  We investigate nondegenerate parametric oscillations in a multimode
superconducting microwave resonator that is terminated by a SQUID. The
parametric effect is achieved by modulating magnetic flux through the SQUID at
a frequency close to the sum of two resonator-mode frequencies. For modulation
amplitudes exceeding an instability threshold, self-sustained oscillations are
observed in both modes. The amplitudes of these oscillations show good
quantitative agreement with a theoretical model. The oscillation phases are
found to be correlated and exhibit strong fluctuations which broaden the
oscillation spectral linewidths. These linewidths are significantly reduced by
applying a weak on-resonance tone, which also suppresses the phase
fluctuations. When the weak tone is detuned, we observe synchronization of the
oscillation frequency with the frequency of the input. For the detuned input,
we also observe an emergence of three idlers in the output. This observation is
in agreement with theory indicating four-mode amplification and squeezing of a
coherent input.
