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The density distribution of the one-dimensional Hubbard model in a harmonictrapping potential is investigated in order to study the effect of theconfining trap. Strong superimposed oscillations are always present on top of auniform density cloud, which show universal scaling behavior as a function ofincreasing interactions. An analytical formula is proposed on the basis ofbosonization, which describes the density oscillations for all interactionstrengths. The wavelength of the dominant oscillation changes with interaction,which indicates the crossover to a spin-incoherent regime. Using the Betheansatz the shape of the uniform fermion cloud is analyzed in detail, which canbe described by a universal scaling form.

Density profile of interacting Fermions in a one-dimensional optical trap