical description for observed phenomena in nonlinear resonators.

Main Methods:

• Experimental investigation of a fully observable micromechanical resonator system.
• Quantitative modeling of system dynamics, focusing on mode interactions and energy exchange.
• Analysis of phase-locked states, coherence times, and energy transfer pathways.

Main Results:

• Persistent nonlinear phase-locked states, specifically a period-tripling state, were experimentally observed and quantitatively described.
• The model accurately predicts phase-locked coherence times, energy exchange direction and magnitude, and nonmonotonic energy evolution.
• System dynamics and relaxation pathways are shown to depend on the initial relative phase, influencing entry into or bypassing of the locked state.

Conclusions:

• Persistent phase locking is a fundamental mechanism governing transient dynamics in nonlinear systems with coupled eigenmodes.
• This phenomenon is not limited by specific frequency ratios or nonlinearity types, offering broad applicability.
• The findings advance nonlinear resonator systems engineering in fields such as nanomechanics and photonics.