can effectively suppress the dissipation.
This can lead to a loss of stability and to an emergence of synchronized
self-excited oscillations of the system as a whole, at a time scale set by the
mechanical beam. In this article we argue this by obtaining a set of
semiclassical, nonlinear equations of motion for the two coupled subsystems,
and showing that this system undergoes a supercritical Hopf bifurcation as the
coupling is increased. We derive analytical expressions for the critical
coupling coefficient and the renormalized mechanical dissipation coefficient
and frequency, and give a complete characterization of the limit cycle behavior
when the qubit and the oscillator are near resonance.
Hopf bifurcation in a flux qubit coupled to a nanomechanical oscillator
We study the nonlinear semiclassical dynamics of a driven flux qubit coupled
to a nanomechanical oscillating beam. While both of these systems are
dissipative, their mutual coupling