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To identify the key parameter for optimal superconductivity in ironpnictides, we measured the $^{31}$P-NMR relaxation rate onBaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ ($x = 0.22$ and 0.28) under pressure andcompared the effects of chemical substitution and physical pressure. For $x =0.22$, structural and antiferromagnetic (AFM) transition temperatures both showminimal changes with pressure up to 2.4~GPa, whereas the superconductingtransition temperature $T_{\rm c}$ increases to twice its former value. Incontrast, for $x=0.28$ near the AFM quantum critical point (QCP), thestructural phase transition is quickly suppressed by pressure and $T_{\rm c}$reaches a maximum. The analysis of the temperature-dependent nuclear relaxationrate indicates that these contrasting behaviors can be quantitatively explainedby a single curve of the $T_{\rm c}$ dome as a function of Weiss temperature$\theta$, which measures the distance to the QCP. Moreover, the $T_{\rmc}$-$\theta$ curve under pressure precisely coincides with that with chemicalsubstitution, which is indicative of the existence of a universal relationshipbetween low-energy AFM fluctuations and superconductivity onBaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$.

Universal relationship between low-energy antiferromagnetic fluctuations and superconductivity in BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$