Quantum state preparation for coupled period tripling oscillators*

We investigate the quantum transition to a correlated state of coupled oscillators in the regime where they display period tripling in response to a drive at triple the eigenfrequency. Correlations are formed between the discrete oscillation phases of individual oscillators. The evolution toward the ordered state is accompanied by the transient breaking of the symmetry between seemingly equivalent configurations. We attribute this to the nontrivial geometric phase that characterizes period tripling. We also show that the Wigner distribution of a single damped quantum oscillator can display a minimum at the classically stable zero-amplitude state.