The superfluid fraction $f$ of a quantum fluid is defined in terms of the response of the system to a weak and constant drag. Notably, Leggett long ago derived two simple expressions providing a rigorous upper bound and a heuristic lower bound for $f$. Here we study the superfluid fraction of bosonic gases in various two-dimensional potentials, such as regular optical lattices and disordered speckles, by solving the Gross-Pitaevskii equation and performing diffusion Monte Carlo simulations. We show that under conditions relevant for most ultracold experiments the bounds proposed by Leggett provide a surprisingly narrow bracketing of the exact value of the superfluid fraction.

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• Bose gases
• Bose-Einstein condensates
• Cold and ultracold molecules
• Cold atoms & matter waves
• Cold gases in optical lattices