  The optomechanical systems produce chaotic behaviour due to nonlinear
interaction between photons and phonons, and the same systems are used to
understand the synthetic fields as well. Here, we report on the study of
chaotic behaviour in the presence of a phononic synthetic magnetic field in a
closed loop configuration consisting of a single optical mode and two
mechanical modes. The modulation phase of the mechanical coupling between the
two mechanical modes plays a critical role in determining the mechanical and
optical intensity dynamics in the nonlinear regime. Our study shows the dark
mode breaking effect in the presence of a synthetic magnetic field, which
brings about a complex way of mechanical energy exchange that causes the cavity
field to alternate between chaotic and regular behaviour periodically in
temporal domain. However in the stronger nonlinear regime the temporal dynamics
demonstrate predominantly chaotic behaviour. Besides, with the advent of
advanced fabrication technologies, this study holds promises in developing
phase tunable integrated low-power chaotic light sources to support efficient
optical secure communication systems.
