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Ultra-light dark matter (ULDM) refers to a class of theories, includingultra-light axions, in which particles with mass $m_{\psi} < 10^{-20}\,\rm{eV}$ comprise a significant fraction of the dark matter. A galactic scalede Broglie wavelength distinguishes these theories from cold dark matter (CDM),suppressing the overall abundance of structure on sub-galactic scales, andproducing wave-like interference phenomena in the density profiles of halos.With the aim of constraining the particle mass, we analyze the flux ratios in asample of eleven quadruple-image strong gravitational lenses. We account forthe suppression of the halo mass function and concentration-mass relationpredicted by ULDM theories, and the wave-like fluctuations in the host halodensity profile, calibrating the model for the wave interference againstnumerical simulations of galactic-scale halos. We show that the granularstructure of halo density profiles, in particular, the amplitude of thefluctuations, significantly impacts image flux ratios, and therefore inferenceson the particle mass derived from these data. We infer relative likelihoods ofCDM to ULDM of 8:1, 7:1, 6:1, and 4:1 for particle masses$\log_{10}(m_\psi/\rm{eV})\in[-22.5,-22.25], [-22.25,-22.0],[-22.0,-21.75],[-21.75,-21.5]$, respectively. Repeating the analysis and omitting fluctuationsassociated with the wave interference effects, we obtain relative likelihoodsof CDM to ULDM with a particle mass in the same ranges of 98:1, 48:1, 26:1 and18:1, highlighting the significant perturbation to image flux ratios associatedwith the fluctuations. Nevertheless, our results disfavor the lightest particlemasses with $m_{\psi} < 10^{-21.5}\,\rm{eV}$, adding to mounting pressure onultra-light axions as a viable dark matter candidate.

Quantum fluctuations masquerade as halos: Bounds on ultra-light dark matter from quadruply-imaged quasars