Fractal quasicondensation in one dimension

We unveil a mechanism for quasicondensation of hard-core bosons in the presence of quasiperiodicity-induced multifractal single-particle states. The observed phase, here dubbed a fractal quasicondensate, is characterized by natural orbitals with multifractal properties and by an occupancy of the lowest natural orbital, ${\ensuremath{\lambda}}_{0}\ensuremath{\simeq}{L}^{\ensuremath{\gamma}}$, which grows with system size but with a nonuniversal scaling exponent, $\ensuremath{\gamma}<1/2$. In contrast to fractal quasicondensates obtained when the chemical potential lies in a region of multifractal single-particle states, placing the chemical potential in regions of localized or delocalized states yields, respectively, no condensation or the usual 1D quasicondensation with $\ensuremath{\gamma}=1/2$. Our findings are established by studying one-dimensional hard-core bosons subjected to various quasiperiodic potentials, including the well-known Aubry-Andr\'e model, employing a mapping to noninteracting fermions that allows for numerically exact results. We discuss how to test our findings in state-of-the-art ultracold atom experiments.