Dissipative phase transition in a mirrorless optical parametric oscillator

We experimentally demonstrate a dissipative phase transition in a mirrorless optical parametric oscillator (MOPO) using a double-$\mathrm{\ensuremath{\Lambda}}$ system in thermal atomic vapor. Bistable behavior is observed in the output power of the beams generated via the MOPO with the variation of the input power of the driving fields. We show that the long-lived hyperfine ground-state coherence induced by the Gaussian pump and the generated fields leads to the observation of optical bistability in the MOPO threshold. We further study the critical slowing-down of nonequilibrium dynamics in the vicinity of the forward threshold where the switching time of the generated fields diverges with the critical exponent, $\ensuremath{\alpha}=\ensuremath{-}0.86\ifmmode\pm\else\textpm\fi{}0.02$. Our observations pave the way to understanding and characterizing the phase transitions in driven-dissipative systems using a simple nonlinear optical system like the MOPO.