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

Abstract

The density distribution of the one-dimensional Hubbard model in a harmonic trapping potential is investigated in order to study the effect of the confining trap. Strong superimposed oscillations are always present on top of a uniform density cloud, which show universal scaling behavior as a function of increasing interactions. An analytical formula is proposed on the basis of bosonization, which describes the density oscillations for all interaction strengths. The wavelength of the dominant oscillation changes with interaction, which indicates the crossover to a spin-incoherent regime. Using the Bethe ansatz the shape of the uniform fermion cloud is analyzed in detail, which can be described by a universal scaling form.

5 pages, 4 figures. Published version. See also http://www.physik.uni-kl.de/eggert/papers/index.html

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• Crossover between few and many fermions in a harmonic trap
• Two-flavor mixture of a few fermions of different mass in a one-dimensional harmonic trap
• Bosonic continuum theory of one-dimensional lattice anyons
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• Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions
• Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
• Non-equilibrium Floquet steady states of time-periodic driven Luttinger liquids
• 2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement
• Spin-independent v-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation
• Fermionic versus bosonic behavior of confined Wigner molecules
• Dipole oscillations of fermionic superfluids along the BEC-BCS crossover in disordered potentials
• Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions