Abstract
We present a model that generalizes the Bose–Fermi mapping for strongly correlated one-dimensional (1D) bosons trapped in combined optical lattice plus parabolic potentials, to cases in which the average number of atoms per site is larger than one. Using a decomposition in arrays of disjoint strongly interacting gases, this model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to non-equilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Excellent agreement is found with results of recent experiments, without the use of any adjustable parameters. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime.
Highlights
Cold bosonic atoms in optical lattices have recently been used to create quasi-one dimensional systems [1, 2, 3, 4, 5, 6]
Because there are always more atoms in the lowest layer than in the upper one, the overall dynamics is overdamped, and this explains the large damping observed in the experiment for Vo 3ER
Summary We have developed a simple model that generalizes the Bose-Fermi mapping to regimes where the filling factor is larger than one
Summary
Cold bosonic atoms in optical lattices have recently been used to create quasi-one dimensional systems [1, 2, 3, 4, 5, 6]. ∆N > 0, the ground state is a superfluid In this case, if γ/n ≫ γc the extra atoms can be thought of as TG bosons with effective hopping energy nJ on top of a Mott state with filling factor n − 1. While the first inequality is the same as for homogeneous lattices, the second one is specific for trapped systems and is necessary to suppress multiple occupancy of single sites In this fermionized regime, for decreasing J the density at the trap center increases, and, when the condition 2J Ω((N − 1)/2) is satisfied, sites around the trap center begin to have unit filling [9, 10]. Is satisfied, the ground state is a unit-filled Mott state in all N sites In this case, fluctuations occur mainly at the edge of the density distribution, due to tunneling of atoms to empty sites.
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