  Coupling two or more self-oscillating systems may stabilize their
zero-amplitude rest-state, therefore quenching their oscillation. This
phenomenon is termed "amplitude death". Well-known and studied in classical
self-oscillators, amplitude death was only recently investigated in quantum
self-oscillators [Ishibashi et al., Phys. Rev. E 96, 052210]. Quantitative
differences between the classical and quantum descriptions were found. Here, we
demonstrate that for quantum self-oscillators with anharmonicity in their
energy spectrum, multiple resonances in the mean phonon number can be observed.
This is a result of the discrete energy spectrum of these oscillators, and is
not present in the corresponding classical model. Experiments can be realized
with current technology and would demonstrate these genuine quantum effects in
the amplitude death phenomenon.
