Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms

Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The prevous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT 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.