  We generated time-multiplexed degenerate optical parametric oscillator (DOPO)
pulses using a nonlinear fiber Sagnac loop as a phase-sensitive amplifier (PSA)
where the pump and amplified light in pump-signal-idler degenerate four-wave
mixing can be spatially separated. By placing the PSA in a fiber cavity, we
successfully generated more than 5,000 time-multiplexed DOPO pulses. We
confirmed the bifurcation of pulse phases to 0 or $\pi$ relative to the pump
phase, which makes them useful for representing Ising spins in an Ising model
solver based on coherent optical oscillator networks. We also confirmed
inherent randomness of the DOPO phases using the NIST random number test.
