The transition temperature Tc of iron-based superconductors has a dome-shaped dependence on chemical doping, and the superconductivity that develops underneath may obscure a potential quantum critical point (QCP) residing at absolute zero. With the aim of detecting signatures of this quantum criticality, Hashimoto et al. (p 1554; see the Perspective by Sachdev ) measured the penetration depth of the pnictide series BaFe2(As1-x Px )2 as a function of x. A sharp peak right around the point where Tc has a maximum (x = 0.30) was observed, implying that the superfluid density diminishes sharply where one would expect it to be the most robust. This unusual finding is interpreted as a sign of a QCP at x = 0.30. In a superconductor, the ratio of the carrier density, n, to its effective mass, m*, is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, λL. In two-dimensional systems, this ratio n/m* (~1/λL2) determines the effective Fermi temperature, TF. We report a sharp peak in the x-dependence of λL at zero temperature in clean samples of BaFe2(As1-xPx)2 at the optimum composition x = 0.30, where the superconducting transition temperature Tc reaches a maximum of 30 kelvin. This structure may arise from quantum fluctuations associated with a quantum critical point. The ratio of Tc/TF at x = 0.30 is enhanced, implying a possible crossover toward the Bose-Einstein condensate limit driven by quantum criticality. PUBLICATION ABSTRACT