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arXiv:quant-ph/0508185 · Physics Letters A

Dynamic response of interacting one-dimensional fermions in the harmonic atom trap: Phase response and the inhomogeneous mobility

W. Wonneberger

Published Apr 6, 2006• 5 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2006.03.062

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We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean-field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.
We calculate the dynamic structure factor $S(q,\ensuremath{\omega})$ of a one-dimensional (1D) interacting Bose gas confined in a harmonic trap. The effective interaction depends on the strength of the confinement enforcing the (1D) motion of atoms; interaction may be further enhanced by superimposing an optical lattice on the trap potential. In the compressible state, we find that the smooth variation in the gas density around the trap center leads to softening of the singular behavior of $S(q,\ensuremath{\omega})$ at the first Lieb excitation mode compared to the behavior predicted for homogeneous 1D systems. Nevertheless, the density-averaged response $\overline{S}(q,\ensuremath{\omega})$ remains a nonanalytic function of qqq and $\ensuremath{\omega}$ at the first Lieb excitation mode in the limit of weak trap confinement. The exponent of the power-law nonanalyticity is modified due to the inhomogeneity in a universal way and thus bears unambiguously the information about the (homogeneous) Lieb-Liniger model. A strong optical lattice causes formation of Mott phases. Deep in the Mott regime, we predict a semicircular peak in $S(q,\ensuremath{\omega})$ centered at the on-site repulsion energy, $\ensuremath{\omega}=U$. Similar peaks of smaller amplitudes exist at multiples of UUU as well. We explain the suppression of the dynamic response with entering into the Mott regime, observed recently by Cl\'ement et al. [Phys. Rev. Lett. 102, 155301 (2009)], based on an fff-sum rule for the Bose-Hubbard model.