  It is shown that coherence resonance, a phenomenon in which regularity of
noise-induced oscillations in nonlinear excitable systems is maximized at a
certain optimal noise intensity, can be observed in quantum dissipative
systems. We analyze a quantum van der Pol system subjected to squeezing, which
exhibits bistable excitability in the classical limit, by numerical simulations
of the quantum master equation. We first demonstrate that quantum coherence
resonance occurs in the semiclassical regime, namely, the regularity of the
system's oscillatory response is maximized at an optimal intensity of quantum
fluctuations, and interpret this phenomenon by analogy with classical noisy
excitable systems using semiclassical stochastic differential equations. This
resonance persists under moderately strong quantum fluctuations for which the
semiclassical description is invalid. Moreover, we investigate even stronger
quantum regimes and demonstrate that the regularity of the system's response
can exhibit the second peak as the intensity of the quantum fluctuations is
further increased. We show that this second peak of resonance is a strong
quantum effect that cannot be interpreted by a semiclassical picture, in which
only a few energy states participate in the system dynamics.
