  Mode locking in lasers is a collective effect, where due to a weak coupling a
large number of frequency modes lock their phases to oscillate in unison,
forming an ultrashort pulse in time. We demonstrate an analogous collective
effect in coupled parametric oscillators, which we term "pairwise
mode-locking", where many pairs of modes with twin frequencies (symmetric
around the center carrier) oscillate simultaneously with a locked phase-sum,
while the phases of individual modes remain undefined. Thus, despite being
broadband and multimode, the emission is not pulsed and lacks first-order
coherence, while possessing a very high degree of second-order coherence. Our
configuration is comprised of two coupled parametric oscillators within
identical multimode cavities, where the coupling between the oscillators is
modulated in time at the repetition rate of the cavity modes, with some analogy
to active mode-locking in lasers. We demonstrate pairwise mode-locking in a
radio-frequency (RF) experiment, covering over an octave of bandwidth with
approximately 20 resonant mode-locked pairs, filling most of the available
bandwidth between DC and the pump frequency. We accompany our experiment with
an analytic model that accounts for the properties of the coupled parametric
oscillators near threshold.
