  Synchronously pumped optical parametric oscillators (SPOPOs) are optical
cavities containing a nonlinear crystal capable of down-converting a frequency
comb to lower frequencies. These have received a lot of attention lately,
because their intrinsic multimode nature makes them compact sources of quantum
correlated light with promising applications in modern quantum information
technologies. In this work we show that SPOPOs are also capable of accessing
the challenging but interesting regime where spontaneous symmetry breaking
plays a crucial role in the quantum properties of the emitted light, difficult
to access with any other nonlinear optical cavity. Apart from opening the
possibility of studying experimentally this elusive regime of dissipative phase
transitions, our predictions will have a practical impact, since we show that
spontaneous symmetry breaking provides a specific spatiotemporal mode with
perfect squeezing for any value of the system parameters, turning SPOPOs into
robust sources of highly nonclassical light above threshold.
