Symmetry in Optical Four-Wave Mixing

Symmetry is a cornerstone of physics. In this talk, we report anti-parity-time symmetry inherent in nonlinear optical interactions based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe the pair of frequency modes undergo a nontrivial anti-PT phase transition between coherent power oscillation and optical parametric amplification in presence of a large phase mismatch. Another symmetry, the exchange symmetry, comes from degenerate biphoton generation from backward spontaneous four-wave mixing. When biphotons are nondegenerate, non-symmetric photonic absorption loss results in exponential decay of the temporal waveform of the two-photon joint probability amplitude, leading to shortened coherence time. In contrast, in the case of degenerate biphotons, when both paired photons propagate with the same group velocity and absorption coefficient, the two-photon coherence time, protected by space-time symmetry, remains unaffected by medium absorptive losses. This outcome highlights the pivotal role of symmetry in manipulating and controlling photonic quantum states.