  The classical self-oscillations can collapse merely due to their mutual
couplings. We investigate this oscillation collapse in quantum van der Pol
oscillators. For a pair of quantum oscillators, the steady-state mean phonon
number is shown to be lower than in the corresponding classical model with a
Gaussian white noise that mimics quantum noise. We further show within the
mean-field theory that a number of globally coupled oscillators undergo a
transition from the synchronized periodic motion to the collective oscillation
collapse. A quantum many-body simulation suggests that the increase in the
number of oscillators leads to a lower steady-state mean phonon number, bounded
below by the mean-field result.

Quantum Physics