Quantum manifestations of homogeneous and inhomogeneous oscillation suppression states

We study the quantum manifestations of homogeneous and inhomogeneous oscillation suppression states in coupled identical quantum oscillators. We consider quantum van der Pol oscillators coupled via weighted mean-field diffusive coupling and, using the formalism of open quantum systems, we show that, depending on the coupling and the density of mean-field, two types of quantum amplitude death occurs, namely, squeezed and nonsqueezed quantum amplitude death. Surprisingly, we find that the inhomogeneous oscillation suppression state (or the oscillation death state) does not occur in the quantum oscillators in the classical limit. However, in the deep quantum regime we discover an oscillation death-like state which is manifested in the phase space through the symmetry-breaking bifurcation of the Wigner function. Our results also hint toward the possibility of the transition from quantum amplitude death to oscillation death state through the "quantum" Turing-type bifurcation. We believe that the observation of quantum oscillation death state will deepen our knowledge of symmetry-breaking dynamics in the quantum domain.