We study coherence properties of a χ^(2) optical parametric oscillator (OPO), which produces 2/3-octave-wide spectrum centered at the subharmonic (3120 nm) of the femtosecond pump laser. Our method consists of interfering the outputs of two identical, but independent OPOs pumped by the same laser. We demonstrate that the two OPOs show stable spatial and temporal interference and are mutually locked in frequency and in phase. By observing a collective heterodyne beat signal between the two OPOs we show that one can deterministically choose, by cavity length adjustment, between the two frequency states corresponding to the two sets of modes shifted with respect to each other by half of the laser pulse repetition rate. Moreover, we observe that the existence of two opposite phase states, a known common feature of a parametrically driven n = 2 subharmonic oscillator, reveals itself in our experiment as a common phase, 0 or π, being established through the whole set of some 300 thousand longitudinal modes
