Controlling complex dynamics with synthetic magnetism in optomechanical systems: A route to enhanced sensor performance

Abstract

This paper investigates the complex nonlinear dynamics of an optomechanical system featuring an optical cavity coupled to two mechanical resonators interconnected by a phase-dependent interaction. We specifically explore the role of this phase-dependent phonon hopping as a mechanism for generating synthetic gauge fields without relying on gain-loss or PT-symmetric elements, offering a potentially more robust approach to manipulate mechanical energy transfer. By deriving the semiclassical dynamical equations, we map out the system's behavior across different parameter regimes. Our findings reveal a rich spectrum of dynamics, including bistability (coexistence of two steady states) and the emergence of complex attractors such as self-excited oscillations, hidden attractors, and chaos. We demonstrate how controlling system parameters, particularly the mechanical coupling phase and optical drive, allows for tunability between these distinct dynamical states. The presence of tunable bistability and sensitive chaotic regimes offers significant potential for practical applications. Specifically, we discuss how these controlled dynamics could be leveraged for state-switching in optical information processing and for enhancing sensitivity in advanced sensor technologies through chaos-based mechanisms. This work deepens our understanding of how synthetic gauge fields, generated via phase-dependent interactions, can sculpt the nonlinear dynamics of optomechanical systems, providing a pathway toward designing robust and tunable devices for signal processing, communication, and sensing.