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, lambda(0 )similar or equal to( ) L gamma , which grows with system size but with a nonuniversal scaling exponent, 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 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 & eacute; 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.