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Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The previous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in the nonlinear optical interaction based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe that 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. 

A bstract Charged-lepton-flavor-violation is predicted in several new physics scenarios. We update the analysis of τ lepton decays into a light charged lepton ( ℓ = e ± or μ ± ) and a vector meson ( V 0 = ρ 0 , ϕ , ω , K *0 , or $$ \overline{K} $$ K ¯ *0 ) using 980 fb − 1 of data collected with the Belle detector at the KEKB collider. No significant excess of such signal events is observed, and thus 90% credibility level upper limits are set on the τ → ℓV 0 branching fractions in the range of (1.7–4 . 3) × 10 − 8 . These limits are improved by 30% on average from the previous results.