  Frequency entrainment of continuous-variable oscillators has to date been
restrained to the weakly nonlinear regime. Here we overcome this bottleneck and
extend frequency entrainment of quantum continuous-variable oscillators to
arbitrary nonlinearities. The previously known steady state of such quantum
oscillators in the weakly nonlinear regime (also known as a Stuart-Landau
oscillator) is shown to emerge as a special case. Most importantly, the
hallmark of strong nonlinearity--relaxation oscillations--is shown in quantum
mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations
are found to occur via two distinct mechanisms in phase space.
